Standard Model and Beyond · Problem 2.27

Lie Groups, Lie Algebras, and Symmetries

Physics — Particle Physics · vector-resonance-breit-wigner

Problem

A vector resonance

V_\mu

of mass

M_V

and width

\Gamma_V

couples to massless fermions

a

and

b

with the interaction in (F.12) of Appendix F. Calculate the total spin-averaged cross section for

a\bar{a} \to b\bar{b}

. Assume that the propagator in (2.129) is modified to the Breit-Wigner form

iD^{\mu\nu}_V(k) = i\left[\frac{-g^{\mu\nu} + \frac{k^\mu k^\nu}{M_V^2}}{k^2 - M_V^2 + iM_V\Gamma_V}\right],

and express the result in a form similar to (F.11).