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 (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 YW, is defined as:

where Q is the electrical charge (in elementary charge units) and Tz 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
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