Standard Model and Beyond · Problem 2.25

Lie Groups, Lie Algebras, and Symmetries

Physics — Particle Physics · z-boson-decay-width

Problem

The interaction of the

Z

(a massive neutral vector boson in the electroweak theory) with a fermion

f

\mathcal{L} = -G\bar{\psi}(x)\gamma^\mu\left(g_V - g_A\gamma^5\right)\psi(x)Z_\mu(x),

where

G

g_V

, and

g_A

are real constants. Calculate the width for

Z \to f\bar{f}

. Let

M_Z

and

m

be the

Z

and

f

masses, and set

G = 1