[QUE/QFT-15002] QFT-PROBLEM

$\newcommand{\Hsc}{\mathscr H}$
The interaction of \(\Lambda^0\) hyperon, responsible for decay into a proton and a \(\pi^-\), is given by \[ \Hsc_\text{int} = \bar{\psi}_p(x) ( g - g^\prime\gamma_5)\psi_\Lambda(x) \phi_\pi ^\dagger + h.c. \] 

• Give examples of three virtual processes allowed in the first order of this interaction term.}
• Show that the partial decay rate of \(\Lambda^0 \longrightarrow p + \pi^-\) is given by \[ \Gamma = \frac{1}{4\pi}\frac{|\vec{p}|}{M_\Lambda}\left(|g|^2(E_p+M_p) + |g^\prime|^2 (E_p-M_p) \right)\]