Glashow-Weinberg-Salam problem with mass terms

1. Aug 13, 2014

Karozo

At the end of spontaneous symmetry breaking I get these mass terms:

$W_{\mu}^{\pm}=\frac{1}{\sqrt{2}}\bigl(W_{\mu}^{1} \mp W_{\mu}^{2} \bigr )$

$\mathcal{L}_{mass}=\frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{+}{W^{\mu}}^{-} + \frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{-}{W^{\mu}}^{+}$

So I have $M_{W^+}=g \frac{v}{2} \quad M_{W^-}=g \frac{v}{2}$

Is it right? Or there are too many terms and it is enough:

$\mathcal{L}_{mass}= \frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{-}{W^{\mu}}^{+}$

2. Aug 15, 2014

ChrisVer

The mass terms seem right.
You can always write it as the last + h.c. which is your 2nd term

3. Aug 15, 2014

Orodruin

Staff Emeritus
Well, the W fields commute so there really is no point in writing it as two terms or with hc., just add a 2.