Leptonic CP violating effective action for Dirac and Majorana neutrinos

TL;DR

This paper calculates the leading CP-violating effects in the effective action of massive neutrinos within the Standard Model extension, revealing new operators and bounds on their couplings.

Contribution

It provides the first detailed computation of CP-violating operators induced by leptons for Dirac and Majorana neutrinos, including their dimensionality and potential for violation.

Findings

CP violation can occur with two neutrino generations for Majorana neutrinos.

Lepton-induced CP-violating couplings are generally suppressed compared to quark-induced ones.

Majorana neutrinos induce unique CP-violating operators via lepton-number violating mechanisms.

Abstract

In the Standard Model minimally extended to include massive neutrinos, we compute the leading CP-violating zero temperature contributions to the one-loop effective action induced by integration of the leptons. Such contributions start at operators of dimension six and they are P even for Dirac neutrinos and P even or odd for Majorana neutrinos. Dimension four operators are allowed in the mixed Dirac-Majorana case. It is verified by explicit calculation that CP can be violated in two generation settings for Majorana neutrinos. Using different neutrino scenarios we give upper bounds for the couplings of the CP-violating operators. As a rule, we find that lepton-induced couplings are suppressed as compared to quark-induced couplings, whenever the latter are allowed, nevertheless, through virtual lepton-number violating mechanisms, Majorana neutrinos induce new CP-violating operators not present in the quark or Dirac-neutrino cases.