Majorana CP-violating phases, RG running of neutrino mixing parameters and charged lepton flavour violating decays

Abstract

We consider the MSSM with see-saw mechanism of neutrino mass generation and soft SUSY breaking with flavour-universal boundary conditions at the GUT scale, in which the lepton flavour violating (LFV) decays μ → e + γ , τ → μ + γ , etc., are predicted with rates that can be within the reach of present and planned experiments. These predictions depend critically on the matrix of neutrino Yukawa couplings Y ν which can be expressed in terms of the light and heavy right-handed (RH) neutrino masses, neutrino mixing matrix U PMNS , and an orthogonal matrix R. We investigate the effects of Majorana CP-violation phases in U PMNS , and of the RG running of light neutrino masses and mixing angles from M Z to the RH Majorana neutrino mass scale M R , on the predictions for the rates of LFV decays μ → e + γ , τ → μ + γ and τ → e + γ . The case of quasi-degenerate heavy RH Majorana neutrinos is considered. Results for neutrino mass spectrum with normal hierarchy, values of the lightest ν-mass in the range 0 ⩽ m 1 ⩽ 0.30 eV , and in the cases of R = 1 and complex matrix R ≠ 1 are presented. We find that the effects of the Majorana CP-violation phases and of the RG evolution of neutrino mixing parameters can change by few orders of magnitude the predicted rates of the LFV decays μ → e + γ and τ → e + γ . The impact of these effects on the τ → μ + γ decay rate is typically smaller and only possible for m 1 ≳ 0.10 eV . If the RG running effects are negligible, in a large region of soft SUSY breaking parameter space the ratio of the branching ratios of the μ → e + γ and τ → e + γ ( τ → μ + γ ) decays is entirely determined in the case of R ≅ 1 by the values of the neutrino mixing parameters at M Z .