The
weak hypercharge in
particle physicsParticle physics is a branch of physics that studies the elementary constituents of matter and radiation, and the interactions between them. It is also called high energy physics, because many elementary particles do not occur under normal circumstances in nature, but can be created and detected...
is a conserved quantum number relating the electrical charge and the third component of
weak isospinThe weak isospin in particle physics 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...
, and is similar to the
Gell-Mann–Nishijima formulaThe Gell-Mann–Nishijima formula relates the baryon number B, the strangeness S, the isospin Iz 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...
for the
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...
of strong interactions (which is not conserved). It is frequently denoted
YW and corresponds to the
gauge symmetryIn gauge symmetry, 'gauge' means 'measure', and symmetry means 'stays the same'. Geometry is the study of the properties of objects that do not change when they move around. An object is symmetric if some motion leaves it looking the same, for instance, rotating an equilateral triangle through 120...
U(1).
It is the generator of the U(1) component of the electroweak gauge group, SU(2)xU(1) and its associated quantum field
B mixes with the
W3 electroweak quantum field to produce the observed
Z0 gauge boson and the
photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic field and the basic "unit" of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
of
quantum electrodynamicsQuantum electrodynamics is a relativistic quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s. It basically describes how light and matter interact. More specifically it deals with the interactions between electrons, positrons and photons...
.
Weak hypercharge, usually written as
YW, is defined as:
where
Q is the electrical charge (in
elementary chargeThe elementary charge, usually denoted e, is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. This is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called the "elementary positive...
units) and
Tz is the third component of
weak isospinThe weak isospin in particle physics 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 physicsParticle physics is a branch of physics that studies the elementary constituents of matter and radiation, and the interactions between them. It is also called high energy physics, because many elementary particles do not occur under normal circumstances in nature, but can be created and detected...
is a conserved quantum number relating the electrical charge and the third component of
weak isospinThe weak isospin in particle physics 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...
, and is similar to the
Gell-Mann–Nishijima formulaThe Gell-Mann–Nishijima formula relates the baryon number B, the strangeness S, the isospin Iz 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...
for the
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...
of strong interactions (which is not conserved). It is frequently denoted
YW and corresponds to the
gauge symmetryIn gauge symmetry, 'gauge' means 'measure', and symmetry means 'stays the same'. Geometry is the study of the properties of objects that do not change when they move around. An object is symmetric if some motion leaves it looking the same, for instance, rotating an equilateral triangle through 120...
U(1).
Definition
It is the generator of the U(1) component of the electroweak gauge group, SU(2)xU(1) and its associated quantum field
B mixes with the
W3 electroweak quantum field to produce the observed
Z0 gauge boson and the
photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic field and the basic "unit" of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
of
quantum electrodynamicsQuantum electrodynamics is a relativistic quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s. It basically describes how light and matter interact. More specifically it deals with the interactions between electrons, positrons and photons...
.
Weak hypercharge, usually written as
YW, is defined as:
where
Q is the electrical charge (in
elementary chargeThe elementary charge, usually denoted e, is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. This is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called the "elementary positive...
units) and
Tz is the third component of
weak isospinThe weak isospin in particle physics 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...
. Rearranging, the weak hypercharge can be expressed as:
Note: sometimes weak hypercharge is scaled so that
although this is a minority usage.
Baryon and lepton number
Weak hypercharge is related to baryon number - lepton number via:
where X is a
GUTGrand Unification, grand unified theory, or GUT refers to any of several very similar unified field theories or models in physics that predicts that at extremely high energies , the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field.Thus far, physicists...
-associated conserved
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...
. Since weak hypercharge is also conserved this implies that baryon number - lepton number is also conserved, within the
Standard ModelThe 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. These particles make up all visible matter in the universe...
and most extensions.
Neutron decay
- → + +
Hence neutron decay conserves
baryon numberIn particle physics, the baryon number is an approximate conserved 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. the total color charge of a particle has to be zero ,...
B and
lepton numberIn 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 separately, so also the difference
B-LIn high energy physics, B − L is the difference between the baryon number and the lepton number .-Details:...
is conserved.
Proton decay
Proton decayIn particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, usually a neutral pion and a positron. Proton decay has not been observed. There is currently no evidence that proton decay occurs.In the Standard Model,...
is a prediction of many
grand unification theoriesGrand Unification, grand unified theory, or GUT refers to any of several very similar unified field theories or models in physics that predicts that at extremely high energies , the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field.Thus far, physicists...
.
- → + → + 2
Hence proton decay conserves
B-LIn high energy physics, B − L is the difference between the baryon number and the lepton number .-Details:...
, even though it violates both
lepton numberIn 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...
and
baryon numberIn particle physics, the baryon number is an approximate conserved 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. the total color charge of a particle has to be zero ,...
conservation.