A non-supersymmetric renormalizable SO(10) model is investigated for its viability in explaining the observed fermion masses and mixing parameters along with the baryon asymmetry produced via thermal leptogenesis. The Yukawa sector of the model consists of complex 10H and $$ {\overline{126}}_H $$ 126 ¯ H scalars with a Peccei-Quinn like symmetry and it leads to strong correlations among the Yukawa couplings of all the standard model fermions including the couplings and masses of the right-handed (RH) neutrinos. The latter implies the necessity to include the second lightest RH neutrino and flavor effects for the precision computation of leptogenesis. We use the most general density matrix equations to calculate the temperature evolution of flavoured leptonic asymmetry. A simplified analytical solution of these equations, applicable to the RH neutrino spectrum predicted in the model, is also obtained which allows one to fit the observed baryon to photon ratio along with the other fermion mass observables in a numerically efficient way. The analytical and numerical solutions are found to be in agreement within a factor of $$ \mathcal{O}(1) $$ O 1 . We find that the successful leptogenesis in this model does not prefer any particular value for leptonic Dirac and Majorana CP phases and the entire range of values of these observables is found to be consistent. The model specifically predicts (a) the lightest neutrino mass $$ {m}_{v_1} $$ m v 1 between 2–8 meV, (b) the effective mass of neutrinoless double beta decay mββ between 4–10 meV, and (c) a particular correlation between the Dirac and one of the Majorana CP phases.

We analyse the implications of right-handed neutrinos on the stability of the electroweak vacuum in two-Higgs-doublet models with supersymmetry at high scale. It is assumed that supersymmetry is broken at scale M S = 2 × 10 16 GeV and effective theory below M S is two-Higgs-doublet model of type II with three generations of singlet neutrinos which induce small masses for the standard model neutrinos through type I seesaw mechanism. We study the high and low scale versions of seesaw mechanism. In both these cases, we show that the presence of right-handed neutrinos significantly improves the stability of electroweak vacuum if their Yukawa couplings with the SM leptons are of O(1) or greater. However, this possibility is severely constrained by the measured mass and couplings of Higgs and limits on the mass of the charged Higgs from the flavour physics data. It is shown that the stable or metastable electroweak vacuum and experimentally viable low energy scalar spectrum require tan β < ∼ 2.5 and the magnitude of neutrino Yukawa couplings smaller than O(1). The results obtained in this case are qualitatively similar to those without right-handed neutrinos.

We compute the one loop corrections to the CP-even Higgs mass matrix in the supersymmetric inverse seesaw model to single out the different cases where the radiative corrections from the neutrino sector could become important. It is found that there could be a significant enhancement in the Higgs mass even for Dirac neutrino masses of O(30) GeV if the left-handed sneutrino soft mass is comparable or larger than the right-handed neutrino mass. In the case where right-handed neutrino masses are significantly larger than the supersymmetry breaking scale, the corrections can utmost account to an upward shift of 3 GeV. For very heavy multi TeV sneutrinos, the corrections replicate the stop corrections at 1-loop. We further show that general gauge mediation with inverse seesaw model naturally accommodates a 125 GeV Higgs with TeV scale stops.

Even if the concerns related to the naturalness of the electroweak scale are repressed, the Higgs mass and stability of the electroweak vacuum do not allow arbitrarily large supersymmetry breaking scale, M S , in the minimal models with split or high-scale supersymmetry. We show that M S can be raised to the GUT scale if the theory below M S contains a Higgs doublet, a pair of TeV scale Higgsino and widely separated gauginos in addition to the Standard Model particles. The presence of wino and gluino below O(100) TeV leads to precision unification of the gauge couplings consistent with the current limits on the proton lifetime. Wino, at this scale, renders the Higgsino as pseudo-Dirac dark matter which in turn evades the existing constraints from the direct detection experiments. Bino mass scale is required to be 10 10 GeV to get the observed Higgs mass respecting the current limit on the charged Higgs mass. The framework predicts, 1 tan β 2.2 and τ [p → e + π 0 ] < 7 × 10 35 years, almost independent of values of the other parameters. The electroweak vacuum is found to be stable or metastable. The underlying framework provides an example of a viable sub-GUT scale theory of supersymmetric grand unified theory in which supersymmetry and unified gauge symmetry are broken at a common scale.

Gravity mediated supersymmetry breaking becomes comparable to gauge mediated supersymmetry breaking contributions when messenger masses are close to the GUT scale. By suitably arranging the gravity contributions one can modify the soft supersymmetry breaking sector to generate a large stop mixing parameter and a light Higgs mass of 125 GeV. In this kind of hybrid models, however the nice features of gauge mediation like flavour conservation etc., are lost. To preserve the nice features, gravitational contributions should become important for lighter messenger masses and should be important only for certain fields. This is possible when the hidden sector contains multiple (at least two) spurions with hierarchical vacuum expectation values. In this case, the gravitational contributions can be organised to be 'just right'.We present a complete model with two spurion hidden sector where the gravitational contribution is from a warped flavour model in a Randall-Sundrum setting. Along the way, we present simple expressions to handle renormalisation group equations when supersymmetry is broken by two different sectors at two different scales.