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Weak Hypercharge




Weak hypercharge is twice the difference between the Electrical Charge and the Weak Isospin . It is the generator of the center of the electroweak gauge group.

In a relation that parallels the Gell-Mann/Nishima Law (see Hypercharge ) we have
:Q = I^W_z + {1 \over 2} Y^W
where ''Q'' is the electrical charge (in Elementary Charge units), I^W_z is the third component of the Weak Isospin , and Y^W is the weak hypercharge. From here we can define the weak hypercharge 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
:\bar Q = {Y^W \over 2}
with
  • ''Y'' = −1 for left-handed leptons (+1 for antileptons)

  • ''Y'' = +1/3 for left-handed quarks (−1/3 for antiquarks)




SEE ALSO