The
Standard Model of
particle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
is a theory concerning the
electromagneticElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
,
weakWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
, and
strongIn particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a noncontact force...
nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon experimental confirmation of the existence of
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s. Since then, discoveries of the
bottom quarkThe bottom quark, also known as the beauty quark, is a thirdgeneration quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...
(1977), the
top quarkThe top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
(1995) and the tau neutrino (2000) have given credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a theory of almost everything.
Still, the Standard Model falls short of being a
complete theory of fundamental interactionsA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
because it does not incorporate the physics of
dark energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
nor of the full theory of
gravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
as described by
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. The theory does not contain any viable
dark matterIn astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
particle that possesses all of the required properties deduced from observational
cosmologyCosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
. It also does not correctly account for neutrino oscillations (and their nonzero masses). Although the Standard Model is theoretically selfconsistent, it has several apparently unnatural properties giving rise to puzzles like the strong CP problem and the
hierarchy problemIn theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...
.
Nevertheless, the Standard Model is important to
theoreticalTheoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
and
experimentalWithin the field of physics, experimental physics is the category of disciplines and subdisciplines concerned with the observation of physical phenomena in order to gather data about the universe...
particle physicists alike. For theorists, the Standard Model is a paradigmatic example of a
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
, which exhibits a wide range of physics including
spontaneous symmetry breakingSpontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
,
anomaliesIn quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics an anomaly is the failure of a symmetry to be restored in the limit in which the symmetrybreaking...
, nonperturbative behavior, etc. It is used as a basis for building more
exotic modelsPhysics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...
which incorporate hypothetical particles, extra dimensions and elaborate symmetries (such as
supersymmetryIn particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
) in an attempt to explain experimental results at variance with the Standard Model such as the existence of dark matter and neutrino oscillations. In turn, the experimenters have incorporated the standard model into simulators to help search for new physics
beyond the Standard ModelPhysics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...
from relatively uninteresting background.
Recently, the standard model has found applications in fields besides particle physics, such as
astrophysicsAstrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
, cosmology, and
nuclear physicsNuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
.
Historical background
The first step towards the Standard Model was
Sheldon GlashowSheldon Lee Glashow is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University.Birth and education:...
's discovery in 1960 of a way to combine the
electromagneticElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and
weak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
s. In 1967
Steven WeinbergSteven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
and
Abdus SalamMohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk (Urdu: محمد عبد السلام, pronounced , (January 29, 1926– November 21, 1996) was a Pakistani theoretical physicist and Nobel laureate in Physics for his work on the electroweak unification of the...
incorporated the
Higgs mechanismIn particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire nonvanishing masses through absorption of NambuGoldstone bosons arising in spontaneous symmetry breaking....
into Glashow's electroweak theory, giving it its modern form.
The Higgs mechanism is believed to give rise to the
massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
es of all the
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s in the Standard Model. This includes the masses of the
W and Z bosonsThe W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
, and the masses of the
fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s, i.e. the
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s and
leptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s.
After the
neutral weak currentsWeak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the boson...
caused by boson exchange
were discoveredGargamelle was a giant bubble chamber detector at CERN, designed mainly for the detection of neutrino interactions. Built in France, with a diameter of nearly 2 meters and 4.8 meters in length, Gargamelle held nearly 12 cubic meters of freon...
at
CERNThe European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
in 1973, the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979
Nobel Prize in PhysicsThe Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
for discovering it. The W and Z bosons were discovered experimentally in 1981, and their masses were found to be as the Standard Model predicted.
The theory of the
strong interactionIn particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a noncontact force...
, to which many contributed, acquired its modern form around 1973–74, when experiments confirmed that the
hadronIn particle physics, a hadron is a composite particle made of quarks held together by the strong force...
s were composed of fractionally charged quarks.
Overview
At present,
matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
and
energyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
are best understood in terms of the
kinematicsKinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
and
interactionsIn particle physics, fundamental interactions are the ways that elementary particles interact with one another...
of
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s. To date, physics has reduced the
lawsA scientific law is a statement that explains what something does in science just like Newton's law of universal gravitation. A scientific law must always apply under the same conditions, and implies a causal relationship between its elements. The law must be confirmed and broadly agreed upon...
governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. A major goal of physics is to find the "common ground" that would unite all of these theories into one integrated
theory of everythingA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
, of which all the other known laws would be special cases, and from which the behavior of all matter and energy could be derived (at least in principle).
The Standard Model groups two major extant theories—
quantum electroweakIn particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different...
and
quantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of colorcharged fermions...
—into an internally consistent theory that describes the interactions between all known particles in terms of
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
. For a technical description of the fields and their interactions, see Standard Model (mathematical formulation).
Fermions
Organization of FermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s

ChargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

First generation In particle physics, a generation is a division of the elementary particles. Between generations, particles differ by their quantum number and mass, but their interactions are identical....

Second generation 
Third generation 
QuarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly... s 
+ 
Up The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...


Charm The charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...


Top The top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...


− 
Down The down quark or d quark is the secondlightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...


Strange The strange quark or s quark is the thirdlightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...


Bottom The bottom quark, also known as the beauty quark, is a thirdgeneration quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...


LeptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral... s 
−1 
Electron The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...


MuonThe muon mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...


Tau 

0 
Electron neutrino The electron neutrino is a subatomic lepton elementary particle which has no net electric charge. Together with the electron it forms the first generation of leptons, hence its name electron neutrino...


Muon neutrino The muon neutrino is a subatomic lepton elementary particle which has the symbol and no net electric charge. Together with the muon it forms the second generation of leptons, hence its name muon neutrino. It was first hypothesized in the early 1940s by several people, and was discovered in 1962 by...


Tau neutrino 

The Standard Model includes 12
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s of spin
{{Other usesStandard model (disambiguation)}}
{{Standard model of particle physics}}
The
Standard Model of
particle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
is a theory concerning the
electromagneticElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
,
weakWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
, and
strongIn particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a noncontact force...
nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon experimental confirmation of the existence of
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s. Since then, discoveries of the
bottom quarkThe bottom quark, also known as the beauty quark, is a thirdgeneration quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...
(1977), the
top quarkThe top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
(1995) and the tau neutrino (2000) have given credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a theory of almost everything.
Still, the Standard Model falls short of being a
complete theory of fundamental interactionsA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
because it does not incorporate the physics of
dark energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
nor of the full theory of
gravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
as described by
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. The theory does not contain any viable
dark matterIn astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
particle that possesses all of the required properties deduced from observational
cosmologyCosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
. It also does not correctly account for neutrino oscillations (and their nonzero masses). Although the Standard Model is theoretically selfconsistent, it has several apparently unnatural properties giving rise to puzzles like the strong CP problem and the
hierarchy problemIn theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...
.
Nevertheless, the Standard Model is important to
theoreticalTheoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
and
experimentalWithin the field of physics, experimental physics is the category of disciplines and subdisciplines concerned with the observation of physical phenomena in order to gather data about the universe...
particle physicists alike. For theorists, the Standard Model is a paradigmatic example of a
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
, which exhibits a wide range of physics including
spontaneous symmetry breakingSpontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
,
anomaliesIn quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics an anomaly is the failure of a symmetry to be restored in the limit in which the symmetrybreaking...
, nonperturbative behavior, etc. It is used as a basis for building more
exotic modelsPhysics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...
which incorporate hypothetical particles, extra dimensions and elaborate symmetries (such as
supersymmetryIn particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
) in an attempt to explain experimental results at variance with the Standard Model such as the existence of dark matter and neutrino oscillations. In turn, the experimenters have incorporated the standard model into simulators to help search for new physics
beyond the Standard ModelPhysics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...
from relatively uninteresting background.
Recently, the standard model has found applications in fields besides particle physics, such as
astrophysicsAstrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
, cosmology, and
nuclear physicsNuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
.
Historical background
The first step towards the Standard Model was
Sheldon GlashowSheldon Lee Glashow is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University.Birth and education:...
's discovery in 1960 of a way to combine the
electromagneticElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and
weak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
s. In 1967
Steven WeinbergSteven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
and
Abdus SalamMohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk (Urdu: محمد عبد السلام, pronounced , (January 29, 1926– November 21, 1996) was a Pakistani theoretical physicist and Nobel laureate in Physics for his work on the electroweak unification of the...
incorporated the
Higgs mechanismIn particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire nonvanishing masses through absorption of NambuGoldstone bosons arising in spontaneous symmetry breaking....
into Glashow's electroweak theory, giving it its modern form.
The Higgs mechanism is believed to give rise to the
massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
es of all the
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s in the Standard Model. This includes the masses of the
W and Z bosonsThe W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
, and the masses of the
fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s, i.e. the
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s and
leptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s.
After the
neutral weak currentsWeak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the boson...
caused by {{SubatomicParticleZ boson}} boson exchange
were discoveredGargamelle was a giant bubble chamber detector at CERN, designed mainly for the detection of neutrino interactions. Built in France, with a diameter of nearly 2 meters and 4.8 meters in length, Gargamelle held nearly 12 cubic meters of freon...
at
CERNThe European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
in 1973, the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979
Nobel Prize in PhysicsThe Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
for discovering it. The W and Z bosons were discovered experimentally in 1981, and their masses were found to be as the Standard Model predicted.
The theory of the
strong interactionIn particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a noncontact force...
, to which many contributed, acquired its modern form around 1973–74, when experiments confirmed that the
hadronIn particle physics, a hadron is a composite particle made of quarks held together by the strong force...
s were composed of fractionally charged quarks.
Overview
At present,
matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
and
energyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
are best understood in terms of the
kinematicsKinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
and
interactionsIn particle physics, fundamental interactions are the ways that elementary particles interact with one another...
of
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s. To date, physics has reduced the
lawsA scientific law is a statement that explains what something does in science just like Newton's law of universal gravitation. A scientific law must always apply under the same conditions, and implies a causal relationship between its elements. The law must be confirmed and broadly agreed upon...
governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. A major goal of physics is to find the "common ground" that would unite all of these theories into one integrated
theory of everythingA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
, of which all the other known laws would be special cases, and from which the behavior of all matter and energy could be derived (at least in principle).
The Standard Model groups two major extant theories—
quantum electroweakIn particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different...
and
quantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of colorcharged fermions...
—into an internally consistent theory that describes the interactions between all known particles in terms of
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
. For a technical description of the fields and their interactions, see Standard Model (mathematical formulation).
Fermions
Organization of FermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s

ChargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

First generation In particle physics, a generation is a division of the elementary particles. Between generations, particles differ by their quantum number and mass, but their interactions are identical....

Second generation 
Third generation 
QuarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly... s 
+{{frac23}} 
Up The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...

{{SubatomicParticleLink=yesUp quark}} 
Charm The charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...

{{SubatomicParticleLink=yesCharm quark}} 
Top The top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...

{{SubatomicParticleLink=yesTop quark}} 
−{{frac13}} 
Down The down quark or d quark is the secondlightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...

{{SubatomicParticleLink=yesDown quark}} 
Strange The strange quark or s quark is the thirdlightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...

{{SubatomicParticleLink=yesStrange quark}} 
Bottom The bottom quark, also known as the beauty quark, is a thirdgeneration quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...

{{SubatomicParticleLink=yesBottom quark}} 
LeptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral... s 
−1 
Electron The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

{{SubatomicParticleLink=yesElectron}} 
MuonThe muon mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...

{{SubatomicParticleLink=yesMuon}} 
Tau 
{{SubatomicParticleLink=yesTau}} 
0 
Electron neutrino The electron neutrino is a subatomic lepton elementary particle which has no net electric charge. Together with the electron it forms the first generation of leptons, hence its name electron neutrino...

{{SubatomicParticleLink=yesElectron neutrino}} 
Muon neutrino The muon neutrino is a subatomic lepton elementary particle which has the symbol and no net electric charge. Together with the muon it forms the second generation of leptons, hence its name muon neutrino. It was first hypothesized in the early 1940s by several people, and was discovered in 1962 by...

{{SubatomicParticleLink=yesMuon neutrino}} 
Tau neutrino 
{{SubatomicParticleLink=yesTau neutrino}} 
The Standard Model includes 12
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s of spin
{{Other usesStandard model (disambiguation)}}
{{Standard model of particle physics}}
The
Standard Model of
particle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
is a theory concerning the
electromagneticElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
,
weakWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
, and
strongIn particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a noncontact force...
nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon experimental confirmation of the existence of
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s. Since then, discoveries of the
bottom quarkThe bottom quark, also known as the beauty quark, is a thirdgeneration quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...
(1977), the
top quarkThe top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
(1995) and the tau neutrino (2000) have given credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a theory of almost everything.
Still, the Standard Model falls short of being a
complete theory of fundamental interactionsA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
because it does not incorporate the physics of
dark energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
nor of the full theory of
gravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
as described by
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. The theory does not contain any viable
dark matterIn astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
particle that possesses all of the required properties deduced from observational
cosmologyCosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
. It also does not correctly account for neutrino oscillations (and their nonzero masses). Although the Standard Model is theoretically selfconsistent, it has several apparently unnatural properties giving rise to puzzles like the strong CP problem and the
hierarchy problemIn theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...
.
Nevertheless, the Standard Model is important to
theoreticalTheoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
and
experimentalWithin the field of physics, experimental physics is the category of disciplines and subdisciplines concerned with the observation of physical phenomena in order to gather data about the universe...
particle physicists alike. For theorists, the Standard Model is a paradigmatic example of a
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
, which exhibits a wide range of physics including
spontaneous symmetry breakingSpontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
,
anomaliesIn quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics an anomaly is the failure of a symmetry to be restored in the limit in which the symmetrybreaking...
, nonperturbative behavior, etc. It is used as a basis for building more
exotic modelsPhysics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...
which incorporate hypothetical particles, extra dimensions and elaborate symmetries (such as
supersymmetryIn particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
) in an attempt to explain experimental results at variance with the Standard Model such as the existence of dark matter and neutrino oscillations. In turn, the experimenters have incorporated the standard model into simulators to help search for new physics
beyond the Standard ModelPhysics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...
from relatively uninteresting background.
Recently, the standard model has found applications in fields besides particle physics, such as
astrophysicsAstrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
, cosmology, and
nuclear physicsNuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
.
Historical background
The first step towards the Standard Model was
Sheldon GlashowSheldon Lee Glashow is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University.Birth and education:...
's discovery in 1960 of a way to combine the
electromagneticElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and
weak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
s. In 1967
Steven WeinbergSteven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
and
Abdus SalamMohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk (Urdu: محمد عبد السلام, pronounced , (January 29, 1926– November 21, 1996) was a Pakistani theoretical physicist and Nobel laureate in Physics for his work on the electroweak unification of the...
incorporated the
Higgs mechanismIn particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire nonvanishing masses through absorption of NambuGoldstone bosons arising in spontaneous symmetry breaking....
into Glashow's electroweak theory, giving it its modern form.
The Higgs mechanism is believed to give rise to the
massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
es of all the
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s in the Standard Model. This includes the masses of the
W and Z bosonsThe W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
, and the masses of the
fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s, i.e. the
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s and
leptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s.
After the
neutral weak currentsWeak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the boson...
caused by {{SubatomicParticleZ boson}} boson exchange
were discoveredGargamelle was a giant bubble chamber detector at CERN, designed mainly for the detection of neutrino interactions. Built in France, with a diameter of nearly 2 meters and 4.8 meters in length, Gargamelle held nearly 12 cubic meters of freon...
at
CERNThe European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
in 1973, the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979
Nobel Prize in PhysicsThe Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
for discovering it. The W and Z bosons were discovered experimentally in 1981, and their masses were found to be as the Standard Model predicted.
The theory of the
strong interactionIn particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a noncontact force...
, to which many contributed, acquired its modern form around 1973–74, when experiments confirmed that the
hadronIn particle physics, a hadron is a composite particle made of quarks held together by the strong force...
s were composed of fractionally charged quarks.
Overview
At present,
matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
and
energyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
are best understood in terms of the
kinematicsKinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
and
interactionsIn particle physics, fundamental interactions are the ways that elementary particles interact with one another...
of
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s. To date, physics has reduced the
lawsA scientific law is a statement that explains what something does in science just like Newton's law of universal gravitation. A scientific law must always apply under the same conditions, and implies a causal relationship between its elements. The law must be confirmed and broadly agreed upon...
governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. A major goal of physics is to find the "common ground" that would unite all of these theories into one integrated
theory of everythingA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
, of which all the other known laws would be special cases, and from which the behavior of all matter and energy could be derived (at least in principle).
The Standard Model groups two major extant theories—
quantum electroweakIn particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different...
and
quantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of colorcharged fermions...
—into an internally consistent theory that describes the interactions between all known particles in terms of
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
. For a technical description of the fields and their interactions, see Standard Model (mathematical formulation).
Fermions
Organization of FermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s

ChargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

First generation In particle physics, a generation is a division of the elementary particles. Between generations, particles differ by their quantum number and mass, but their interactions are identical....

Second generation 
Third generation 
QuarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly... s 
+{{frac23}} 
Up The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...

{{SubatomicParticleLink=yesUp quark}} 
Charm The charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...

{{SubatomicParticleLink=yesCharm quark}} 
Top The top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...

{{SubatomicParticleLink=yesTop quark}} 
−{{frac13}} 
Down The down quark or d quark is the secondlightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...

{{SubatomicParticleLink=yesDown quark}} 
Strange The strange quark or s quark is the thirdlightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...

{{SubatomicParticleLink=yesStrange quark}} 
Bottom The bottom quark, also known as the beauty quark, is a thirdgeneration quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...

{{SubatomicParticleLink=yesBottom quark}} 
LeptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral... s 
−1 
Electron The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

{{SubatomicParticleLink=yesElectron}} 
MuonThe muon mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...

{{SubatomicParticleLink=yesMuon}} 
Tau 
{{SubatomicParticleLink=yesTau}} 
0 
Electron neutrino The electron neutrino is a subatomic lepton elementary particle which has no net electric charge. Together with the electron it forms the first generation of leptons, hence its name electron neutrino...

{{SubatomicParticleLink=yesElectron neutrino}} 
Muon neutrino The muon neutrino is a subatomic lepton elementary particle which has the symbol and no net electric charge. Together with the muon it forms the second generation of leptons, hence its name muon neutrino. It was first hypothesized in the early 1940s by several people, and was discovered in 1962 by...

{{SubatomicParticleLink=yesMuon neutrino}} 
Tau neutrino 
{{SubatomicParticleLink=yesTau neutrino}} 
The Standard Model includes 12
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s of spin{{frac known as
fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s. According to the
spinstatistics theoremIn quantum mechanics, the spinstatistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic angular momentum...
, fermions respect the
Pauli exclusion principleThe Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is antisymmetric with respect to exchange of the particles...
. Each fermion has a corresponding
antiparticleCorresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...
.
The fermions of the Standard Model are classified according to how they interact (or equivalently, by what
chargesIn physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers.Formal definition:...
they carry). There are six
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s (
upThe up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
,
downThe down quark or d quark is the secondlightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...
,
charmThe charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...
,
strangeThe strange quark or s quark is the thirdlightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...
,
topThe top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
,
bottomThe bottom quark, also known as the beauty quark, is a thirdgeneration quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...
), and six
leptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s (
electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
,
electron neutrinoThe electron neutrino is a subatomic lepton elementary particle which has no net electric charge. Together with the electron it forms the first generation of leptons, hence its name electron neutrino...
,
muonThe muon mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
,
muon neutrinoThe muon neutrino is a subatomic lepton elementary particle which has the symbol and no net electric charge. Together with the muon it forms the second generation of leptons, hence its name muon neutrino. It was first hypothesized in the early 1940s by several people, and was discovered in 1962 by...
, tau, tau neutrino). Pairs from each classification are grouped together to form a
generationIn particle physics, a generation is a division of the elementary particles. Between generations, particles differ by their quantum number and mass, but their interactions are identical....
, with corresponding particles exhibiting similar physical behavior (see table).
The defining property of the quarks is that they carry
color chargeIn particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
, and hence, interact via the
strong interactionIn particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a noncontact force...
. A phenomenon called color confinement results in quarks being perpetually (or at least since very soon after the start of the
Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
) bound to one another, forming colorneutral composite particles (
hadronIn particle physics, a hadron is a composite particle made of quarks held together by the strong force...
s) containing either a quark and an antiquark (
mesonIn particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of subparticles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s) or three quarks (
baryonA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quarkbased particles...
s). The familiar
protonThe proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
and the
neutronThe neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
are the two baryons having the smallest mass. Quarks also carry
electric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
and
weak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
. Hence they interact with other fermions both
electromagneticallyElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and via the
weak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
.
The remaining six fermions do not carry color charge and are called leptons. The three
neutrinoA neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a halfinteger spin, chirality and a disputed but small nonzero mass. It is able to pass through ordinary matter almost unaffected...
s do not carry electric charge either, so their motion is directly influenced only by the
weak nuclear forceWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
, which makes them notoriously difficult to detect. However, by virtue of carrying an electric charge, the electron, muon, and tau all interact electromagnetically.
Each member of a generation has greater mass than the corresponding particles of lower generations. The first generation charged particles do not decay; hence all ordinary (baryonic) matter is made of such particles. Specifically, all atoms consist of electrons orbiting
atomic nucleiThe nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
ultimately constituted of up and down quarks. Second and third generations charged particles, on the other hand, decay with very short half lives, and are observed only in very highenergy environments. Neutrinos of all generations also do not decay, and pervade the universe, but rarely interact with baryonic matter.
Gauge bosons
In the Standard Model,
gauge bosonIn particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles....
s are defined as
force carrierIn particle physics, quantum field theories such as the Standard Model describe nature in terms of fields. Each field has a complementary description as the set of particles of a particular type...
s that mediate the strong, weak, and electromagnetic
fundamental interactionIn particle physics, fundamental interactions are the ways that elementary particles interact with one another...
s.
Interactions in physics are the ways that particles influence other particles. At a macroscopic level, electromagnetism allows particles to interact with one another via electric and
magneticA magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
fields, and gravitation allows particles with mass to attract one another in accordance with Einstein's theory of
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. The standard model explains such forces as resulting from matter particles
exchanging other particlesStatic force fields are fields, such as a simple electric, magnetic or gravitational fields, that exist without excitations. The most common approximation method that physicists use for scattering calculations can be interpreted as static forces arising from the interactions between two bodies...
, known as
force mediating particles (strictly speaking, this is only so if interpreting literally what is actually an
approximation method known as
perturbation theoryPerturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...
){{Citation neededdate=August 2010}}. When a force mediating particle is exchanged, at a macroscopic level the effect is equivalent to a force influencing both of them, and the particle is therefore said to have
mediated (i.e., been the agent of) that force. The
Feynman diagramFeynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prizewinning American physicist Richard Feynman, and first introduced in 1948...
calculations, which are a graphical representation of the perturbation theory approximation, invoke "force mediating particles", and when applied to analyze
highenergy scattering experimentsA particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in welldefined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...
are in reasonable agreement with the data. However, perturbation theory (and with it the concept of a "forcemediating particle") fails in other situations. These include lowenergy
quantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of colorcharged fermions...
,
bound stateIn physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space...
s, and
solitonIn mathematics and physics, a soliton is a selfreinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium...
s.
The gauge bosons of the Standard Model all have
spinIn quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
(as do matter particles). The value of the spin is 1, making them
bosonIn particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s. As a result, they do not follow the
Pauli exclusion principleThe Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is antisymmetric with respect to exchange of the particles...
that constrains
leptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s: thus bosons (e.g. photons) do not have a theoretical limit on their spatial density (number per volume). The different types of gauge bosons are described below.
 Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s mediate the electromagnetic force between electrically charged particles. The photon is massless and is welldescribed by the theory of quantum electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
.
 The {{SubatomicParticle
The W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
gauge bosons mediate the weak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
s between particles of different flavors (all quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s and leptons). They are massive, with the {{SubatomicParticleZ boson}} being more massive than the {{SubatomicParticleW boson+}}. The weak interactions involving the {{SubatomicParticleW boson+}} exclusively act on lefthanded particles and righthanded antiparticles only. Furthermore, the {{SubatomicParticleW boson+}} carries an electric charge of +1 and −1 and couples to the electromagnetic interaction. The electrically neutral {{SubatomicParticleZ boson}} boson interacts with both lefthanded particles and antiparticles. These three gauge bosons along with the photons are grouped together, as collectively mediating the electroweak interaction.
 The eight gluon
Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
s mediate the strong interactionIn particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a noncontact force...
s between color chargeIn particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
d particles (the quarks). Gluons are massless. The eightfold multiplicity of gluons is labeled by a combination of color and anticolor charge (e.g. red–antigreen).[Technically, there are nine such color–anticolor combinations. However, there is one colorsymmetric combination that can be constructed out of a linear superposition of the nine combinations, reducing the count to eight.] Because the gluon has an effective color charge, they can also interact among themselves. The gluons and their interactions are described by the theory of quantum chromodynamics.
The interactions between all the particles described by the Standard Model are summarized by the diagram at the top of this section.
Higgs boson
{{MainHiggs boson}}
The Higgs particle is a hypothetical massive
scalarIn theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a "scalar", in contrast to a vector or tensor field...
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
theorized by
Robert BroutRobert Brout was an AmericanBelgian theoretical physicist who has made significant contributions in elementary particle physics...
,
François EnglertFrançois Englert is a Belgian theoretical physicist. He was awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics , the Wolf Prize in Physics in 2004 and the High Energy and Particle Prize of the European Physical Society François Englert (born 6 November 1932) is a...
,
Peter HiggsPeter Ware Higgs, FRS, FRSE, FKC , is an English theoretical physicist and an emeritus professor at the University of Edinburgh....
,
Gerald GuralnikGerald Stanford Guralnik is the Chancellor’s Professor of Physics at Brown University. He is most famous for his codiscovery of the Higgs mechanism and Higgs Boson with C. R. Hagen and Tom Kibble...
,
C. R. HagenCarl Richard Hagen is a professor of particle physics at the University of Rochester. He is most noted for his contributions to the Standard Model and Symmetry breaking as well as the codiscovery of the Higgs mechanism and Higgs boson with Gerald Guralnik and Tom Kibble...
, and
Tom KibbleThomas Walter Bannerman Kibble, FRS, is a British scientist and senior research investigator at The Blackett Laboratory, at Imperial College London, UK. His research interests are in quantum field theory, especially the interface between highenergy particle physics and cosmology...
in 1964 (see 1964 PRL symmetry breaking papers) and is a key building block in the Standard Model. It has no intrinsic
spinIn quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
, and for that reason is classified as a
bosonIn particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
(like the gauge bosons, which have
integerThe integers are formed by the natural numbers together with the negatives of the nonzero natural numbers .They are known as Positive and Negative Integers respectively...
spin). Because an exceptionally large amount of energy and beam luminosity are theoretically required to observe a Higgs boson in high energy colliders, it is the only fundamental particle predicted by the Standard Model that has yet to be observed.
The Higgs boson plays a unique role in the Standard Model, by explaining why the other elementary particles, except the
photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
and
gluonGluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
, are massive. In particular, the Higgs boson would explain why the photon has no mass, while the
W and Z bosonsThe W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
are very heavy. Elementary particle masses, and the differences between
electromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
(mediated by the photon) and the weak force (mediated by the W and Z bosons), are critical to many aspects of the structure of microscopic (and hence macroscopic) matter. In
electroweak theoryIn particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different...
, the Higgs boson generates the masses of the leptons (electron, muon, and tau) and quarks.
As yet, no experiment has conclusively detected the existence of the Higgs boson. It is hoped that the
Large Hadron ColliderThe Large Hadron Collider is the world's largest and highestenergy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
at
CERNThe European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
will confirm the existence of this particle. As of August 2011, a significant portion of the possible masses for the Higgs have been excluded at 95% confidence level:
CMSThe Compact Muon Solenoid experiment is one of two large generalpurpose particle physics detectors built on the protonproton Large Hadron Collider at CERN in Switzerland and France. Approximately 3,600 people from 183 scientific institutes, representing 38 countries form the CMS collaboration...
has excluded the mass ranges 145216 GeV, 226288 GeV and 310400 GeV, while the
ATLASAn atlas is a collection of maps; it is typically a map of Earth or a region of Earth, but there are atlases of the other planets in the Solar System. Atlases have traditionally been bound into book form, but today many atlases are in multimedia formats...
experiment has excluded 146232 GeV, 256282 GeV and 296466 GeV. Note that these exclusions apply only to the Standard Model Higgs, and that more complex Higgs sectors which are possible in
Beyond the Standard ModelPhysics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...
scenarios may be significantly more difficult to characterize. CERN director general
Rolf HeuerRolfDieter Heuer is a German particle physicist and the Director General of CERN since 2009.Heuer studied physics at the University of Stuttgart...
has predicted that by the end of 2012 either the Standard Model Higgs boson will be observed, or excluded in all mass ranges, implying that the Standard Model is not the whole story.
Spin 1
 A U(1) gauge field B_{μν} with coupling g′ (weak U(1), or weak hypercharge
The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions...
)
 An SU(2) gauge field W_{μν} with coupling g (weak SU(2), or weak isospin
In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
)
 An SU(3) gauge field G_{μν} with coupling g_{s} (strong SU(3), or color charge
In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
)
Spin {{frac12}}
The spin {{frac12}} particles are in
representationsRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
of the gauge groups. For the U(1) group, we list the value of the
weak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions...
instead. The lefthanded fermionic fields are:
 An SU(3) triplet, SU(2) doublet, with U(1) weak hypercharge {{frac13}} (lefthanded quarks)
 An SU(3) triplet, SU(2) singlet, with U(1) weak hypercharge {{frac23}} (lefthanded downtype antiquark)
 An SU(3) singlet, SU(2) doublet with U(1) weak hypercharge −1 (lefthanded lepton)
 An SU(3) triplet, SU(2) singlet, with U(1) weak hypercharge −{{frac43}} (lefthanded uptype antiquark)
 An SU(3) singlet, SU(2) singlet with U(1) weak hypercharge 2 (lefthanded antilepton)
By CPT symmetry, there is a set of righthanded fermions with the opposite quantum numbers.
This describes one
generation of leptons and quarks, and there are three generations, so there are three copies of each field. Note that there are twice as many lefthanded lepton field components as lefthanded antilepton field components in each generation, but an equal number of lefthanded quark and antiquark fields.
Spin 0
 An SU(2) doublet H with U(1) hypercharge −1 (Higgs field)
Note that 
H
^{2}, summed over the two SU(2) components, is invariant under both SU(2) and under U(1), and so it can appear as a
renormalizableIn quantum field theory, the statistical mechanics of fields, and the theory of selfsimilar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....
term in the
LagrangianThe Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
, as can its square.{{ClarifySo... abs(H)^4? Or is abs(H) the renormalizable term, and abs(H)^2 what is meant?date=July 2009}}
This field acquires a
vacuum expectation valueIn quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...
, leaving a combination of the
weak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
, I
_{3}, and weak hypercharge unbroken. This is the electromagnetic gauge group, and the photon remains massless. The standard formula for the electric charge (which defines the normalization of the
weak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions...
,
Y, which would otherwise be somewhat arbitrary) is:
[The normalization Q = I_{3} + Y is sometimes used instead.]
Lagrangian
The
LagrangianThe Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
for the spin 1 and spin {{frac12}} fields is the most general renormalizable gauge field Lagrangian with no fine tunings:
 Spin 1:
where the traces are over the SU(2) and SU(3) indices hidden in
W and
G respectively. The twoindex objects are the field strengths derived from
W and
G the vector fields. There are also two extra hidden parameters: the theta angles for SU(2) and SU(3).
The spin{{frac12}} particles can have no mass terms because there is no right/left helicity pair with the same SU(2) and SU(3) representation and the same weak hypercharge. This means that if the gauge charges were conserved in the vacuum, none of the spin {{frac12}} particles could ever swap helicity, and they would all be massless.
For a neutral fermion, for example a hypothetical righthanded lepton
N (or
N^{α} in relativistic twospinor notation), with no SU(3), SU(2) representation and zero charge, it is possible to add the term:{{ClarifyAdd to what?date=July 2009}}
This term gives the neutral fermion a Majorana mass. Since the generic value for
M will be of order 1, such a particle would generically be unacceptably heavy. The interactions are completely determined by the theory – the leptons introduce no extra parameters.
Higgs mechanism
{{MainHiggs mechanism}}
The Lagrangian for the Higgs includes the most general renormalizable self interaction:

The parameter
v^{2} has dimensions of mass squared, and it gives the location where the classical Lagrangian is at a minimum. In order for the Higgs mechanism to work,
v^{2} must be a positive number.
v has units of mass, and it is the only parameter in the standard model which is not dimensionless. It is also much smaller than the Planck scale; it is approximately equal to the Higgs mass, and sets the scale for the mass of everything else. This is the only real finetuning to a small nonzero value in the standard model, and it is called the
Hierarchy problemIn theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...
.
It is traditional to choose the SU(2) gauge so that the Higgs doublet in the vacuum has expectation value (
v,0).
Masses and CKM matrix
{{mainCabibbo–Kobayashi–Maskawa matrix}}
The rest of the interactions are the most general spin0 spin{{frac12}}
Yukawa interactionIn particle physics, Yukawa's interaction, named after Hideki Yukawa, is an interaction between a scalar field \phi and a Dirac field \Psi of the typeV \approx g\bar\Psi \phi \Psi or g \bar \Psi \gamma^5 \phi \Psi ....
s, and there are many of these. These constitute most of the free parameters in the model. The Yukawa couplings generate the masses and mixings once the Higgs gets its vacuum expectation value.
The terms
L^{*}HR{{ClarifyThis is the only occurrence of this term in the article, and it is not defined. Are these three matrices?date=July 2009}} generate a mass term for each of the three generations of leptons. There are 9 of these terms, but by relabeling L and R, the matrix can be diagonalized. Since only the upper component of
H is nonzero, the upper SU(2) component of
L mixes with
R to make the electron, the muon, and the tau, leaving over a lower massless component, the neutrino. Note: Neutrino oscillations show neutrinos have mass. See also:
Pontecorvo–Maki–Nakagawa–Sakata matrixIn particle physics, the Pontecorvo–Maki–Nakagawa–Sakata matrix , Maki–Nakagawa–Sakata matrix , lepton mixing matrix, or neutrino mixing matrix, is a unitary matrixThe PMNS matrix is not unitary in the seesaw model which contains information on the mismatch of quantum states of leptons when they...
.
The terms QHU{{Clarifydate=July 2009}} generate up masses, while QHD{{Clarifydate=July 2009}} generate down masses. But since there is more than one righthanded singlet in each generation, it is not possible to diagonalize both with a good basis for the fields, and there is an extra CKM matrix.
Construction of the Standard Model Lagrangian
Parameters of the Standard Model
Symbol 
Description 
Renormalization scheme (point) 
Value 
m_{e} 
Electron mass 

511 keV 
m_{μ} 
Muon mass 

105.7 MeV 
m_{τ} 
Tau mass 

1.78 GeV 
m_{u} 
Up quark mass 
μ_{{{overline} = 2 GeV 
1.9 MeV 
m_{d} 
Down quark mass 
μ_{{{overlineMS}}} = 2 GeV 
4.4 MeV 
m_{s} 
Strange quark mass 
μ_{{{overlineMS}}} = 2 GeV 
87 MeV 
m_{c} 
Charm quark mass 
μ_{{{overlineMS}}} = m_{c} 
1.32 GeV 
m_{b} 
Bottom quark mass 
μ_{{{overlineMS}}} = m_{b} 
4.24 GeV 
m_{t} 
Top quark mass 
Onshell scheme 
172.7 GeV 
θ_{12} 
CKM 12mixing angle 

13.1° 
θ_{23} 
CKM 23mixing angle 

2.4° 
θ_{13} 
CKM 13mixing angle 

0.2° 
δ 
CKM CPviolating In particle physics, CP violation is a violation of the postulated CPsymmetry: the combination of Csymmetry and Psymmetry . CPsymmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped... Phase 

0.995 
g_{1} 
U(1) gauge coupling 
μ_{{{overlineMS}}} = m_{Z} 
0.357 
g_{2} 
SU(2) gauge coupling 
μ_{{{overlineMS}}} = m_{Z} 
0.652 
g_{3} 
SU(3) gauge coupling 
μ_{{{overlineMS}}} = m_{Z} 
1.221 
θ_{QCD} 
QCD vacuum angle In quantum gauge theories, in the Hamiltonian formulation, the wave function is a functional of the gauge Connection A and matter fields \,\phi. Being a quantum gauge theory, we have to impose first class constraints in the form of functional differential equations. Basically, the Gauss...


~0 
μ 
Higgs quadratic coupling 

Unknown 
λ 
Higgs selfcoupling strength 

Unknown 
Technically,
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
provides the mathematical framework for the standard model, in which a
LagrangianThe Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
controls the dynamics and kinematics of the theory. Each kind of particle is described in terms of a dynamical
fieldIn physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...
that pervades spacetime. The construction of the standard model proceeds following the modern method of constructing most field theories: by first postulating a set of symmetries of the system, and then by writing down the most general
renormalizableIn quantum field theory, the statistical mechanics of fields, and the theory of selfsimilar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....
Lagrangian from its particle (field) content that observes these symmetries.
The
globalA global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.See also:...
Poincaré symmetryIn physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime.Simple explanation:...
is postulated for all relativistic quantum field theories. It consists of the familiar
translational symmetryIn geometry, a translation "slides" an object by a a: Ta = p + a.In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation...
,
rotational symmetryGenerally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag has...
and the inertial reference frame invariance central to the theory of
special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
. The
localIn physics, a local symmetry is symmetry of some physical quantity, which smoothly depends on the point of the base manifold. Such quantities can be for example an observable, a tensor or the Lagrangian of a theory....
SU(3)×SU(2)×U(1) gauge symmetry is an internal symmetry that essentially defines the standard model. Roughly, the three factors of the gauge symmetry give rise to the three fundamental interactions. The fields fall into different
representationsIn mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry. A great deal is known about such representations, a basic tool in their study being the use of the corresponding 'infinitesimal' representations of Lie...
of the various symmetry groups of the Standard Model (see table). Upon writing the most general Lagrangian, one finds that the dynamics depend on 19 parameters, whose numerical values are established by experiment. The parameters are summarized in the table at right.
Quantum chromodynamics sector
{{MainQuantum chromodynamics}}
The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, with SU(3) symmetry, generated by T
^{a}. Since leptons do not interact with gluons, they are not affected by this sector. The Dirac Lagrangian of the quarks coupled to the gluon fields is given by

is the SU(3) gauge field containing the gluons,
are the Dirac matrices, D and U are the Dirac spinors associated with up and downtype
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s, and g
_{s} is the strong coupling constant.
Electroweak sector
{{MainElectroweak interaction}}
The electroweak sector is a Yang–Mills gauge theory with the symmetry group U(1)×SU(2)
_{L},
where
B_{μ} is the U(1) gauge field;
Y_{W} is the
weak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions...
—the generator of the U(1) group;
is the
threecomponent SU(2) gauge field;
are the
Pauli matricesThe Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary. Usually indicated by the Greek letter "sigma" , they are occasionally denoted with a "tau" when used in connection with isospin symmetries...
—infinitesimal generators of the SU(2) group. The subscript L indicates that they only act on left fermions;
g′ and
g are coupling constants.
Higgs sector
In the Standard Model, the Higgs field is a complex
spinorIn mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...
of the group SU(2)
_{L}:
where the indexes + and 0 indicate the electric charge (
Q) of the components. The weak isospin (
Y_{W}) of both components is 1.
Before symmetry breaking, the Higgs Lagrangian is:
which can also be written as:
Additional symmetries of the Standard Model
From the theoretical point of view, the Standard Model exhibits four additional global symmetries, not postulated at the outset of its construction, collectively denoted
accidental symmetries, which are continuous U(1)
global symmetriesA global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.See also:...
. The transformations leaving the Lagrangian invariant are:
The first transformation rule is shorthand meaning that all quark fields for all generations must be rotated by an identical phase simultaneously. The fields
,
and
,
are the 2nd (muon) and 3rd (tau) generation analogs of
and
fields.
By
Noether's theoremNoether's theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918...
, each symmetry above has an associated
conservation lawIn physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
: the conservation of
baryon number,
electron numberIn particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and nonleptonic particles 0...
,
muon numberIn particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and nonleptonic particles 0...
, and
tau numberIn particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and nonleptonic particles 0...
. Each quark is assigned a baryon number of 1/3, while each antiquark is assigned a baryon number of 1/3. Conservation of baryon number implies that the number of quarks minus the number of antiquarks is a constant. Within experimental limits, no violation of this conservation law has been found.
Similarly, each electron and its associated neutrino is assigned an electron number of +1, while the
antielectronThe positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
and the associated antineutrino carry a −1 electron number. Similarly, the muons and their neutrinos are assigned a muon number of +1 and the tau leptons are assigned a tau lepton number of +1. The Standard Model predicts that each of these three numbers should be conserved separately in a manner similar to the way baryon number is conserved. These numbers are collectively known as lepton family numbers (LF).
Symmetry works differently for quarks than for leptons, mainly because the Standard Model predicts (incorrectly) that
neutrinoA neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a halfinteger spin, chirality and a disputed but small nonzero mass. It is able to pass through ordinary matter almost unaffected...
s are massless. However, in 2002 it was discovered that neutrinos have mass (now established to be not greater than 0.28 electron volts), and as neutrinos
oscillateNeutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates...
between flavors (muon neutrinos have been observed changing to tau neutrinos) the discovery of neutrino mass indicates that the conservation of lepton family number is violated.
In addition to the accidental (but exact) symmetries described above, the Standard Model exhibits several
approximate symmetries. These are the "SU(2) custodial symmetry" and the "SU(2) or SU(3) quark flavor symmetry."
Symmetries of the Standard Model and Associated Conservation Laws
Symmetry In physics, symmetry includes all features of a physical system that exhibit the property of symmetry—that is, under certain transformations, aspects of these systems are "unchanged", according to a particular observation...

Lie GroupIn mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...

Symmetry Type 
Conservation Law In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....

Poincaré In physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime.Simple explanation:...

Translations In geometry, a translation "slides" an object by a a: Ta = p + a.In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation... ×In mathematics, specifically in the area of abstract algebra known as group theory, a semidirect product is a particular way in which a group can be put together from two subgroups, one of which is a normal subgroup. A semidirect product is a generalization of a direct product... SO(3,1)In physics , the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical setting for all physical phenomena...

Global symmetry A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.See also:...

EnergyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems... , MomentumIn classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object... , Angular momentumIn physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

Gauge 
SU(3)×SU(2)×U(1) 
Local symmetry In physics, a local symmetry is symmetry of some physical quantity, which smoothly depends on the point of the base manifold. Such quantities can be for example an observable, a tensor or the Lagrangian of a theory....

Color chargeIn particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , Weak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , Electric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two... , Weak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions...

BaryonA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quarkbased particles... phase 
U(1) 
Accidental Global symmetry A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.See also:...

Baryon number 
Electron The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton... phase 
U(1) 
Accidental Global symmetry A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.See also:...

Electron number In particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and nonleptonic particles 0...

MuonThe muon mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton... phase 
U(1) 
Accidental Global symmetry A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.See also:...

Muon number In particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and nonleptonic particles 0...

Tau phase 
U(1) 
Accidental Global symmetry A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.See also:...

Tau number In particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and nonleptonic particles 0...

Field content of the Standard Model
FieldIn physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...
(1st generation) 
Spin In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

Gauge group Representation 
Baryon Number 
Electron In particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and nonleptonic particles 0...
Number 
Lefthanded quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...


In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...

(In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions... ) 


Lefthanded up antiquark 

In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...

(In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions... ) 


Lefthanded down antiquark 

In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...

(In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions... ) 


Lefthanded lepton 

In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...

(In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions... ) 


Lefthanded antielectron 

In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...

(In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions... ) 


HyperchargeIn particle physics, the hypercharge Y of a particle is related to the strong interaction, and is distinct from the similarly named weak hypercharge, which has an analogous role in the electroweak interaction... gauge field 

In the theory of relativity, a fourvector is a vector in a fourdimensional real vector space, called Minkowski space. It differs from a vector in that it can be transformed by Lorentz transformations. The usage of the fourvector name tacitly assumes that its components refer to a standard basis...

(In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions... ) 


IsospinIn physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number... gauge field 

In the theory of relativity, a fourvector is a vector in a fourdimensional real vector space, called Minkowski space. It differs from a vector in that it can be transformed by Lorentz transformations. The usage of the fourvector name tacitly assumes that its components refer to a standard basis...

(In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions... ) 


Gluon Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles.... field 

In the theory of relativity, a fourvector is a vector in a fourdimensional real vector space, called Minkowski space. It differs from a vector in that it can be transformed by Lorentz transformations. The usage of the fourvector name tacitly assumes that its components refer to a standard basis...

(In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions... ) 


Higgs field 

In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or spacetime translations . This is in contrast to a vector...

(In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... , In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3... , The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions... ) 


List of standard model fermions
This table is based in part on data gathered by the
Particle Data GroupThe Particle Data Group is an international collaboration of particle physicists that compiles and reanalyzes published results related to the properties of particles and fundamental interactions. It also publishes reviews of theoretical results that are phenomenologically relevant, including...
.
Lefthanded fermions in the Standard Model
Generation 1 
Fermion (lefthanded) 
Symbol 
Electric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

Weak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...

Weak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions...

Color chargeIn particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,... * 
MassMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:... ** 
Electron The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...






511 keV 
PositronThe positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...






511 keV 
Electron neutrino The electron neutrino is a subatomic lepton elementary particle which has no net electric charge. Together with the electron it forms the first generation of leptons, hence its name electron neutrino...






< 0.28 eV **** 
Electron antineutrino 





< 0.28 eV **** 
Up quark The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...






~ 3 MeV *** 
Up antiquark 





~ 3 MeV *** 
Down quark The down quark or d quark is the secondlightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...






~ 6 MeV *** 
Down antiquark 





~ 6 MeV *** 

Generation 2 
Fermion (lefthanded) 
Symbol 
Electric charge 
Weak isospin 
Weak hypercharge 
Color charge * 
Mass ** 
MuonThe muon mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...






106 MeV 
Antimuon 





106 MeV 
Muon neutrino The muon neutrino is a subatomic lepton elementary particle which has the symbol and no net electric charge. Together with the muon it forms the second generation of leptons, hence its name muon neutrino. It was first hypothesized in the early 1940s by several people, and was discovered in 1962 by...






< 0.28 eV **** 
Muon antineutrino 





< 0.28 eV **** 
Charm quark The charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...






~ 1.337 GeV 
Charm antiquark 





~ 1.3 GeV 
Strange quark The strange quark or s quark is the thirdlightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...






~ 100 MeV 
Strange antiquark 





~ 100 MeV 

Generation 3 
Fermion (lefthanded) 
Symbol 
Electric charge 
Weak isospin 
Weak hypercharge 
Color charge * 
Mass ** 
Tau 





1.78 GeV 
Antitau 





1.78 GeV 
Tau neutrino 





< 0.28 eV **** 
Tau antineutrino 





< 0.28 eV **** 
Top quark The top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...






171 GeV 
Top antiquark 





171 GeV 
Bottom quark The bottom quark, also known as the beauty quark, is a thirdgeneration quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...






~ 4.2 GeV 
Bottom antiquark 





~ 4.2 GeV 
Notes:
 * These are not ordinary abelian
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order . Abelian groups generalize the arithmetic of addition of integers... chargesElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two... , which can be added together, but are labels of group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication... s of Lie groupIn mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure... s.
 ** Mass is really a coupling between a lefthanded fermion and a righthanded fermion. For example, the mass of an electron is really a coupling between a lefthanded electron and a righthanded electron, which is the antiparticle
Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The... of a lefthanded positronThe positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron... . Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a lefthanded electron antineutrino.
 *** The mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:... es of baryonA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quarkbased particles... s and hadronIn particle physics, a hadron is a composite particle made of quarks held together by the strong force... s and various crosssections are the experimentally measured quantities. Since quarks can't be isolated because of QCDIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of colorcharged fermions... confinementColor confinement, often simply called confinement, is the physics phenomenon that color charged particles cannot be isolated singularly, and therefore cannot be directly observed. Quarks, by default, clump together to form groups, or hadrons. The two types of hadrons are the mesons and the baryons... , the quantity here is supposed to be the mass of the quark at the renormalizationIn quantum field theory, the statistical mechanics of fields, and the theory of selfsimilar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.... scale of the QCD scale.
 **** The Standard Model assumes that neutrinos are massless. However, several contemporary experiments prove that neutrinos oscillate
Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates... between their flavourIn particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry... states, which could not happen if all were massless. It is straightforward to extend the model to fit these data but there are many possibilities, so the mass eigenstates are still open. See Neutrino#Mass. 
Tests and predictions
{{Ref improve sectiondate=April 2008}}
The Standard Model (SM) predicted the existence of the W and Z bosons,
gluonGluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
, and the top and
charm quarkThe charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...
s before these particles were observed. Their predicted properties were experimentally confirmed with good precision. To give an idea of the success of the SM, the following table compares the measured masses of the W and Z bosons with the masses predicted by the SM:
Quantity  Measured (GeV)  SM prediction (GeV) 
Mass of W boson 
80.398 ± 0.025 
80.390 ± 0.018 
Mass of Z boson 
91.1876 ± 0.0021 
91.1874 ± 0.0021 
The SM also makes several predictions about the decay of Z bosons, which have been experimentally confirmed by the
Large ElectronPositron ColliderThe Large Electron–Positron Collider was one of the largest particle accelerators ever constructed.It was built at CERN, a multinational centre for research in nuclear and particle physics near Geneva, Switzerland. LEP was a circular collider with a circumference of 27 kilometres built in a...
at
CERNThe European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
.
Challenges
{{See alsoBeyond the Standard Model}}
{{Unreferenced sectiondate=March 2009}}
{{unsolvedphysics
 What gives rise to the Standard Model of particle physics?
 Why do particle masses and coupling constant
In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part...
s have the values that we measure?
 Does the Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
really exist?
 Why are there three generations
In particle physics, a generation is a division of the elementary particles. Between generations, particles differ by their quantum number and mass, but their interactions are identical....
of particles?
 Why is there more matter than antimatter
In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...
in the universe?
 Where does Dark Matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
fit into the model? Is it even a new particle?
}}
There is some experimental evidence consistent with neutrinos having
massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, which the Standard Model does not allow. To accommodate such findings, the Standard Model can be modified by adding a nonrenormalizable interaction of lepton fields with the square of the Higgs field. This is natural in certain grand unified theories, and if new physics appears at about 10
^{16} GeVIn physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...
, the neutrino masses are of the right order of magnitude.
Currently, there is one elementary particle predicted by the Standard Model that has yet to be observed: the
Higgs bosonThe Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
. A major reason for building the
Large Hadron ColliderThe Large Hadron Collider is the world's largest and highestenergy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
is that the high energies of which it is capable are expected to make the Higgs observable. However, as of January 2011, there is only indirect empirical evidence for the existence of the Higgs boson, so that its discovery cannot be claimed. Moreover, some theoretical concerns have been raised positing that elementary scalar Higgs particles cannot exist (see
Quantum trivialityIn a quantum field theory, charge screening can restrict the value of the observable "renormalized" charge of a classical theory. Ifthe only allowed value of the renormalized charge is zero, the theory is said to be "trivial" or noninteracting...
).
A fair amount of theoretical and experimental
researchResearch can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...
has attempted to extend the Standard Model into a
Unified Field TheoryIn physics, a unified field theory, occasionally referred to as a uniform field theory, is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a single field. There is no accepted unified field theory, and thus...
or a
Theory of everythingA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
, a complete theory explaining all physical phenomena including constants. Inadequacies of the Standard Model that motivate such research include:
 It does not attempt to explain gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
, and unlike for the strong and electroweak interactions of the Standard Model, there is no known way of describing general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, the canonical theory of gravitation, consistently in terms of quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
. The reason for this is among other things that quantum field theories of gravity generally break down before reaching the Planck scaleIn particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...
. As a consequence, we have no reliable theory for the very early universe;
 It is considered by experts{{Citation neededdate=March 2011}} to be adhoc and inelegant, requiring 19 numerical constants whose values are unrelated and arbitrary. Although the Standard Model, as it now stands, can explain why neutrinos have masses, the specifics of neutrino mass are still unclear. It is believed that explaining neutrino mass will require an additional 7 or 8 constants, which are also arbitrary parameters;
 The Higgs mechanism gives rise to the hierarchy problem
In theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...
if any new physics (such as quantum gravity) is present at high energy scales. In order for the weak scale to be much smaller than the Planck scaleIn particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...
, severe fine tuning of Standard Model parameters is required;
 It should be modified so as to be consistent with the emerging "standard model of cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
." In particular, the Standard Model cannot explain the observed amount of cold dark matterCold dark matter is the improvement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation and whose constituent particles move slowly...
(CDM) and gives contributions to dark energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
which are far too large. It is also difficult to accommodate the observed predominance of matter over antimatter (matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
/antimatterIn particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...
asymmetryThe baryon asymmetry problem in physics refers to the apparent fact that there is an imbalance in baryonic matter and antibaryonic matter in the universe. Neither the standard model of particle physics, nor the theory of general relativity provide an obvious explanation for why this should be so;...
). The isotropy and homogeneityIn general, homogeneity is defined as the quality or state of being homogeneous . For instance, a uniform electric field would be compatible with homogeneity...
of the visible universe over large distances seems to require a mechanism like cosmic inflation, which would also constitute an extension of the Standard Model.
Currently no proposed
Theory of everythingA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
has been conclusively verified.
See also
{{PortalMathematics}}
{{Wikipedia booksParticles of the Standard Model}}
 Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
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 Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
, FermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
 Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...
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 Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
 Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a noncontact force...
:
 Color charge
In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
, Quantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of colorcharged fermions...
, Quark modelIn physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons....
 Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
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 Electroweak theory, Fermi theory of beta decay, Weak hypercharge
The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the GellMann–Nishijima formula for the hypercharge of strong interactions...
, Weak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
 Gauge theory
In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
 Nontechnical introduction to gauge theory
 Open questions: BTeV experiment, CP violation
In particle physics, CP violation is a violation of the postulated CPsymmetry: the combination of Csymmetry and Psymmetry . CPsymmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
, Neutrino masses, Quark matter
 Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
 Standard Model:
 Beyond the...
Physics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...
 Mathematical formulation of
 Diagram
A diagram is a twodimensional geometric symbolic representation of information according to some visualization technique. Sometimes, the technique uses a threedimensional visualization which is then projected onto the twodimensional surface...
s:
 Feynman
Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prizewinning American physicist Richard Feynman, and first introduced in 1948...
 Penguin
In quantum field theory, penguin diagrams are a class of Feynman diagrams which are important for understanding CP violating processes in the standard model. They refer to oneloop processes in which a quark temporarily changes flavor , and the flavorchanged quark engages in some tree interaction,...
 Flavour
In particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry...
 Generation
In particle physics, a generation is a division of the elementary particles. Between generations, particles differ by their quantum number and mass, but their interactions are identical....
 Higgs mechanism
In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire nonvanishing masses through absorption of NambuGoldstone bosons arising in spontaneous symmetry breaking....
 Higgsless model
In particle physics, a Higgsless model is a model that does not involve the Higgs boson or in which the Higgs field is not dynamic. Such models must employ a different mechanism of mass generation, electroweak symmetry breaking and unitarity....
 Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
 Unparticle physics
 1964 PRL symmetry breaking papers
 Lagrangian
The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
 Noncommutative standard model
In theoretical particle physics, the noncommutative Standard Model, mainly due to the French mathematician Alain Connes, uses his noncommutative geometry to devise an extension of the Standard Model to include a modified form of general relativity. This unification implies a few constraints on the...
 J. J. Sakurai Prize for Theoretical Particle Physics
The J. J. Sakurai Prize for Theoretical Particle Physics, is presented by the American Physical Society at its annual "April Meeting", and honors outstanding achievement in particle physics theory...
 C.R. Hagen
Further reading
Introductory textbooks
Advanced textbooks Highlights the
gauge theoryIn physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
aspects of the Standard Model. Highlights dynamical and phenomenological aspects of the Standard Model. Highlights
grouptheoreticalIn mathematics and abstract algebra, a finite group is a group whose underlying set G has finitely many elements. During the twentieth century, mathematicians investigated certain aspects of the theory of finite groups in great depth, especially the local theory of finite groups, and the theory of...
aspects of the Standard Model.
Journal articles
External links
 "Standard Model may be found incomplete," New Scientist
New Scientist is a weekly nonpeerreviewed Englishlanguage international science magazine, which since 1996 has also run a website, covering recent developments in science and technology for a general audience. Founded in 1956, it is published by Reed Business Information Ltd, a subsidiary of...
.
 "Observation of the Top Quark" at Fermilab
Fermi National Accelerator Laboratory , located just outside Batavia, Illinois, near Chicago, is a US Department of Energy national laboratory specializing in highenergy particle physics...
.
 "The Standard Model Lagrangian." After electroweak symmetry breaking
Symmetry breaking in physics describes a phenomenon where small fluctuations acting on a system which is crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations , the choice will appear arbitrary...
, with no explicit Higgs bosonThe Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
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 "Standard Model Lagrangian" with explicit Higgs terms. PDF, PostScript, and LaTeX versions.
 "The particle adventure." Web tutorial.
 Nobes, Matthew (2002) "Introduction to the Standard Model of Particle Physics" on Kuro5hin
Kuro5hin is a collaborative discussion website. Articles are created and submitted by Kuro5hin's users and submitted to queue for evaluation. Site members can vote for or against publishing an article and, once the article has reached a certain number of votes, it is then published to the site...
: Part 1, Part 2, Part 3a, Part 3b.
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