Charged Lepton Decays li → lj + γ, Leptogenesis CP-Violating Parameters and Majorana Phases

We analyse the dependence of the rates of the LFV charged lepton decays µ → e + γ, τ → e+γ, τ → µ+γ (l i → l j +γ) and their ratios, predicted in the class of SUSY theories with seesaw mechanism of ν-mass generation and soft SUSY breaking with universal boundary conditions at the GUT scale, on the Majorana CP-violation phases in the PMNS neutrino mixing matrix and the " leptogenesis " CP-violating (CPV) parameters. The case of quasi-degenerate in mass heavy Majorana neutrinos is considered. The analysis is performed for normal hierarchical (NH), inverted hierarchical (IH) and quasi-degenerate (QD) light neutrino mass spectra. We show, in particular, that for NH and IH ν-mass spectrum and negligible lightest neutrino mass, all three l i → l j + γ decay branching ratios, BR(l i → l j + γ), depend on one Majorana phase, one leptogenesis CPV parameter and on the 3-neutrino oscillation parameters; if the CHOOZ mixing angle θ 13 is sufficiently large, they depend on the Dirac CPV phase in the PMNS matrix. The " double ratios " R(21/31) ∼ BR(µ → e + γ)/BR(τ → e + γ) and R(21/32) ∼ BR(µ → e + γ)/BR(τ → µ + γ) are determined by these parameters. The same Majorana phase enters into the NH and IH expressions for the effective Majorana mass in neutrinoless double beta decay, < m >.