Leptogenesis and the Violation of Lepton Number and CP at Low Energies

Abstract

In the context of the minimal supersymmetric seesaw model, we study the implications of the current neutrino data for thermal leptogenesis, $\beta {\beta }_{0\nu }$ decay, and leptonic flavour- and CP-violating low-energy observables. We express the heavy singlet-neutrino Dirac Yukawa couplings $(Y_{\nu }{)}_{ij}$ and Majorana masses $M_{N_i}$ in terms of the light-neutrino observables and an auxiliary hermitian matrix $H$, which enables us to scan systematically over the allowed parameter space. If the lightest heavy neutrino $N_1$ decays induce the baryon asymmetry, there are correlations between the $M_{N_1}$, the lightest active neutrino mass and the primordial lepton asymmetry ${ϵ}_1$ on the one hand, and the $\beta {\beta }_{0\nu }$ decay parameter $m_{ee}$ on the other hand. {\it However, leptogenesis is insensitive to the neutrino oscillation phase}. We find lower bounds $M_{N_1}\text{gsim}10^{10}$ GeV for the normal light-neutrino mass hierarchy, and $M_{N_1}\text{gsim}10^{11}$ GeV for the inverted mass hierarchy, respectively, indicating a potentially serious conflict with the gravitino problem. Depending on $M_{N_1}$, we find upper (upper and lower bounds) on the lightest active neutrino mass for the normal (inverted) mass hierarchy, and a lower bound on $m_{ee}$ even for the normal mass ordering. The low-energy lepton-flavour- and CP-violating observables induced by renormalization are almost independent of leptogenesis. The electron electric dipole moment may be close to the present bound, reaching $d_e\sim 10^{-(27-28)}$ e cm in our numerical examples, while $d_{\mu }$ may reach $d_{\mu }\sim 10^{-25}$ e cm.

Comments: 23 pages, 12 postscript figures