Srednicki — Quantum Field Theory · Problem 87.2

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · standard-model-gauge-higgs-sector

Problem

a) Ignoring loop corrections, find the numerical values of

v

g_1

, and

g_2

. Take

e^2/4\pi = \alpha(M_Z) = 1/127.9

and

\sin^2\theta_{\rm W} = 0.231

. b) The Fermi constant is defined (at tree level) as

G_{\rm F} \equiv \frac{e^2}{4\sqrt{2}\sin^2\theta_{\rm W} M_{\rm W}^2} \,. \tag{87.29}

Find its numerical value in

\text{GeV}^{-2}

. c) Express

G_{\rm F}

in terms of

v