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[QUE/QFT-12004] QFT-PROBLEM

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

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