A. Zee, Quantum Field Theory in a Nutshell · Problem VIII.3.4

Field Theory Redux

Physics — QFT

Problem

Given the conclusion of the previous exercise show that the decay rate for the processes

p \to \pi^+ + \bar{\nu}

p \to \pi^0 + e^+

n \to \pi^0 + \bar{\nu}

, and

n \to \pi^- + e^+

are proportional to each other, with the proportionality factors determined by a single unknown constant [the ratio of the coefficients of

(l_L C q_L)(u_R C d_R)

and

(e_R C u_R)(q_L C q_L)