Schwache Hyperladung

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

$Q=I_{z}^{W}+{1 \over 2}Y^{W}$

where Q is the electrical charge (in elementary charge units), $I_{z}^{W}$ 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

• Field theoretical formulation of the standard model
• Weak isospin