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 (which is not conserved).

[edit] 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 of quantum electrodynamics.

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

where Q is the electrical charge (in elementary charge units) and T_z is the third component of weak isospin. Rearranging, the weak hypercharge can be expressed as:

Note: sometimes weak hypercharge is scaled so that

although this is a minority usage.

[edit] Baryon and lepton number

Weak hypercharge is related to baryon number - lepton number via:

where X is a GUT-associated conserved quantum number. Since weak hypercharge is also conserved this implies that baryon number - lepton number is also conserved, within the Standard Model and most extensions.

[edit] Neutron decay

n⁰ → p⁺ + e⁻ + ν0e

Hence neutron decay conserves B-L.

[edit] Proton decay

Proton decay is a prediction of many grand unification theories.

p⁺ → e⁺ + 2γ

Hence proton decay conserves B-L, even though it violates both lepton number and baryon number conservation.

[edit] See also

• Standard Model (mathematical formulation)