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Flavour (particle physics)
 
 
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In particle physics
Particle physics

Particle physics is a branch of physics that studies the elementary particle constituents of matter and radiation, and the interactions between them....
, flavour or flavor (see spelling differences
American and British English spelling differences

American and British English spelling differences are one aspect of American and British English differences.The spelling systems of Commonwealth of Nations countries, for the most part, closely resemble the British system....
) is a quantum number
Quantum number

Quantum numbers describe values of conserved numbers in the dynamics of the quantum system. They often describe specifically the energies of electrons in atoms, but other possibilities include angular momentum, Spin etc....
 of elementary particle
Elementary particle

In particle physics, an elementary particle or fundamental particle is a wiktionary:particle not known to have substructure; that is, it is not known to be made up of smaller particles....
s. In quantum chromodynamics
Quantum chromodynamics

Quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons ....
 flavour is a global symmetry. In the electroweak theory, on the other hand, this symmetry is broken, and flavour changing processes exist.

Definition
If there are two or more particles which have identical interactions, then they may be interchanged without affecting the physics. Any (complex) linear combination of these two particles give the same physics, as long as they are orthogonal or perpendicular to each other.






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In particle physics
Particle physics

Particle physics is a branch of physics that studies the elementary particle constituents of matter and radiation, and the interactions between them....
, flavour or flavor (see spelling differences
American and British English spelling differences

American and British English spelling differences are one aspect of American and British English differences.The spelling systems of Commonwealth of Nations countries, for the most part, closely resemble the British system....
) is a quantum number
Quantum number

Quantum numbers describe values of conserved numbers in the dynamics of the quantum system. They often describe specifically the energies of electrons in atoms, but other possibilities include angular momentum, Spin etc....
 of elementary particle
Elementary particle

In particle physics, an elementary particle or fundamental particle is a wiktionary:particle not known to have substructure; that is, it is not known to be made up of smaller particles....
s. In quantum chromodynamics
Quantum chromodynamics

Quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons ....
 flavour is a global symmetry. In the electroweak theory, on the other hand, this symmetry is broken, and flavour changing processes exist.

Definition


If there are two or more particles which have identical interactions, then they may be interchanged without affecting the physics. Any (complex) linear combination of these two particles give the same physics, as long as they are orthogonal or perpendicular to each other. In other words, the theory possesses symmetry transformations such as , where and are the two fields, and is any 2 x 2 unitary matrix with a unit determinant. Such matrices form a Lie group
Lie group

In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the Differential structure....
 called SU(2) (see special unitary group
Special unitary group

In mathematics, the special unitary group of degree n, denoted SU, is the group of n×n unitary matrix Matrix with determinant 1....
). This is an example of flavour symmetry.

The term "flavour" was first coined for use in the quark model
Quark model

In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, i.e., the quarks which give rise to the quantum numbers of the hadrons....
 of hadron
Hadron

In particle physics, a hadron is a bound state of quarks. Hadrons are held together by the strong interaction, similarly to how molecules are held together by the electromagnetic force....
s in 1968. A name for the set of quantum numbers related to isospin
Isospin

In 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 of nucleons....
, hypercharge
Hypercharge

In particle physics, the hypercharge 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....
 and strangeness
Strangeness

In particle physics, strangeness, denoted as , is a property of particles, expressed as a quantum number for describing decay of particles in strong interaction and electromagnetic interaction reactions, which occur in a short period of time....
 is said to have been found on the way to lunch by Murray Gell-Mann
Murray Gell-Mann

Murray Gell-Mann is an United States physicist who received the 1969 Nobel Prize in physics for his work on the theory of particle physicss.Among his many accomplishments, he formulated the quark model of hadronic resonances, and identified the SU flavor symmetry of the light quarks, extending isospin to include strange quark, which he als...
 and Harald Fritzsch when they passed a Baskin-Robbins
Baskin-Robbins

Baskin-Robbins is a global chain of ice cream parlors founded by Burt Baskin and Irv Robbins in 1945 in Glendale, California. It claims to be the world's largest ice cream franchise, with more than 5,800 locations, 2,800 of which are located in the United States....
 advertising 31 flavours.

Flavour quantum numbers


Leptons


All lepton
Lepton

Leptons are a family of elementary particles, alongside quarks and gauge bosons . Like quarks, leptons are fermions and are subject to the electromagnetic force, the gravitational force, and weak interaction....
s carry a lepton number
Lepton number

In high energy 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 non-leptonic particles 0....
 L  =  1. In addition, leptons carry weak isospin
Weak isospin

The weak isospin in particle physics is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction....
, Tz, which is -½ for the three charged leptons (i.e. e, µ and t) and ½ for the three associated neutrino
Neutrino

Neutrinos are elementary particles that travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect....
s. Each doublet of a charged lepton and a neutrino consisting of opposite Tz are said to constitute one generation
Generation (particle physics)

In particle physics, a generation is a division of the elementary particles. Between generations, particles differ only by their mass. All fundamental interactions and quantum numbers are identical....
 of leptons. In addition, one defines a quantum number called weak hypercharge
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 Gell-Mann?Nishijima formula for the hypercharge of strong interactions ....
, YW which is -1 for the charged leptons and +1 for the neutrinos. Weak isospin
Weak isospin

The weak isospin in particle physics is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction....
 and weak hypercharge
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 Gell-Mann?Nishijima formula for the hypercharge of strong interactions ....
 are gauged in the Standard Model
Standard Model

The Standard Model of particle physics is a theory of three of the four known fundamental interactions and the elementary particles that take part in these interactions....
.

Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos. These are conserved in electromagnetic interactions, but violated by weak interactions. Therefore, such flavour quantum numbers are not of great use. A quantum number for each generation is more useful. However, neutrinos of different generations can mix; that is, a neutrino of one flavour can transform into another flavour
Neutrino oscillation

Neutrino oscillation is a quantum mechanics phenomenon predicted by Bruno Pontecorvo whereby a neutrino created with a specific lepton flavor can later be Quantum measurement to have a different flavor....
. The strength of such mixings is specified by a matrix called the MNS matrix.

Quarks

All quark
Quark

Quarks are a type of elementary particle and major constituents of matter. They are the only particles in the Standard Model to experience all four fundamental interaction, which are also known as fundamental interactions....
s carry a baryon number
Baryon number

In particle physics, the baryon number is an conservation laws quantum number of a system. It is defined as:whereWhy one third? According to the laws of strong interaction there cannot be any bare color charge, i.e....
 B  =  ?. In addition they carry weak isospin
Weak isospin

The weak isospin in particle physics is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction....
, Tz  =  ±½. The positive Tz particles are called up-type quarks and the remainder are down-type quarks. Each doublet of up and down type quarks constitutes one generation
Generation (particle physics)

In particle physics, a generation is a division of the elementary particles. Between generations, particles differ only by their mass. All fundamental interactions and quantum numbers are identical....
 of quarks.

Quarks have the following flavour quantum numbers:
  • Isospin
    Isospin

    In 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 of nucleons....
     which has value Iz = ½ for the up quark and value Iz = -½ for the down quark.
  • Strangeness
    Strangeness

    In particle physics, strangeness, denoted as , is a property of particles, expressed as a quantum number for describing decay of particles in strong interaction and electromagnetic interaction reactions, which occur in a short period of time....
     (S): a quantum number introduced by Murray Gell-Mann
    Murray Gell-Mann

    Murray Gell-Mann is an United States physicist who received the 1969 Nobel Prize in physics for his work on the theory of particle physicss.Among his many accomplishments, he formulated the quark model of hadronic resonances, and identified the SU flavor symmetry of the light quarks, extending isospin to include strange quark, which he als...
    . The strange antiquark is defined to have strangeness +1. This is a down-type quark.
  • Charm
    Charm quark

    The charm quark is a second-generation quark with an electric charge of + elementary charge. It is the third most massive of the quarks, at about ....
     (C) number which is +1 for the charm quark. This is an up-type quark.
  • Bottom
    Bottom quark

    The bottom quark is a third-generation quark with a charge of -elementary charge. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a distinctive signature that makes it re...
     (or beauty) quantum number, B': which is +1 for the down-type bottom antiquark.
  • Top
    Top quark

    The top quark is the third-generation up-type quark with a charge of +elementary charge. It was discovered in 1995 by the Collider Detector at Fermilab and D0 experiment experiments at Fermilab, and is the most massive of known elementary particles....
     (or truth) quantum number, T: +1 for the up-type top quark.
These are useful quantum numbers since they are conserved by both the electromagnetic and strong forces. Out of them can be built the derived quantum numbers:
  • hypercharge
    Hypercharge

    In particle physics, the hypercharge 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....
    : Y = B+S+C+B'+T and
  • electric charge
    Electric charge

    Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
    : Q = Iz+Y/2.


A quark of a given flavour is an eigenstate of the weak interaction
Weak interaction

The weak interaction is one of the four fundamental interactions of nature. In the Standard Model of particle physics, it is due to the exchange of the heavy W and Z bosons....
 part of the Hamiltonian
Hamiltonian (quantum mechanics)

In quantum mechanics, the Hamiltonian H is the observable corresponding to the total energy of the system. As with all observables, the Spectrum of the Hamiltonian is the set of possible outcomes when one measures the total energy of a system....
: it will interact in a definite way with the W+, W- and Z boson
Boson

In particle physics, bosons are subatomic particle which obey Bose-Einstein statistics; they are named after Satyendra Nath Bose and Albert Einstein....
s. On the other hand, a fermion
Fermion

In particle physics, fermions are subatomic particle which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In contrast to bosons, which have Bose-Einstein statistics, only one fermion can occupy a quantum state at a given time; this is the Pauli Exclusion Principle....
 of a fixed mass (an eigenstate of the kinetic and strong interaction parts of the Hamiltonian) is normally a superposition of various flavours. As a result, the flavour content of a quantum state
Quantum state

In quantum physics, a quantum State is a mathematical object that fully describes a Quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state; the mathematical object then reflects the setup of the apparatus....
 may change as it propagates freely. The transformation from flavour to mass basis for quarks is given by the so-called Cabibbo-Kobayashi-Maskawa matrix (CKM matrix
CKM Matrix

#REDIRECTCabibbo?Kobayashi?Maskawa matrix...
). By definition therefore, this matrix defines the strength of flavour changes under weak interactions of quarks.

The CKM matrix allows for CP violation
CP violation

In particle physics, CP violation is a violation of the postulated CP symmetry, the combination of C symmetry and P symmetry. CP symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle , and left and right were swapped ....
 if there are at least three generations.

Antiparticles and hadrons


Flavour quantum numbers are additive. Hence antiparticles have flavour equal in magnitude to the particle but opposite in sign. Hadron
Hadron

In particle physics, a hadron is a bound state of quarks. Hadrons are held together by the strong interaction, similarly to how molecules are held together by the electromagnetic force....
s inherit their flavour quantum number from their valence quarks: this is the basis of the classification in the quark model
Quark model

In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, i.e., the quarks which give rise to the quantum numbers of the hadrons....
. The relations between the hypercharge, electric charge and other flavour quantum numbers hold for hadron
Hadron

In particle physics, a hadron is a bound state of quarks. Hadrons are held together by the strong interaction, similarly to how molecules are held together by the electromagnetic force....
s as well as quark
Quark

Quarks are a type of elementary particle and major constituents of matter. They are the only particles in the Standard Model to experience all four fundamental interaction, which are also known as fundamental interactions....
s.

Quantum chromodynamics


(Flavour symmetry is closely related to chiral symmetry
Chirality (physics)

A phenomenon is said to be chiral if it is not identical to its mirror image . The Spin of a particle may be used to define a handedness for that particle....
. This part of the article is best read along with the one on chirality (physics)
Chirality (physics)

A phenomenon is said to be chiral if it is not identical to its mirror image . The Spin of a particle may be used to define a handedness for that particle....
.)

Quantum chromodynamics
Quantum chromodynamics

Quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons ....
 contains six flavours of quark
Quark

Quarks are a type of elementary particle and major constituents of matter. They are the only particles in the Standard Model to experience all four fundamental interaction, which are also known as fundamental interactions....
s. However, their masses differ. As a result, they are not strictly interchangeable with each other. Two of the flavours, called up
Up

Up is a relative direction, the opposite of down.Up may also refer to:*A railroad direction in the United Kingdom and China*At bat, in baseball, when a player is facing the pitcher...
 and down
Down

Down may refer to:* Relative direction, where down is the direction towards the centre of gravity of a celestial object.* Railroad directions, where down and up have locally significant meanings...
, are close to having equal masses, and the theory of these two quarks possesses an approximate SU(2) symmetry. Under some circumstances one can take Nf flavours to have the same masses and obtain an effective SU(Nf) flavour symmetry.

Under some circumstances, the masses of the quarks can be neglected entirely. In that case, each flavour of quark possesses a chiral symmetry
Chirality (physics)

A phenomenon is said to be chiral if it is not identical to its mirror image . The Spin of a particle may be used to define a handedness for that particle....
. One can then make flavour transformations independently on the left- and right-handed parts of each quark field. The flavour group is then a chiral group .

If all quarks have equal mass, then this chiral symmetry is broken to the vector symmetry of the diagonal flavour group which applies the same transformation to both helicities
Helicity

The term helicity has several meanings in physics, all referring to a phenomenon that resembles a helix. See:*helicity *helicity *magnetic helicity...
 of the quarks. Such a reduction of the symmetry is called explicit symmetry breaking. The amount of explicit symmetry breaking is controlled by the current quark masses in QCD.

Even if quarks are massless, chiral flavour symmetry can be spontaneously broken if for some reason the vacuum of the theory contains a chiral condensate (as it does in low-energy QCD). This gives rise to an effective mass for the quarks, often identified with the valence quark mass in QCD.

Symmetries of QCD

Analysis of experiments indicate that the current quark masses of the lighter flavours of quarks are much smaller than the QCD scale, ?QCD, hence chiral flavour symmetry is a good approximation to QCD
Quantum chromodynamics

Quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons ....
 for the up, down and strange quarks. The success of chiral perturbation theory
Chiral perturbation theory

Chiral perturbation theory is an effective field theory constructed with a Lagrangian consistent with the chiral symmetry of quantum chromodynamics , as well as the other symmetries of parity and charge conjugation....
 and the even more naive chiral model
Chiral model

In nuclear physics, the chiral model is a Phenomenology model describing mesons in the chiral limit where the masses of the quarks go to zero ....
s spring from this fact. The valence quark masses extracted from the quark model
Quark model

In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, i.e., the quarks which give rise to the quantum numbers of the hadrons....
 are much larger than the current quark mass. This indicates that QCD has spontaneous chiral symmetry breaking with the formation of a chiral condensate. Other phases of QCD may break the chiral flavour symmetries in other ways.

Conservation laws


Absolutely conserved flavour quantum numbers are
  • the electric charge
    Electric charge

    Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
     Q
  • the difference of the baryon number
    Baryon number

    In particle physics, the baryon number is an conservation laws quantum number of a system. It is defined as:whereWhy one third? According to the laws of strong interaction there cannot be any bare color charge, i.e....
     and the lepton number
    Lepton number

    In high energy 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 non-leptonic particles 0....
    : B-L
    B-L

    In high energy physics, B-L is the baryon number minus the lepton number....
All other flavour quantum numbers are violated by the electroweak interactions. Baryon number
Baryon number

In particle physics, the baryon number is an conservation laws quantum number of a system. It is defined as:whereWhy one third? According to the laws of strong interaction there cannot be any bare color charge, i.e....
 and lepton number
Lepton number

In high energy 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 non-leptonic particles 0....
 are separately violated in the electroweak interactions through the chiral anomaly
Chiral anomaly

A chiral anomaly is the anomaly nonconservation of a chirality current. In some theories of chiral fermion the quantization may lead to the breaking of this chiral symmetry....
. Strong interactions conserve all flavours.

History

Some of the historical events that lead to the development of flavour symmetry are discussed in the article on isospin
Isospin

In 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 of nucleons....
.

See also

  • Field theoretical formulation of the standard model
    Standard model (basic details)

    This is a detailed description of the Standard Model of particle physics. It describes how the leptons, quarks, gauge bosons and the Higgs boson fit together....
  • Weak interactions, flavour changing processes and CP violation
    CP violation

    In particle physics, CP violation is a violation of the postulated CP symmetry, the combination of C symmetry and P symmetry. CP symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle , and left and right were swapped ....
  • Quantum chromodynamics
    Quantum chromodynamics

    Quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons ....
    , strong CP problem and chirality (physics)
    Chirality (physics)

    A phenomenon is said to be chiral if it is not identical to its mirror image . The Spin of a particle may be used to define a handedness for that particle....
  • Chiral symmetry breaking
    Chiral symmetry breaking

    In particle physics, chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the chiral symmetry of gauge theory such as Quantum Chromodynamics....
     and quark matter
  • Quark
    Quark

    Quarks are a type of elementary particle and major constituents of matter. They are the only particles in the Standard Model to experience all four fundamental interaction, which are also known as fundamental interactions....
    s, lepton
    Lepton

    Leptons are a family of elementary particles, alongside quarks and gauge bosons . Like quarks, leptons are fermions and are subject to the electromagnetic force, the gravitational force, and weak interaction....
    s and hadron
    Hadron

    In particle physics, a hadron is a bound state of quarks. Hadrons are held together by the strong interaction, similarly to how molecules are held together by the electromagnetic force....
    s.
  • Quark flavour tagging is an example of particle identification
    Particle identification

    Particle identification is the process of using information left by a Subatomic particle passing through a particle detector to identify the type of particle....
     in experimental particle physics.