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Weak hypercharge
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Weak hypercharge is twice the difference between the electrical charge and the weak isospin. It is the generator of the U(1) component of the electroweak gauge group, SU(2)xU(1).
In a relation similar to the Gell-Mann–Nishijima formula there is:
where Q is the electrical charge (in elementary charge units), Tz is the weak isospin, and YW is the weak hypercharge. From this relation the weak hypercharge can be defined in terms of particle electrical charge and weak isospin:
Given that weak isospin is 1/2 for all left-handed fermions (and 0 for all right-handed fermions), all weak isospin doublets will have an average charge:
with
- YW = −1 for left-handed leptons (+1 for antileptons)
- YW = +1/3 for left-handed quarks (−1/3 for antiquarks)
Which also gives YW = B-L.