[QUE/QFT-15014] QFT-PROBLEM

The matrix element for the decay process \(\pi \to \mu + \nu\) is given by

\[ m_{fi} =\frac{g}{\surd 2} \bar{u}^{(r)}(p) (i \gamma^\mu Q_\mu) (1-\gamma_5)v^{(s)}(k)\]

for the life time computation we need to take absolute square, to average over initial spin and sum over final spin states. You may assume neutrino to be have a mass \(m_\nu\) and take limit \(m_\nu \to 0\). Compute the life time of pion decay.