An Introduction To Quantum Field Theory - M. Peskin, D. Schroeder (Perseus, 1995) · Problem 20.2

Electroweak Theory: Basics — M. Peskin, D. Schroeder (Perseus, 1995)

Physics — QFT · w-z-boson-decay-modes

Problem

**20.2 Decay modes of the

W

and

Z

bosons.** (a) Compute the partial decay widths of the

W

boson into pairs of quarks and leptons. Assume that the top quark mass

m_t

is larger than

m_W

, and ignore the other quark masses. The decay widths to quarks are enhanced by QCD corrections. Show that the correction is given, to order

\alpha_s

, by Eq. (17.9). Using

\sin^2\theta_w = 0.23

, find a numerical value for the total width of the

W^+

. (b) Compute the partial decay widths of the

Z

boson into pairs of quarks and leptons, treating the quarks in the same way as in part (a). Determine the total width of the

Z

boson and the fractions of the decays that give hadrons, charged leptons, and invisible modes

\nu\bar{\nu}