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A new approach to SO(10) grand unification was recently proposed by three of the authors (D.C., R.N.M., and M.K.P.), where the mass scale M p at which the D-parity symmetry present in the SO(10) group breaks was decoupled from the scale M W R of the right-handed currents. In contrast with the conventional treatment of the SO(10) model, SU(2), XSU(2)R X G [ G is SU(4lc or SU(3)c XU( 1 ) B -L ] can appear as an intermediate symmetry with g L # g~. Calculations in the oneloop approximation lead to a substantially different picture of intermediate mass scales for SO(10)-symmetry breaking than before. In this paper, this analysis is extended to include two-loop contributions which are significant for several symmetry-breaking chains. All possible chains descending to the standard group SU(2IL XU( I I Y X SU( 3)c are exatnined. A unique chain emerges if one imposes a minimality condition (using the lowest-dimensional Higgs multiplet at each symmetrybreaking stage) and the phenomenological requirements of rp+e+rro22X yr, s i n 2 0 w (~w ) =0.22+0.02, and a,(Mw)=O. 10-0.12. This chain is SO (10)+SU(2)L X SU(2IR XSU(4)c X P * S U (~) L XSU(2)R X S U (~) C + S U (~) L XU(I)R XU(l)B-IXSU(3)c + S U (~) L X U ( l ) r XSU(3)c and allows for the following detectable consequences: (a) neutron oscillations with 5, -10~-10~ sec; (b) a branching ratio for KL +pB of 7 X ( lo-'-(c) a second neutral Z R boson in the tto-10-TeV range; (dl a proton lifetime .rp =6.5X 1 0 '~ 0i0.9(bs/160 M~v )~ yr (Ms denotes the modi-fied minimal subtraction scheme), which, given the theoretical uncertainties, may barely be within experimental reach; (el a Majorana mass for the electron neutrino in the range of electron volts. This experimentally interesting chain also predicts M~,~o '~.~~' .~ GeV, which satisfies all cosmological constraints. All other symmetry-breaking chains that satisfy the phenomenological requirements do not have experimentally testable consequences at low energies.

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We compute the threshold uncertainties due to unknown masses of the Higgs bosons on the predictions for the intermediate and unification scales, M I and M u , respectively, in SO(10) models. We focus on models with separate breaking scales for parity and SU(2), symmetries since they provide a natural realization of the seesaw mechanism for neutrino masses. For the two-step symmetry-breaking chains, where left-right-symmetric gauge groups appear at the intermediate scale, we find that parity invariance of the theory at the unification scale drastically reduces the grand-unification-theory (GUT) threshold effects in some cases. Including the effects of the intermediate-scale thresholds, we compute the uncertainty in the above mass scales and study their implications for proton lifetime and neutrino masses. An important outcome of our analysis is that if the Mikheyev-Smirnov-Wolfenstein (MSW) solution to the solar-neutrino puzzle is accepted at the 1u level, it rules out SU(2), X SU (2), XU( 1 ) , -, X SU( 3 1, as an intermediate symmetry for SO(10) breaking whereas the intermediate symmetry SU(2), X SU(2), XSU(4), is quite consistent with it. PACS numberk): 12.10.Dm, 11.1 5.Ex, 12.15.Ff I. INTRODUCTION Supersymmetric SU(5) theories have been studied with the goal of predicting the scale of supersymmetry breaking [5]. These models, however, do not have any room The grand unified theories [I] (GUTS) provide an elegant extension of physics beyond the standard model. The requirement that the gauge couplings constants in these theories become equal at the G U T scale ( M u ) lends them a predictive power which makes it possible to test them in experiments such as those looking for the decay of the proton. The most predictive such theory is the minimal SU(5) model of Georgi and Glashow [I], where the SU(5) symmetry breaks in one step to the standard model. The only new mass scale in this model is M , which can be determined by the unification requiremeit using the low-energy values of any two gauge couplings from the standard model. One then predicts not only M u , but also the remaining low-energy gauge coupling constant (for example, sin2Bw). It is well known that for the minimal SU(5) model they lead to predictions for the proton lifetime as well as sin2Bw, both of which are inconsistent with experiments.This, however, does not invalidate the idea of grand unification arid attention has rightly been focussed on SO(10) [2] G U T models which can accommodate more than one new mass scale. Supersymmetric SU (5) [3] models also belong to this class. In this class of two-massscale theories, the values of low-energy gauge coupling constants can determine both the mass scales again making these theories experimentally testable. The determination of the values of the new mass scales become more precise as the low-energy values of the gauge coupling constants become better known. It is therefore not surprising that the recent high precision measurement of n,,,,,, and sin2Bw at the CERN e + e -collider LEP [4] once again revived...

Starting with the hypothesis that quark and lepton mixings are identical at or near the GUT scale, we show that the large solar and atmospheric neutrino mixing angles together with the small reactor angle Ue3 can be understood purely as a result of renormalization group evolution provided the three neutrinos are quasi-degenerate and have same CP parity. It predicts the common Majorana mass for the neutrinos larger than 0.1 eV, which falls right in the range reported recently and also the range which will be probed in the planned experiments.

While the detection of W R -boson at the Large Hadron Collider is likely to resolve the mystery of parity violation in weak interaction, observation of neutrinoless double beta decay (0νββ) is expected to determine whether neutrinos are Majorana fermions. In this work we consider a class of LR models with TeV scale W R , Z R bosons but having parity restoration at high scales where they originate from well known Pati-Salam symmetry or SO(10) grand unified theory minimally extended to accommodate inverse seesaw frame work for neutrino masses. Most dominant new contribution to neutrinoless double beta decay is noted to occur via W − L W − L mediation involving lighter sterile neutrino exchanges. The next dominant contribution is found to be through W − L W − R mediation involving both light and heavy right-handed neutrino or sterile neutrino exchanges. The quark-lepton symmetric origin of the computed value of the Dirac neutrino mass matrix is also found to play a crucial role in determining these and other results on lepton flavor violating branching ratios for τ → e + γ, τ → µ + γ, and µ → e + γ accessible to ongoing search experiments. The underlying non-unitarity matrix is found to manifest in substantial CPviolating effects even when the leptonic Dirac phase δ CP ≃ 0, π, 2π. Finally we explore a possible origin of the model in non-supersymmetric SO(10) grand unified theory where, in addition to low mass W ± R and Z R bosons accessible to Large Hadron Collider, the model is found to predict observable neutron-antineutron oscillation and lepto-quark gauge boson mediated rare kaon decay with Br (K L → µē) ≃ 10 −9 − 10 −11 .

We present our best estimates of the uncertainties due to heavy particle threshold corrections on the unification scale M u , intermediate scale M I , and coupling constant au in the minimal nonsupersymmetric SO(10) models. Using recent data from the CERN e+e-collider LEP on sin2& and to obtain the two-loop-level predictions for Mu and a u , we update the predictions for the proton lifetime in minimal nonsupersymmetric SO(10) models.PACS number(s): 12.10. Dm, 13.30.Ce, 14.20.Dh