Glashow-Weinberg-Salam problem with mass terms

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

    [itex]W_{\mu}^{\pm}=\frac{1}{\sqrt{2}}\bigl(W_{\mu}^{1} \mp W_{\mu}^{2} \bigr )[/itex]

    [itex]\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}}^{+} [/itex]

    So I have [itex] M_{W^+}=g \frac{v}{2} \quad M_{W^-}=g \frac{v}{2} [/itex]

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

    [itex]\mathcal{L}_{mass}= \frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{-}{W^{\mu}}^{+} [/itex]
  2. jcsd
  3. ChrisVer

    ChrisVer 2,403
    Gold Member

    The mass terms seem right.
    You can always write it as the last + h.c. which is your 2nd term
  4. Well, the W fields commute so there really is no point in writing it as two terms or with hc., just add a 2.
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