(How) to grow an oasis in the desert (?)
It is well-known that in physics beyond the Standard Model (SM) very often one has to think about the violation of two SM symmetries, Baryon (B) and Lepton (L) numbers, and postulate the existence of a large desert between the low and high scales. It was pointed out by S. Weinberg  long time ago that one can write down operators such as, O5=cνLLHH/Λ, and O6=cBLQQQL/Λ², where the ﬁrst one breaks total lepton number and the second operator violates both symmetries. Typically, one can compute the coefficient in front of these operators in a grand uniﬁed theory deﬁned at the high scale. The scale Λ in O6 has to be very large, i.e. Λ>1014−16GeV, in order to satisfy the bounds on the proton decay lifetime.
Pavel Fileviez Perez (Submitted on 23 Sep 2012)
Interactions which violate baryon number (B) are not present in the renormalizable part of the SM Lagrangian, but can arise through effective higher dimensional operators... [which] arise naturally when SM is embedded in grand uniﬁed theories (GUTs) such as SU(5) and SO(10). They lead to nucleon decay modes such as p→e+π0 and p→νK+, which conserve baryon number minus lepton number (B − L) symmetry. Experimental searches to date have primarily focused on these modes with the latest limits on proton lifetime constraining the masses of the heavy mediators to be larger than about 1015GeV. This is in accord with the scale inferred from the uniﬁcation of gauge couplings. Going beyond the d = 6 baryon number violating operators, the next–to–leading ones have d = 7, and obey the selection rule ∆(B − L) = −2 for nucleon decay . These operators lead to novel nucleon decay modes such as n→e−K+,e−π+, and p→νπ+, which have received less attention. In this Letter we show that these d = 7 operators arise naturally in uniﬁed theories based on SO(10), upon the spontaneous breaking of (B−L), which is part of the gauge symmetry. In particular, we ﬁnd that in non–supersymmetric SO(10) models with an intermediate scale so that gauge couplings unify, the partial lifetime to these decay modes can be within reach of ongoing and proposed experiments. Furthermore, we show that these new modes provides a novel way to understand the origin of matter in the universe. This mechanism relies on the fact that, owing to their (B − L) breaking nature, a GUT scale induced baryon asymmetry would not be affected by the electroweak sphalerons  and would survive down to low temperatures. Observed baryon number of the universe then carries the direct imprint of GUT scale physics. This is unlike the (B −L)–preserving baryon asymmetry induced in the decays of GUT mass particles such as in SU(5), which is however washed out by the sphaleron interactions, leaving no trace of GUT physics. We show that in minimal SO(10) models  which have been highly successful in predicting large neutrino oscillation angles, including a relatively large value of sin²(2θ13)≃(0.085−0.095), consistent with recent results , the baryon asymmetry of the right magnitude is generated by the new (B−L)–violating mechanism. The results of this paper should provide motivations to search for (B−L)–violating semi-leptonic decay modes of the nucleon in the ongoing and the next round of searches. Their observation would furnish evidence against the simple one–step breaking of GUT symmetry, and could also resolve the mystery behind the origin of matter in the universe.
A detail study of the literatures... gives an idea about many intriguing features of the SO(10) grand unified theory (including both non-SUSY and SUSY). One of these features is that when left-right gauge symmetry appears as an intermediate symmetry breaking step in a novel symmetry breaking chain, then seesaw mechanism can be naturally incorporated into it. In conventional seesaw models associated with thermal leptogenesis the mass scale for heavy Right Handed Majorana neutrino is at 1010GeV which makes it unsuitable for direct detectability at current accelerator experiments like LHC. Therefore, it is necessary to construct a theory having SU(2)L×SU(2)R×U(1)B-L×SU(3)C and SU(2)L×SU(2)R×SU(4)C gauge groups as intermediate symmetry breaking steps which results in low mass right-handed Majorana neutrinos along with WR, Z′ gauge bosons at TeV scale. At the same time it should be capable of explaining post-sphaleron baryogenesis elegantly along with other derivable predictions like proton decay and neutron-antineutron oscillation.
We intend to discuss TeV scale post-sphaleron baryogenesis, neutron-antineutron oscillation having mixing time close to the experimental limit with the Pati-Salam symmetry or SO(10) GUT as mentioned in a recent work  slightly modifying the Higgs content where non-zero light neutrino masses can be accommodated via gauged extended inverse seesaw mechanism along with TeV scale WR, Z′ gauge bosons. The Dirac neutrino mass and hence, the corresponding Yukawa coupling (≃ 10-1-10-2) found in this work can be much larger than the Yukawa coupling values (10-6) in the conventional type-I seesaw mechanism with TeV scale RH Majorana neutrinos.
Post-Sphaleron baryogenesis and n−n¯oscillation in non-SUSY SO(10) GUT with gauge coupling unification and proton decay
Recent developments in particle physics have had profound impact on cosmology. One of the most far–reaching consequences has been the possibility that new interactions beyond the standard model can explain the origin of matter–antimatter asymmetry of the universe as a dynamical phenomenon. There are currently several attractive scenarios which achieve this, the two most widely discussed ones being (i) baryogenesis via leptogenesis , which is connected to the seesaw mechanism and neutrino masses, and (ii) weak scale baryogenesis , which involves supersymmetric or multi–Higgs extensions of the standard model. Both these proposals depend crucially on the properties of the electroweak sphaleron  which serves as the source of B violation. Since the nature of new physics beyond the standard model remains unknown presently, it is important to explore alternative mechanisms that can explain the matter–antimatter asymmetry while yielding testable consequences. In this letter we suggest and explore one such alternative.
The salient feature of our proposal is that baryogenesis occurs via the direct decay of a scalar boson Sr having a weak scale mass and a high dimensional baryon violating coupling. Sr is the real part of a baryon number carrying complex scalar S, which acquires a vacuum expectation value (vev). The decays Sr → 6q... will then be allowed, providing the source for B asymmetry. These decays occur when the temperature of the universe is T ∼ 0.1 − 100 GeV. By this time the electroweak sphalerons have gone out of thermal equilibrium, and thus play no role in the B asymmetry generation. We call this mechanism “post–sphaleron baryogenesis”. The three Sakharov conditions for successful baryogenesis  are satisﬁed rather easily in our scheme. The high dimensionality of the B violating coupling of Sr to the quark ﬁelds allows the ∆B 6= 0 decays to go out of equilibrium at weak scale temperatures. CP violation occurs in the decay via loop diagrams involving the exchange of the standard model W± gauge bosons. This amplitude has sufficient light quark mass suppression to explain naturally the observed (small) value of the baryon to photon ratio ηB ∼ 10−10. The simplest realization of our mechanism involves interactions that violate B by two units and therefore gives rise to neutron–antineutron oscillations. We ﬁnd that the successful implementation of our mechanism sets an upper limit on the transition time for N ↔ N¯ oscillation bringing it to within the realm of observability. This connection provides a strong motivation for improved searches for N ↔ N¯ oscillation 
Post-Sphaleron Baryogenesis K.S. Babu, R.N. Mohapatra, S. Nasri (last revised 27 Jun 2006 (this version, v2))