Charged Lepton Flavour Violating Decays: Leading Logarithmic Approximation versus Full RGE Results

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 $\mu \rightarrow e + \gamma$, $\tau \rightarrow \mu + \gamma$, $\etc$., 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 $\mathbf{Y_{\nu}}$ which can be expressed in terms of the light and heavy right-handed (RH) neutrino masses, neutrino mixing matrix $\pmns$, and an orthogonal matrix $\mathbf{R}$. We investigate the effects of Majorana CP-violation phases in $\pmns$, 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 $\mu \rightarrow e + \gamma$, $\tau \rightarrow \mu + \gamma$ and $\tau \rightarrow e + \gamma$. The case of quasi-degenerate heavy RH Majorana neutrinos is considered. Results for neutrino mass spectrum with normal hierarchy, values of the lightest $\nu$-mass in the range $0 \leq m_1 \leq 0.30$ eV, and in the cases of $\mathbf{R} = \mathbf{1}$ and complex matrix $\mathbf{R} \neq \mathbf{1}$ 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 $\mu \to e + \gamma$ and $\tau \to e + \gamma$. The impact of these effects on the $\tau \to \mu + \gamma$ decay rate is typically smaller and only possible for $m_1 \gtap 0.10$ 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 $\mu \to e + \gamma$ and $\tau \to e + \gamma$ ($\tau \to \mu + \gamma$) decays is entirely determined in the case of $\mathbf{R} \cong \mathbf{1}$ by the values of the neutrino mixing parameters at $M_Z$.