# A HIggs coupling to electroweak gauge bosons

1. Feb 18, 2017

### spaghetti3451

The coupling of the Higgs boson to the electroweak gauge bosons in the Standard model is given by

$$\mathcal{L}_{\text{H-g}} = - \left( \frac{H}{v} + \frac{H^{2}}{2v^{2}} \right) \left(2M_{W}^{2}W_{\mu}^{+}W^{-\mu} + M_{Z}^{2}Z_{\mu}Z^{\mu} \right).$$

However, in Cliff Burgess' textbook 'The Standard Model: A Primer,' the author suppresses the contribution $H^{2}/2v^{2}$ in equation (4.55) on page 146 when he discusses the decay of the Higgs boson to electroweak gauge bosons.

Is there a reason why the contribution $H^{2}/2v^{2}$ is suppressed?

2. Feb 21, 2017

### ChrisVer

Maybe because of the extra suppression term $1/2v \approx 1/500$ at the corresponding vertex connecting $HHVV$ to that $HVV$?