[QUE/QFT-15004] QFT-PROBLEM

The original four fermion interaction for beta decay of neutron \[n \longrightarrow p + e^- + \bar{\nu} \] is of the of form \[ \bar{\psi}_p(x)\gamma_\mu\psi_n(x) \bar{\psi}_\nu(x) \gamma^\mu \psi_e(x) + h.c.\] 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?

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

Give brief reason in each case.