Superheavy threshold corrections to the matching condition between matter Yukawa couplings of the effective Minimal Supersymmetric Standard Model (MSSM) and the New Minimal Supersymmetric (SO(10)) GUT(NMSGUT) provide a novel and generic mechanism for reducing the long standing and generically problematic operator dimension 5 Baryon decay rates. In suitable regions of the parameter space strong wave function renormalization of the effective MSSM Higgs doublets due to the large number of heavy fields can take the wave function renormalization of the MSSM Higgs field close to the dissolution value (Z H,H = 0). Rescaling to canonical kinetic terms lowers the SO(10) Yukawas required to match the MSSM fermion data. Since the same Yukawas determine the dimension 5 B violation operator coefficients, the associated rates can be suppressed to levels compatible with current limits. Including these threshold effects also relaxes the constraint y b −y τ ≃ y s −y µ operative between 10−120 plet generated tree level MSSM matter fermion Yukawas y f . We exhibit accurate fits of the MSSM fermion mass-mixing data in terms of NMSGUT superpotential couplings and 5 independent soft Susy breaking parameters specified at 10 16.25 GeV with the claimed suppression of Baryon decay rates. As before, our s-spectra are of the mini split supersymmetry type with large |A 0 |, µ, m H,H > 100 TeV, light gauginos and normal s-hierarchy. Large A 0 , µ and soft masses allow significant deviation from the canonical GUT gaugino mass ratios and ensure vacuum safety. Even without optimization, prominent candidates for BSM discovery such as the muon magnetic anomaly, b → sγ and Lepto-genesis CP violation emerge in the preferred ball park. 1 aulakh@pu.ac.in ; http://physics.puchd.ac.in/aulakh/

We consider singlet extensions of the standard model, both in the fermion and the scalar sector, to account for the generation of neutrino mass at the TeV scale and the existence of dark matter respectively.For the neutrino sector we consider models with extra singlet fermions which can generate neutrino mass via the so called inverse or linear seesaw mechanism whereas a singlet scalar is introduced as the candidate for dark matter. We show that although these two sectors are disconnected at low energy, the coupling constants of both the sectors get correlated at high energy scale by the constraints coming from the perturbativity and stability/metastability of the electroweak vacuum. The singlet fermions try to destabilize the electroweak vacuum while the singlet scalar aids the stability. As an upshot, the electroweak vacuum may attain absolute stability even upto the Planck scale for suitable values of the parameters. We delineate the parameter space for the singlet fermion and the scalar couplings for which the electroweak vacuum remains stable/metastable and at the same time giving the correct relic density and neutrino masses and mixing angles as observed.

Supersymmetric Unified theories which incorporate a renormalizable Type I seesaw mechanism for small neutrino masses can also provide slow roll inflection point inflation along a flat direction associated with a gauge invariant combination of the Higgs, slepton and right handed sneutrino superfields. Inflationary parameters are related to the Majorana and Dirac couplings responsible for neutrino masses with the scale of inflation set by a righthanded neutrino mass M ν c ∼ 10 6 − 10 12 GeV. Tuning of the neutrino Dirac and Majorana superpotential couplings and soft Susy breaking parameters is required to enforce flatness of the inflationary potential. In contrast to previous inflection point inflation models the cubic term is dominantly derived from superpotential couplings rather than soft A-terms. Thus since M ν c >> M Susy the tuning condition is almost independent of the soft supersymmetry breaking parameters and therefore more stable. The required fine tuning is also less stringent than for Minimal SUSY Standard Model (MSSM) inflation or Dirac neutrino "A-term" inflation scenarios due to the much larger value of the inflaton mass. Reheating proceeds via 'instant preheating' which rapidly dumps all the inflaton energy into a MSSM mode radiation bath giving a high reheat temperature T rh ≈ M 3 4 ν c 10 6 GeV ∼ 10 11 − 10 15 GeV. Thus our scenario requires large gravitino mass > 50 TeV to avoid a gravitino problem. The 'instant preheating' and Higgs component of the inflaton also imply a 'non-thermal' contribution to Leptogenesis due to facilitated production of right handed neutrinos during inflaton decay. We derive the tuning conditions for the scenario to work in the realistic New Minimal Supersymmetric SO(10) GUT and show that they can be satisfied by realistic fits.

We show that a supersymmetric renormalizable theory based on gauge group SO(10) and Higgs system 10 ⊕ 210 ⊕ 126 ⊕ 126 with no scale supergravity can lead to a Starobinsky kind of potential for inflation. Successful inflation is possible in the cases where the potential during inflation corresponds to SU (3) C × SU (2) L × SU (2) R × U (1) B−L , SU (5) × U (1) and flipped SU (5) × U (1) intermediate symmetry with a suitable choice of superpotential parameters. The reheating in such a scenario can occur via non perturbative decay of inflaton i.e. through "preheating". After the end of reheating, when universe cools down, the finite temperature potential can have a minimum which corresponds to MSSM.