The weak hypercharge in particle physics

Particle physics

Particle 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 conserved quantum number relating the electrical charge and the third component of weak isospin

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...

, and is similar to the Gell-Mann–Nishijima formula

Gell-Mann–Nishijima formula

The 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"...

 for the hypercharge

Hypercharge

In 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 Y_W and corresponds to the gauge symmetry 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 photon

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...

 of quantum electrodynamics

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...

.

Weak hypercharge, usually written as Y_W, is defined as:

where Q is the electrical charge (in elementary charge

Elementary charge

The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...

 units) and T₃ is the third component of weak isospin

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...

. 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

X (charge)

In particle physics, the X-charge is a conserved quantum number associated with the SO grand unification theory....

 is a GUT

Grand unification theory

The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...

-associated conserved quantum number

Quantum number

Quantum 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 minus lepton number is also conserved, within the Standard Model

Standard Model

The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong 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...

 and most extensions.

Neutron decay

→ + +

Hence neutron decay conserves baryon number B and lepton number

Lepton 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 non-leptonic particles 0...

 L separately, so also the difference B-L

B-L

In high energy physics, B − L is the difference between the baryon number and the lepton number .-Details:...

 is conserved.

Proton decay

Proton decay

Proton decay

In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron...

 is a prediction of many grand unification theories

Grand unification theory

The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...

.

→ + → + 2

Hence proton decay conserves B-L

B-L

In high energy physics, B − L is the difference between the baryon number and the lepton number .-Details:...

, even though it violates both lepton number

Lepton 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 non-leptonic particles 0...

 and baryon number conservation.