Leptonic CP violating effective action for Dirac and Majorana neutrinos

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.

Renormalization of vector fields with mass-like coupling in curved spacetime

“…The method was introduced in [14] for flat spacetime and extended to curved spacetime in [15], and also to finite temperature in [16]. It has been applied to fermions [17][18][19][20] and to obtain a strict derivative expansion of the heat kernel in curved spacetime [21]. The method covariant of symbols is related to the method of symbols (of pseudodifferential operators) as described in [22] and [23], where the shift ∇ µ → ∇ µ + p µ is applied and p µ represents the momentum of the particle running in the quantum loop.…”