The right-handed neutrinos within the type-I seesaw mechanism can induce large radiative corrections to the Higgs mass, and naturalness arguments can then be used to set limits on their mass scale and Yukawa couplings. Driven by minimality, we consider the presence of two degenerate right-handed neutrinos. We compare the limits from naturalness with the ones from the stability of the electroweak vacuum and from lepton flavor violation. Implications from neutrinoless double beta decay are also discussed and renormalization effects for the light neutrino parameters are presented. Adding small perturbations to the degenerate heavy neutrino spectrum allows for successful leptogenesis.

We present a minimal renormalizable non-supersymmetric SO(10) grand unified model with a symmetry breaking sector consisting of Higgs fields in the 54 H + 126 H + 10 H representations. This model admits a single intermediate scale associated with Pati-Salam symmetry along with a discrete parity. Spontaneous symmetry breaking, the unification of gauge couplings and proton lifetime estimates are studied in detail in this framework. Including threshold corrections self-consistently, obtained from a full analysis of the Higgs potential, we show that the model is compatible with the current experimental bound on proton lifetime. The model generally predicts an upper bound of few times 10 35 yrs for proton lifetime, which is not too far from the present Super-Kamiokande limit of τ p 1.29 × 10 34 yrs. With the help of a Pecci-Quinn symmetry and the resulting axion, the model provides a suitable dark matter candidate while also solving the strong CP problem. The intermediate scale, M I ≈ (10 13 − 10 14 ) GeV which is also the B − L scale, is of the right order for the righthanded neutrino mass which enables a successful description of light neutrino masses and oscillations. The Yukawa sector of the model consists of only two matrices in family space and leads to a predictive scenario for quark and lepton masses and mixings. The branching ratios for proton decay are calculable with the leading modes being p → e + π 0 and p → νπ + .Even though the model predicts no new physics within the reach of LHC, the next generation proton decay detectors and axion search experiments have the capability to pass verdict on this minimal scenario. *

We consider the minimal seesaw model in which two gauge singlet right handed neutrinos with opposite lepton numbers are added to the Standard Model. In this model, the smallness of the neutrino mass is explained by the tiny lepton number violating coupling between one of the singlets with the standard left-handed neutrinos. This allows one to have the right handed neutrino mass at the TeV scale as well as appreciable mixing between the light and heavy states. This model is fully reconstructible in terms of the neutrino oscillation parameters apart from the overall coupling strengths. We show that the overall coupling strength yν for the Dirac type coupling between the left handed neutrino and one of the singlets can be restricted by consideration of the (meta)stability bounds on the electroweak vacuum. In this scenario the lepton flavor violating decays of charged leptons can be appreciable which can put further constraint on yν, for right-handed neutrinos at TeV scale. We discuss the combined constraints on yν for this scenario from the process µ → eγ and from the consideration of vacuum (meta)stability constraints on the Higgs self coupling. We also briefly discuss the implications for neutrinoless double beta decay and possible signatures of the model that can be expected at colliders. The phase factor, e i π 2 , is inserted to ensure the positive definiteness of the mass eigen values.

We consider the problem of a degenerate electron gas in the background of a uniformly distributed positive charge, ensuring overall neutrality of the system, in the presence of non-commutativity. In contrast to previous calculations [3] that did not include twisted statistics, we find corrections to the ground state energy already at first order in perturbation theory when the twisted statistics is taken into account. These corrections arise since the interaction energy is sensitive to two particle correlations, which are modified for twisted anti-commutation relations.