The lepton flavour violating charged lepton decays mu to e + gamma and thermal leptogenesis are analysed in the minimal supersymmetric standard model with see-saw mechanism of neutrino mass generation and soft supersymmetry breaking terms with universal boundary conditions. Hierarchical spectrum of heavy Majorana neutrino masses, M_1 << M_2 << M_3, is considered. In this scenario, the requirement of successful thermal leptogenesis implies a lower bound on M_1. For the natural GUT values of the heaviest right-handed Majorana neutrino mass, M_3 > 5 times 10^{13} GeV, and supersymmetry particle masses in the few times 100 GeV range, the predicted mu to e + gamma decay rate exceeds by few order of magnitude the experimental upper limit. This problem is avoided if the matrix of neutrino Yukawa couplings has a specific structure. The latter leads to a correlation between the baryon asymmetry of the Universe predicted by leptogenesis, BR(mu to e + gamma) and the effective Majorana mass in neutrinoless double beta decay.
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