[QUE/QFT-14002]

The original four fermion interaction for four fermion  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.
   \( \bar{p} \longrightarrow \bar{n} + e^-  +\bar{\nu} \); &

1.    \( \bar{p} \longrightarrow \bar{n} + e^-  +\nu \); &
2.     \( n \longrightarrow p + e^+  + \nu \);\\
3.     \( p \longrightarrow n + e^+  + \bar{\nu} \); &
4.    \( \bar{n} \longrightarrow \bar{p} + e^+  + \nu \);&
5.   \( \bar{n} \longrightarrow \bar{p} + e^+  + \bar{\nu} \).