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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 that

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 YW 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 fermions, all weak isospin doublets will have an averge charge

\bar Q = {Y^W \over 2}

with

  • Y = −1 for leptons (+1 for antileptons)
  • Y = +1/3 for quarks (−1/3 for antiquarks)


01-04-2007 01:16:19
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