We consider a version of the low-scale type I seesaw mechanism for generating small neutrino masses, as an alternative to the standard seesaw scenario. It involves two right-handed (RH) neutrinos $ u_{1R}$ and $ u_{2R}$ having a Majorana mass term wi
th mass $M$, which conserves the lepton charge $L$. The RH neutrino $ u_{2R}$ has lepton-charge conserving Yukawa couplings $g_{ell 2}$ to the lepton and Higgs doublet fields, while small lepton-charge breaking effects are assumed to induce tiny lepton-charge violating Yukawa couplings $g_{ell 1}$ for $ u_{1R}$, $l=e,mu,tau$. In this approach the smallness of neutrino masses is related to the smallness of the Yukawa coupling of $ u_{1R}$ and not to the large value of $M$: the RH neutrinos can have masses in the few GeV to a few TeV range. The Yukawa couplings $|g_{ell 2}|$ can be much larger than $|g_{ell 1}|$, of the order $|g_{ell 2}| sim 10^{-4} - 10^{-2}$, leading to interesting low-energy phenomenology. We consider a specific realisation of this scenario within the Froggatt-Nielsen approach to fermion masses. In this model the Dirac CP violation phase $delta$ is predicted to have approximately one of the values $delta simeq pi/4,, 3pi/4$, or $5pi/4,, 7pi/4$, or to lie in a narrow interval around one of these values. The low-energy phenomenology of the considered low-scale seesaw scenario of neutrino mass generation is also briefly discussed.
Effects of the lightest neutrino mass in flavoured leptogenesis when the CP-violation necessary for the generation of the baryon asymmetry of the Universe is due exclusively to the Dirac and/or Majorana phases in the neutrino mixing matrix $U$ are di
scussed. The type I see-saw scenario with three heavy right-handed Majorana neutrinos having hierarchical spectrum is considered. The orthogonal parametrisation of the matrix of neutrino Yukawa couplings, which involves a complex orthogonal matrix $R$, is employed. Results for light neutrino mass spectrum with normal and inverted ordering (hierarchy) are reviewed.
The effects of the lightest neutrino mass in ``flavoured leptogenesis are investigated in the case when the CP-violation necessary for the generation of the baryon asymmetry of the Universe is due exclusively to the Dirac and/or Majorana phases in th
e neutrino mixing matrix U. The type I see-saw scenario with three heavy right-handed Majorana neutrinos having hierarchical spectrum is considered. The ``orthogonal parametrisation of the matrix of neutrino Yukawa couplings, which involves a complex orthogonal matrix R, is employed. Results for light neutrino mass spectrum with normal and inverted ordering (hierarchy) are obtained. It is shown, in particular, that if the matrix R is real and CP-conserving and the lightest neutrino mass m_3 in the case of inverted hierarchical spectrum lies the interval 5 times 10^{-4} eV < m_3 < 7 times 10^{-3} eV, the predicted baryon asymmetry can be larger by a factor of sim 100 than the asymmetry corresponding to negligible m_3 cong 0. As consequence, we can have successful thermal leptogenesis for 5 times 10^{-6} eV < m_3 < 5 times 10^{-2} eV even if R is real and the only source of CP-violation in leptogenesis is the Majorana and/or Dirac phase(s) in U.
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 univer
sal 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.
We analyse the dependence of the rates of the LFV charged lepton decays mu to e + gamma, tau to e + gamma, tau to mu + gamma (l_i to l_j + gamma) and their ratios, predicted in the class of SUSY theories with see-saw mechanism of nu-mass generation a
nd 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 nu-mass spectrum and negligible lightest neutrino mass, all three l_i to l_j + gamma decay branching ratios, BR(l_i to l_j + gamma), depend on one Majorana phase, one leptogenesis CPV parameter and on the 3-neutrino oscillation parameters; if the CHOOZ mixing angle theta_13 is sufficiently large, they depend on the Dirac CPV phase in the PMNS matrix. The ``double ratios R(21/31) sim BR(mu to e + gamma)/BR(tau to e + gamma) and R(21/32) sim BR(mu to e + gamma)/BR(tau to mu + 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, <m>.
The LFV charged lepton decays mu to e + gamma, tau to e + gamma and tau to mu + gamma and thermal leptogenesis are analysed in the MSSM with see-saw mechanism of neutrino mass generation and soft SUSY breaking with universal boundary conditions. The
case of hierarchical heavy Majorana neutrino mass spectrum, M_1 << M_2 << M_3, is investigated. Leptogenesis requires M_1 > 10^9 GeV. Considering the natural range of values of the heaviest right-handed Majorana neutrino mass, M_3 > 5*10^{13} GeV, and assuming that the soft SUSY breaking universal gaugino and/or scalar masses have values in the range of few 100 GeV, we derive the combined constraints, which the existing stringent upper limit on the mu to e + gamma decay rate and the requirement of successful thermal leptogenesis impose on the neutrino Yukawa couplings, heavy Majorana neutrino masses and SUSY parameters. Results for the three possible types of light neutrino mass spectrum -- normal and inverted hierarchical and quasi-degenerate -- are obtained.
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 muto e + gamma, tauto 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 bf{Y_{ u}} which can be expressed in terms of the light and heavy right-handed (RH) neutrino masses, neutrino mixing matrix U_{PMNS}, and an orthogonal matrix bf{R}. We investigate the effects of Majorana CP-violation phases in U_{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 muto e + gamma, tau to mu + gamma and tauto e + gamma. Results for neutrino mass spectrum with normal hierarchy, values of the lightest u-mass in the range 0 leq m_1 leq 0.30 eV, and quasi-degenerate heavy RH Majorana neutrinos in the cases of bf{R} = bf{1} and complex matrix bf{R} 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 > 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 bf{R} cong bf{1} by the values of the neutrino mixing parameters at M_Z.
Assuming 3 neutrino mixing and massive Majorana neutrinos, we analyze the implications of the results of the solar neutrino experiments, including the latest SNO data, which favor the LMA MSW solution of the solar neutrino problem with tan^2 theta_so
l < 1, for the predictions of the effective Majorana mass |<m>| in neutrinoless double beta decay. For cos (2 theta_sol) geq 0.26, which follows from the analysis of the new solar neutrino data, we find significant lower limits on |<m>| in the cases of quasi-degenerate and inverted hierarchy neutrino mass spectrum, |<m>| geq 0.035 eV and |<m>| geq 8.5 10^-3 eV, respectively. If the spectrum is hierarchical the upper limit holds |<m>| leq 8.2 10^-3 eV. Correspondingly, not only a measured value of |<m>| eq 0, but even an experimental upper limit on |<m>| of the order of few 10^-2 eV can provide information on the type of the neutrino mass spectrum; it can provide also a significant upper limit on the mass of the lightest neutrino m1. A measured value of |<m>| geq 0.2 eV, combined with data on neutrino masses from the tritium beta-decay experiment KATRIN might allow to establish whether the CP-symmetry is violated in the lepton sector.
If the present or upcoming searches for neutrinoless double beta decay give a positive result, the Majorana nature of massive neutrinos will be established. From the determination of the value of the effective Majorana mass parameter |<m>|, it woul
d be possible to obtain information on the type of neutrino mass spectrum. Assuming 3-neutrino mixing and massive Majorana neutrinos, we discuss the information a measurement of, or an upper bound on, |<m>| can provide on the value of the lightest neutrino mass m1. With additional data on the neutrino masses obtained in tritium beta decay experiments, it might be possible to establish whether the CP-symmetry is violated in the lepton sector. This would require very high precision measurements. If CP-invariance holds, the allowed patterns of the relative CP-parities of the massive Majorana neutrinos would be determined.
The effective Majorana mass which determines the rate of the neutrinoless double beta decay, |<m>|, is considered in the case of three-neutrino mixing and massive Majorana neutrinos. Assuming a rather precise determination of the parameters character
izing the neutrino oscillation solutions of the solar and atmospheric neutrino problems has been made, we discuss the information a measurement of |<m>| > (0.005 - 0.010) eV can provide on the value of the lightest neutrino mass and on the CP-violation in the lepton sector. The implications of combining a measurement of |<m>| with future measurement of the neutrino mass in tritium beta-decay experiments for the possible determination of leptonic CP-violation are emphasized.
