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The $SU(2)$ weak isospin group has three bosons, before symmetry breaking: The $W^1$, $W^2$, and $W^3$ weak isospin bosons.

The $W^1$ and $W^2$ mix to form the $W^+$ and $W^-$ bosons with electric charges $+1$ and $-1$, respectively.

So far, I can assume that the $W^3$ boson carries a neutral charge. However, I am not sure what the electric charges (which are somewhat present before the photon exists) of the $SU(2)$ triplet bosons ($W^1$, $W^2$, and $W^3$) are.

According to Wikipedia, the $SU(2)$ triplet bosons form a Weak Isospin triplet (so one boson has Weak Isospin $+1$, another one has $-1$, and the last one has 0). Also, the formula for electric charge is $Q=T_3+\frac12 Y_w$.

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$W^1,W^2$ do not have well defined electric charge. They are not charge eigenstates: $$ \begin{aligned} Q|W^1\rangle&=+i|W^2\rangle\\ Q|W^2\rangle&=-i|W^1\rangle \end{aligned} $$

On the other hand, $W^\pm\propto W^1\pm iW^2$ do have well-defined charge: $$ Q|W^\pm\rangle=\pm |W^\pm\rangle $$

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  • $\begingroup$ (+1) Thanks, but do you know what Hypercharge and Weak Isospin each SU(2) boson has? $\endgroup$
    – ComputersAreCool
    Dec 19, 2016 at 21:07
  • $\begingroup$ $W^\pm$ has $T_3=\pm1$, and $W^3$ has $T_3=0$. They all have zero hypercharge. $\endgroup$
    – AccidentalFourierTransform
    Dec 19, 2016 at 21:11
  • $\begingroup$ $W^\pm$ don't have well defined isospin, but their hypercharge is zero. $\endgroup$
    – AccidentalFourierTransform
    Dec 19, 2016 at 21:16
  • $\begingroup$ $W^\pm$ or $W^{1,2}$? $\endgroup$
    – fuenfundachtzig
    Feb 9, 2017 at 13:57
  • $\begingroup$ @fuenfundachtzig ah, yes. I meant $W^{1,2}$. Thanks! $\endgroup$
    – AccidentalFourierTransform
    Feb 9, 2017 at 13:59

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