[QUE/QFT-14002] QFT-PROBLEM

The original four fermion interaction for beta decay of neutron \[n \longrightarrow p + e^- + \bar{\nu} \] is of the of form \[ \big(\bar{\psi}_p(x)\gamma_\mu\psi_n(x)\big)\big( \bar{\psi}_\nu(x) \gamma^\mu \psi_e(x)\big) + h.c.\] Now consider other processes given below. Which of these processes (real or virtual) are permitted and which ones are not permitted by the above interaction in the first order? Give brief reason in each case.

• \( \bar{p} \longrightarrow \bar{n} + e^- +\bar{\nu} \); 
• \( \bar{p} \longrightarrow \bar{n} + e^- +\nu \); 
• \( n \longrightarrow p + e^+ + \nu \);
• \( p \longrightarrow n + e^+ + \bar{\nu} \); 
• \( \bar{n} \longrightarrow \bar{p} + e^+ + \nu \);
• \( \bar{n} \longrightarrow \bar{p} + e^+ + \bar{\nu} \).