In
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...
, the
hypercharge Y of a particle is related to 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 non-contact force...
, and is distinct from the similarly named
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 Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
, which has an analogous role in the
electroweak interactionIn 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 concept of hypercharge combines and unifies
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...
and
flavourIn particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry...
into a single
chargeIn 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:...
.
Definition
Hypercharge in particle physics is a
quantum numberQuantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
relating 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 non-contact force...
s of the SU(3) model.
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...
is defined in the SU(2) model while the SU(3) model defines hypercharge.
SU(3) weight diagrams (see below) are 2 dimensional with the coordinates referring to two quantum numbers,
Iz, which is the z-component of isospin and
Y, which is the hypercharge (the sum of
strangenessIn particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...
(
S),
charm (
C),
bottomnessIn physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a...
(
B′),
topness (
T), and
baryon number (
B)). Mathematically, hypercharge is
and conservation of hypercharge implies a conservation of
flavourIn particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry...
. Strong interactions conserve hypercharge, but weak interactions do not.
Relation with Electric charge and Isospin
The
Gell-Mann–Nishijima formulaThe Gell-Mann–Nishijima formula relates the baryon number B, the strangeness S, the isospin I3 of hadrons to the charge Q. It was originally given by Kazuhiko Nishijima and Tadao Nakano in 1953, and lead to the proposal of strangeness as a concept, which Nishijima originally called "eta-charge"...
relates isospin and
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...
where
I3 is the third component of isospin and
Q is the particle's charge.
Isospin creates multiplets of particles whose average charge is related to the hypercharge by:
since the hypercharge is the same for all members of a multiplet, and the average of the
I3 values is 0.
SU(3) model in relation to hypercharge
The SU(2) model has
multipletIn group theory, a multiplet is formally a group representation of an algebra.In physics, multiplet can mean:* A group of related spectral lines* A group of related subatomic particles...
s characterized by a quantum number
J, which is the total
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...
. Each multiplet consists of 2
J + 1
substates with equally spaced values of
Jz, forming a symmetric arrangement seen in atomic spectra and isospin. This formalises the observation that certain strong baryon decay were not observed, leading to the prediction of the mass, strangeness and charge of the
{{Expert-subject|Physics|date=November 2008}}
{{Flavour quantum numbers}}
In
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...
, the
hypercharge Y of a particle is related to 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 non-contact force...
, and is distinct from the similarly named
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 Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
, which has an analogous role in the
electroweak interactionIn 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 concept of hypercharge combines and unifies
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...
and
flavourIn particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry...
into a single
chargeIn 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:...
.
Definition
Hypercharge in particle physics is a
quantum numberQuantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
relating 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 non-contact force...
s of the SU(3) model.
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...
is defined in the SU(2) model while the SU(3) model defines hypercharge.
SU(3) weight diagrams (see below) are 2 dimensional with the coordinates referring to two quantum numbers,
Iz, which is the z-component of isospin and
Y, which is the hypercharge (the sum of
strangenessIn particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...
(
S),
charm (
C),
bottomnessIn physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a...
(
B′),
topness (
T), and
baryon number (
B)). Mathematically, hypercharge is
and conservation of hypercharge implies a conservation of
flavourIn particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry...
. Strong interactions conserve hypercharge, but weak interactions do not.
Relation with Electric charge and Isospin
{{Main|Gell-Mann–Nishijima formula}}
The
Gell-Mann–Nishijima formulaThe Gell-Mann–Nishijima formula relates the baryon number B, the strangeness S, the isospin I3 of hadrons to the charge Q. It was originally given by Kazuhiko Nishijima and Tadao Nakano in 1953, and lead to the proposal of strangeness as a concept, which Nishijima originally called "eta-charge"...
relates isospin and
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...
where
I3 is the third component of isospin and
Q is the particle's charge.
Isospin creates multiplets of particles whose average charge is related to the hypercharge by:
since the hypercharge is the same for all members of a multiplet, and the average of the
I3 values is 0.
SU(3) model in relation to hypercharge
The SU(2) model has
multipletIn group theory, a multiplet is formally a group representation of an algebra.In physics, multiplet can mean:* A group of related spectral lines* A group of related subatomic particles...
s characterized by a quantum number
J, which is the total
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...
. Each multiplet consists of 2
J + 1
substates with equally spaced values of
Jz, forming a symmetric arrangement seen in atomic spectra and isospin. This formalises the observation that certain strong baryon decay were not observed, leading to the prediction of the mass, strangeness and charge of the
{{Expert-subject|Physics|date=November 2008}}
{{Flavour quantum numbers}}
In
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...
, the
hypercharge Y of a particle is related to 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 non-contact force...
, and is distinct from the similarly named
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 Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
, which has an analogous role in the
electroweak interactionIn 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 concept of hypercharge combines and unifies
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...
and
flavourIn particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry...
into a single
chargeIn 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:...
.
Definition
Hypercharge in particle physics is a
quantum numberQuantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
relating 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 non-contact force...
s of the SU(3) model.
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...
is defined in the SU(2) model while the SU(3) model defines hypercharge.
SU(3) weight diagrams (see below) are 2 dimensional with the coordinates referring to two quantum numbers,
Iz, which is the z-component of isospin and
Y, which is the hypercharge (the sum of
strangenessIn particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...
(
S),
charm (
C),
bottomnessIn physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a...
(
B′),
topness (
T), and
baryon number (
B)). Mathematically, hypercharge is
and conservation of hypercharge implies a conservation of
flavourIn particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry...
. Strong interactions conserve hypercharge, but weak interactions do not.
Relation with Electric charge and Isospin
{{Main|Gell-Mann–Nishijima formula}}
The
Gell-Mann–Nishijima formulaThe Gell-Mann–Nishijima formula relates the baryon number B, the strangeness S, the isospin I3 of hadrons to the charge Q. It was originally given by Kazuhiko Nishijima and Tadao Nakano in 1953, and lead to the proposal of strangeness as a concept, which Nishijima originally called "eta-charge"...
relates isospin and
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...
where
I3 is the third component of isospin and
Q is the particle's charge.
Isospin creates multiplets of particles whose average charge is related to the hypercharge by:
since the hypercharge is the same for all members of a multiplet, and the average of the
I3 values is 0.
SU(3) model in relation to hypercharge
The SU(2) model has
multipletIn group theory, a multiplet is formally a group representation of an algebra.In physics, multiplet can mean:* A group of related spectral lines* A group of related subatomic particles...
s characterized by a quantum number
J, which is the total
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...
. Each multiplet consists of 2
J + 1
substates with equally spaced values of
Jz, forming a symmetric arrangement seen in atomic spectra and isospin. This formalises the observation that certain strong baryon decay were not observed, leading to the prediction of the mass, strangeness and charge of the {{SubatomicParticle.
The SU(3) has
supermultiplets containing SU(2) multiplets. SU(3) now needs 2 numbers to specify all its sub-states which are denoted by
λ1 and
λ2.
(
λ1 + 1) specifies the number of points in the topmost side of the
hexagon while (
λ2 + 1) specifies the number of points on the bottom side.
Examples
- The nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
group (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....
s with Q = +1 and 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...
s with Q = 0) have an average charge of +1/2, so they both have hypercharge Y = 1 (baryon number B = +1, S = C = B′ = T = 0). From the Gell-Mann–Nishijima formula we know that proton has isospin I3 = +1/2, while neutron has I3 = −1/2.
- This also works for quark
A 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: for the up quark, with a charge of +2/3, and an I3 of +1/2, we deduce a hypercharge of 1/3, due to its baryon number (since you need 3 quarks to make a baryon, a quark has baryon number of 1/3).
- For a strange quark, with charge −1/3, a baryon number of 1/3 and strangeness
In particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...
of −1 we get a hypercharge Y = −2/3, so we deduce an I3 = 0. That means that a strange quark makes a singlet of its own (same happens with charm, bottom and top quarks), while up and down constitute an isospin doublet.
Practical obsolescence
Hypercharge was a concept developed in the 1960s, to organize groups of particles in the
"particle zooIn particle physics, the term particle zoo is used colloquially to describe a relatively extensive list of the known elementary particles that almost look like hundreds of species in the zoo....
" and to develop ad-hoc conservation laws based on their observed transformations. With the advent of the
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....
, it is now obvious that (if one only includes the up, down and strange quarks out of the total 6 quarks in the Standard Model), hypercharge
Y is the following combination of the numbers of
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...
(
nu) ,
downThe down quark or d quark is the second-lightest 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...
(
nd), and
strange quarkThe strange quark or s quark is the third-lightest 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...
s(
ns):
In modern descriptions of
hadronIn particle physics, a hadron is a composite particle made of quarks held together by the strong force...
interaction, it has become more obvious to draw
Feynman diagramFeynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
s that trace through individual quarks composing the interacting
baryonA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...
s and
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 sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s, rather than counting hypercharge quantum numbers.
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 Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
, however, remains of practical use in various theories of the
electroweak interactionIn 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...
.