Charged lepton decays l(i) ---> l(j) + gamma, leptogenesis CP-violating parameters and Majorana phases

We analyze the dependence of the rates of the LFV charged-lepton decays $\ensuremath{\mu}\ensuremath{\rightarrow}e+\ensuremath{\gamma}$, $\ensuremath{\tau}\ensuremath{\rightarrow}e+\ensuremath{\gamma}$, $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}+\ensuremath{\gamma}$ (${l}_{i}\ensuremath{\rightarrow}{l}_{j}+\ensuremath{\gamma}$) and their ratios, predicted in the class of SUSY theories with see-saw mechanism of $\ensuremath{\nu}$-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 ($CP\mathrm{V}$) parameters. The case of quasidegenerate in mass heavy Majorana neutrinos is considered. The analysis is performed for normal hierarchical (NH), inverted hierarchical (IH) and quasidegenerate (QD) light neutrino mass spectra. We show, in particular, that for NH and IH $\ensuremath{\nu}$-mass spectrum and negligible lightest neutrino mass, all three ${l}_{i}\ensuremath{\rightarrow}{l}_{j}+\ensuremath{\gamma}$ decay branching ratios, $BR({l}_{i}\ensuremath{\rightarrow}{l}_{j}+\ensuremath{\gamma})$, depend on one Majorana phase, one leptogenesis $CP\mathrm{V}$ parameter and on the 3-neutrino oscillation parameters; if the CHOOZ mixing angle ${\ensuremath{\theta}}_{13}$ is sufficiently large, they depend on the Dirac $CP\mathrm{V}$ phase in the PMNS matrix. The ``double ratios'' $\mathrm{R}(21/31)\ensuremath{\sim}BR(\ensuremath{\mu}\ensuremath{\rightarrow}e+\ensuremath{\gamma})/BR(\ensuremath{\tau}\ensuremath{\rightarrow}e+\ensuremath{\gamma})$ and $\mathrm{R}(21/32)\ensuremath{\sim}BR(\ensuremath{\mu}\ensuremath{\rightarrow}e+\ensuremath{\gamma})/BR(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}+\ensuremath{\gamma})$ 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, $⟨\mathrm{m}⟩$.