Srednicki — Quantum Field Theory · Problem 90.6

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · electroweak-interactions-of-hadrons

Problem

Compute the rate for the decay process

\pi^- \to \pi^0 e^-\bar{\nu}_e

. Note that, since

m_{\pi^+} - m_{\pi^0} = 4.594\,\text{MeV} \ll m_{\pi^0}

, the outgoing

\pi^0

is nonrelativistic. Compare your calculated rate with the measured value of

0.397\,\text{s}^{-1}

to determine

c_1

. Your answer is about 1\% too low, due to neglect of loop corrections.