Standard coupling unification in SO(10), hybrid seesaw neutrino mass and leptogenesis, dark matter, and proton lifetime predictions

Journal of High Energy Physics, Apr 2017

We discuss gauge coupling unification of SU(3) C × SU(2) L × U(1) Y descending directly from non-supersymmetric SO(10) while providing solutions to the three out-standing problems of the standard model: neutrino masses, dark matter, and the baryon asymmetry of the universe. Conservation of matter parity as gauged discrete symmetry for the stability and identification of dark matter in the model calls for high-scale spontaneous symmetry breaking through 126 H Higgs representation. This naturally leads to the hybrid seesaw formula for neutrino masses mediated by heavy scalar triplet and right-handed neutrinos. Being quadratic in the Majorana coupling, the seesaw formula predicts two distinct patterns of right-handed neutrino masses, one hierarchical and another not so hierarchical (or compact), when fitted with the neutrino oscillation data. Predictions of the baryon asymmetry via leptogenesis are investigated through the decays of both the patterns of RHν masses. A complete flavor analysis has been carried out to compute CP-asymmetries including washouts and solutions to Boltzmann equations have been utilised to predict the baryon asymmetry. The additional contribution to vertex correction mediated by the heavy left-handed triplet scalar is noted to contribute as dominantly as other Feynman diagrams. We have found successful predictions of the baryon asymmetry for both the patterns of right-handed neutrino masses. The SU(2) L triplet fermionic dark matter at the TeV scale carrying even matter parity is naturally embedded into the non-standard fermionic representation 45 F of SO(10). In addition to the triplet scalar and the triplet fermion, the model needs a nonstandard color octet fermion of mass ∼ 5 × 107 GeV to achieve precision gauge coupling unification at the GUT mass scale M U 0 = 1015.56 GeV. Threshold corrections due to superheavy components of 126H and other representations are estimated and found to be substantial. It is noted that the proton life time predicted by the model is accessible to the ongoing and planned experiments over a wide range of parameter space.

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Standard coupling unification in SO(10), hybrid seesaw neutrino mass and leptogenesis, dark matter, and proton lifetime predictions

Received: August Standard coupling uni cation in SO(10), hybrid seesaw neutrino mass and leptogenesis, dark matter, M.K. Parida 0 1 2 4 5 Bidyut Prava Nayak 0 1 2 4 5 Rajesh Satpathy 0 1 2 4 5 Ram Lal Awasthi 0 1 2 3 5 0 Knowledge City , Sector 81, SAS Nagar, Manauli 140306 , India 1 Khandagiri Square , Bhubaneswar 751030 , India 2 Siksha `O' Anusandhan University 3 Indian Institute of Science Education and Research 4 Centre of Excellence in Theoretical and Mathematical Sciences 5 Open Access , c The Authors We discuss gauge coupling uni cation of SU(3)C the stability and identi cation of dark matter in the model calls for high-scale spontaneous symmetry breaking through 126H Higgs representation. This naturally leads to the hybrid seesaw formula for neutrino masses mediated by heavy scalar triplet and right-handed neutrinos. Being quadratic in the Majorana coupling, the seesaw formula predicts two distinct patterns of right-handed neutrino masses, one hierarchical and another not so hierarchical tted with the neutrino oscillation data. Predictions of the baryon asymmetry via leptogenesis are investigated through the decays of both the patterns of seesaw; neutrino; mass and leptogenesis; dark - U(1)Y descending directly from non-supersymmetric SO(10) while providing solutions to the three outstanding problems of the standard model: neutrino masses, dark matter, and the baryon asymmetry of the universe. Conservation of matter parity as gauged discrete symmetry for masses. A complete avor analysis has been carried out to compute CP-asymmetries including washouts and solutions to Boltzmann equations have been utilised to predict the baryon asymmetry. The additional contribution to vertex correction mediated by the heavy left-handed triplet scalar is noted to contribute as dominantly as other Feynman diagrams. We have found successful predictions of the baryon asymmetry for both the patterns of right-handed neutrino masses. The SU(2)L triplet fermionic dark matter at the TeV scale carrying even matter parity is naturally embedded into the non-standard fermionic representation 45F of SO(10). In addition to the triplet scalar and the triplet fermion, the model needs a nonstandard color octet fermion of mass Threshold corrections due to superheavy components of 126H and other representations are estimated and found to be substantial. It is noted that the proton life time predicted by the model is accessible to the ongoing and planned experiments over a wide range of ArXiv ePrint: 1608.03956 1 Introduction 3.1 3.2 3.3 2 Hybrid seesaw t to neutrino oscillation data 3 Baryon asymmetry of the Universe Boltzmann equations Baryon asymmetry in the compact scenario Baryon asymmetry in the hierarchical scenario 4 Fermionic triplet as dark matter candidate General considerations with matter parity Light non-standard fermion masses from SO(10) Triplet fermion dark matter phenomenology Prospects from indirect searches 5 Gauge coupling uni cation 5.1 Uni cation with lighter fermions and scalars 6 Threshold corrections and proton lifetime prediction 6.1 6.2 Threshold e ects on the GUT scale Proton lifetime prediction 7 Summary and conclusion A Renormalization group coe cients for uni cation of gauge couplings and threshold uncertainties A.1 Decomposition of representations and beta function coe cients Particle content and beta function coe cients A.2 Super-heavy particles and coe cients for threshold e ects A.3 A discussion on charged fermion mass parametrization The standard model (SM) of particle interactions based upon the gauge symmetry SU(3)C U(1)Y has been tested by numerous experiments. Also the last piece of evidence in favour of the SM has been vindicated with the discovery of the Higgs boson at the CERN Large Hadron Collider [1, 2]. Yet the model fails to explain the three glaring physical phenomena: neutrino oscillation [3{6], baryon asymmetry of the universe (BAU) [7{12], and dark matter (DM) [13{18]. Although the electroweak part of the SM provides excellent description of weak interaction phenomenology manifesting in V A structure of neutral and charged currents, it fails to answer why parity violation is exhibited by weak interaction alone. On the fundamental side, the SM itself can not explain the disparate values of its gauge couplings. The minimal gauge theory which has the potential to unify the three gauge couplings [19, 20] and explain the origin of parity violation is SO(10) grand uni ed theory (GUT) [21, 22] that contains the Pati-Salam [23, 24] and left-right gauge theories [25{27] as its subgroups. However, it is well known that direct breaking of all non-supersymmetric (non-SUSY) GUTs [20{22] to the SM gauge theory under the assumption of minimal ne tuning hypothesis [28, 29] fails to unify the gauge couplings of the SM whereas supersymmetric GUTs like SU(5) [20] and SO(10) [21, 22] achieve this objective in a profound manner. In fact the prediction of coupling uni cation in the minimal supersymmetric standard model (MSSM) [30, 31] evidenced through the CERN-LEP data [32{35] led to the belief that a SUSY GUT [36{45] with its underlying mechanism for solutions to the gauge hierarchy problem [46{50] could be the realistic model for high energy physics. SUSY GUTs also predict wino or neutralino as popular candidates of cold dark matter (CDM). Compared to SUSY SU(5) [30], SUSY SO(10) has a number of advantages. Whereas parity violation in SO(10) has its spontaneous breaking origin, for SU(5) it is explicit and intrinsic. The right-handed neutrino (RH ) as a member of spinorial representation 16 of SO(10) mediates the well known canonical seesaw mechanism [51{56] that accounts for small neutrino masses evidenced by the neutrino oscillation data. Further the Dirac neutrino mass matrix that occurs as an important ingredient of type-I seesaw [51{56] is predicted in this model due to its underlying quark-lepton symmetry [23, 24]. In addition, the presence of the left-handed (LH) triplet scalar, rally leads to the possibility of Type-II seesaw formula for neutrino masses [56{59]. Both the heavy RH neutrinos and the LH triplet scalar have the high potential to account for BAU via leptogenesis [60{62, 87]. With R-Parity as its gauged discrete symmetry [63{66], the model also guarantees stability of dark matter. Another attractive aspect of SUSY SO(10) [67] has been its capability to make a reasonably good representation of all fermion masses and mixings at the GUT scale [68, 69]. Such a data set exhibiting b Yukawa uni cation and very approximately satisfying Georgi-Jarlskog [70] type relation is obtained using RG extrapolated values of the masses and mixings at the electroweak scale following the bottom-up approach [71{73]. In particular 2 estimation has been carried out to examine goodness of t to all fermion masses in SUSY SO(10) [69]. Other interesting aspects of the SUSY GUT such as Yukawa uni cation and a heavier gluino [74], viability of GUT-scale tribimaximal mixing [75], and uni ed description of fermion masses with quasi-degenerate (QD) neutrinos [76] have been explored. A comparison of quality of di erent models has been also discussed [77]. Recently existence of avour symmetries [78] and emergence of ordered anarchy from 5:dim: theory [79, 80], and Sparticle spectroscopy [81] have been also investigated with numerical analyses on fermion masses. However, there exists a large class of SUSY SO(10) models where a qualitative or at most a semi-quantitative representation of fermion masses have been considered adequate without 2 estimation. Examples from a very small part while confronting other challenging problems through SUSY SO(10), explanation of neutrino data only has been considered adequate; some examples out of many such works in this direction include derivation of new seesaw mechanism with TeV scale Z0 [93], prediction of Axions [98], low-mass Z0 induced by avor symmetry [100], realization of SUSY SO(10) from M theory [99, 101], predictions of in aton mass [102], and Starobinsky type in ation [103], or quartic in ation [104] from SUSY SO(10). Generalised hidden avour symmetries have been explored without con ning to any particular type of fermion mass ts [105]. Despite many attractive qualities of SUSY GUTs including the resolution of the gauge hierarchy problem, no experimental evidence of supersymmetry has been found so far. This has led to search for gauge coupling uni cation of the standard gauge theory in non-supersymmetric (non-SUSY) GUTs while sacri cing the elegant solution to the gauge hierarchy problem in favour of ne-tuning to every loop order [106, 107]. above, single step breakings of all popular non-SUSY GUTs including SU(5) [20] and SO(10) [21, 22] under the constraint of the minimal ne-tuning hypothesis [28, 29] fail to unify gauge couplings. Introducing gravity induced corrections through higher dimensional operators [108, 109] or additional ne-tuning of parameters with lighter scalars or fermions, gauge coupling uni cation in non-SUSY SU(5) GUT has been implemented [110{119] including RH neutrino as DM [120]. Such uni cation has been also achieved including triplet fermionic DM [121]. A color octet fermion with mass > 108 GeV which is also needed for uni cation has been suggested as a source of non-thermal DM via non-renormalizable interactions [121]. As the model does not use matter parity [122{128], the stabilising discrete symmetry for DM has to be imposed externally and appended to the GUT framework. Further, issues like neutrino masses and mixings and the baryon asymmetry of the universe have not been addressed in this model. Naturally the non-SUSY SU(5) models [108{ 117, 120, 121] have no explanation for the monopoly of parity violation in weak interaction However, with or without broken D-Parity at the GUT scale [129{132], non-SUSY SO(10) has been shown to unify gauge couplings having one or more intermediate symmetries [129{135]. Extensive investigations in such models have been reported with high intermediate scales [69, 129{141] and also with TeV scale WR; ZR bosons and veri able seesaw mechanisms [142{153]. Out of a large number of possible models that are predicted from non-SUSY SO(10) [132] fermion mass t has been investigated only in one class of models with Pati-Salam intermediate symmetry [69, 137, 139, 140] and also including additional vector-like fermions [138]. The issue of DM has been also addressed with di erent types of high scale intermediate symmetries and by introducing additional fermions or scalars beyond those needed by extended survival hypothesis [154{158] but without addressing fermion mass ts. The problem of TeV scale WR boson prediction along with DM have been also addressed in non-SUSY SO(10) by invoking external Z2 symmetry [148] without tting charged fermion masses as also in a number of other models [132, 133, 135, 136, 141{147, 159{162]. As there has been no experimental evidence of supersymmetry so far, likewise there has been also no de nite evidence of any new gauge boson beyond those of the SM. This in turn has prompted authors to implement gauge coupling uni cation with the SM gauge symmetry below the GUT scale [110{123, 125{128] by the introduction of additional particle degrees of freedom with lighter masses. A natural question in this context is how much of the advantages of the SUSY GUT paradigm is maintained in the case of non-SUSY gauge coupling uni cation models. While SUSY SO(10) is well known for its intrinsic R-Parity [63, 65] as gauged discrete symmetry [64] for the stability of dark matter, as an encouraging factor in favour of the non-SUSY GUT it has been be the corresponding discrete symmetry intrinsic to non-SUSY SO(10) where B(L) stands for baryon (lepton) number. Whereas neutralino or wino are predicted as dark matter candidates in SUSY GUTs, in non-SUSY SO(10) the DM candidates could be non-standard fermions (scalars) carrying even (odd) matter parity. In fact all SO(10) representations have been identi ed to carry de nite values of matter parity which makes the identi cation of a dark matter candidate transparent from among the non-standard scalar(fermion) representations. Thus there is enough scope within non-SUSY SO(10) to implement the DM paradigm along with an intrinsic stabilising symmetry. Compared to SUSY GUTs, the non-SUSY GUTs do not have the problems associated with the Higgsino mediated proton decay [88, 163] while the canonical proton decay mode p ! e+ 0 has been accepted as the hall mark of predictions of non-SUSY GUTs since more than four decades. Further, the non-SUSY GUT also does not su er from the well known gravitino problem. [164{169]. Coupling uni cation in the single step breaking of non-SUSY SO(10) has been addressed in an interesting paper by Frigerio and Hambye (FH) [125] by exploiting the intrinsic matter parity of SO(10) leading to triplet fermion in 45F as dark matter candidate. The presence of a color octet fermion of mass 1010 GeV has been also noted for uni cation. The proton lifetime has been predicted in this model at two-loop level of gauge coupling uni cation. However details of tting the neutrino oscillation data including derivation of Dirac neutrino mass matrix and the RH mass spectrum have not been addressed. Likewise related details of derivation of the baryon asymmetry of the universe via leptogenesis has been left out from the purview of discussion. An added attractive aspect of the model is the discussion of various methods, both renormalizable and non-renormalizable, by which the triplet fermionic DM can have TeV scale mass. Although proton lifetime has been predicted from the two-loop determination of the GUT scale, important modi cation due to threshold e ects that could arise from the superheavy components of various representations [170{178] need further investigation. The contents of the present paper are substantially di erent from earlier works in many respects. We have discussed the matching with the neutrino oscillation data in detail where, instead of type-I seesaw, we have used hybrid seesaw which is a combination of both type-I and type-II [179{181]. Both of the seesaw mechanisms are naturally predicted in matter parity based SO(10) model having their origins rooted in the Higgs representation 126H and the latter's coupling to the fermions in the spinorial representation 16 through f 16:16:126yH . Unlike a number of neutrino mass models adopted earlier, in this work we have not assumed dominance of any one of the two seesaw mechanisms over the other. For the purpose of the present work we have determined the Dirac neutrino mass matrix at the GUT scale from the extrapolated values of charged fermion masses [71{73] and exploiting the exact quark lepton symmetry [23, 24] at that scale. With a view to investigating basis dependence of leptogenesis, the Dirac neutrino mass estimation has been carried out in two ways: by using the u-quark diagonal basis as well as the d-quark diagonal basis. Using these in the hybrid seesaw formula which is quadratic in the Majorana coupling f gives two distinct patterns of mass eigen values for the heavy RH masses: (i) Compact scenario where all masses are heavier than the Davidson-Ibarra (DI) bound, and (ii) The hierarchical scenario where only the lightest N1 mass is below the DI bound. Thus each of these sets of RH neutrino masses corresponds to two types of Dirac neutrino mass matrices or Yukawa couplings which play crucial roles in the determination of CP-asymmetry resulting from RH decays. We have carried out a complete avour analysis in determining the CP asymmetries. We have also exploited solutions of Boltzmann equations in every case to arrive at the predicted results on baryon asymmetry. Successful ansatz for baryogenesis via leptogenesis is shown to emerge for each pattern of RH masses. With the compact pattern of RH this occurs when the Dirac neutrino masses are determined in the u-quark or the d-quark diagonal basis. However, in the hierarchical scenario of RH masses, the dominant CP asymmetry that survives the washout due to N1-decay and contributes to the desired baryon asymmetry is generated by the decay of the second generation RH Dirac neutrino mass corresponds to the u-quark diagonal basis. Because of the heavier mass of the LH triplet scalar, although its direct decay to two leptons [62] gives negligible contribution to the generated CP-asymmetry, the additional vertex correction generated by its mediation to the RH decay is found to lead to a CP-asymmetry component comparable to other dominant contributions. Thus the same heavy triplet scalar L and the RH s which drive the hybrid seesaw formula for neutrino masses and mixings are shown to generate the leptonic CP asymmetry leading to the experimentally observed value for the baryon asymmetry of the universe over a wide range of the parameter space in the model. For the embedding of the suggested triplet fermionic DM [182] in SO(10) [125], we assume it to originate from the non-standard fermionic representation 45F rying even matter parity. Having exploited the triplet fermionic DM F (1; 3; 0) and the LH triplet Higgs scalar L(1; 3; 1) mediating the hybrid seesaw for neutrino masses and leptogenesis, we justify the presence of these light degrees of freedom as ingredients for coupling uni cation through their non-trivial contribution to the SU(2)L U(1)Y gauge coupling evolutions. In addition, we need lighter scalar or fermionic octets with mass 107 GeV under SU(3)C to complete the precision gauge coupling uni cation. The degrees of freedom used in this model having their origins from SO(10) representations 126H ; 10H ; 45H , and 45F are expected to contribute substantially to GUT threshold e ects on the uni cation scale through their superheavy components even without resorting to make the superheavy gauge boson masses non-degenerate as has been adopted in a number of earlier works for proton stability. It is important to note that if we accept the stabilising symmetry for DM to be matter parity, then the participation of 126H in its spontaneous symmetry breaking is inevitable. This in turn dictates a dominant contribution to threshold e ects on proton lifetime which has been ignored earlier but estimated in this direct breaking chain for the rst time. In addition the superheavy fermions in 45F have been noted to contribute substantially. A possibility of partial cancellation of scalar and fermionic threshold e ects is also pointed out. Although it is challenging to rule out the present model by proton decay experiments, the predicted proton lifetime in this model for the p ! e+ 0 is found to be within the accessible range of the ongoing search limits [183{189] for a wider range of the parameter space. Unlike the case of direct breaking of SUSY SO(10) to MSSM [69] or non-SUSY SO(10) through Pati-Salam intermediate symmetry [69], but like very large number of cases of model building in non-SUSY GUTs, it is not our present goal to address charged fermion mass t. But we discuss in appendix A.3 how all fermion masses may be tted at least approximately in future without substantially a ecting this model predictions. This paper is planned in the following manner. In section 2 we discuss successful t to the neutrino oscillation data where we estimate the LH Higgs triplet and the RH In section 3.1 we present the estimations of CP-asymmetry for di erent avor states. In section 3.2 we discuss Boltzmann equations for avour based analysis. In section 3.3 and section 3.4 we present the results of nal baryon asymmetry. In section 4 we discuss why the neutral component of fermionic triplet is a suitable dark matter candidate. In section 5 we discuss uni cation of gauge couplings and determine the uni cation scale. In section 6 we discuss proton lifetime prediction including GUT-threshold uncertainties. In section 7 we summarize and state conclusions. In appendix A.1 and appendix A.2 we provide renormalization group coe cients for gauge coupling evolution and estimation of threshold e ects. In appendix A.3 we discuss the possibility of parameterization of fermion masses. Hybrid seesaw t to neutrino oscillation data In this section we address the issue of tting the neutrino masses and mixings as determined from the neutrino oscillation data by the hybrid seesaw formula. We then infer on the masses of heavy left-handed triplet and RH neutrinos necessary for leptogenesis. After SO(10) breaking, the relevant part of the Lagrangian under SM symmetry is rst term on the right-hand side (r.h.s.) of eq. (2.1) is from the SO(10) symmetric Yukawa term Y (10):16:16:10H whereas the second and the third terms are from f:16:16:126y [67]. Also we have de ned vR vR. Although the associated RH scalar eld 126H has the respective quantum number under the LR gauge group SU(2)L G2213), it is the singlet comSimilarly the LH triplet scalar eld 126H has the transformation property L(1; 3; 1). Here is the quartic coupling of the SO(10) invariant Lagrangian resulting from the combination of 10H and 126H : 102H :126yH :126H has its origin from M 2 126yH 126H . Other notations are self explanatory. The hybrid formula for the light neutrino mass matrix is the sum of type-I and type-II seesaw contributions [29] HT i 2 LH. The Higgs triplet mass-squared term = f vL where vL = vRve2w=M 2 is the induced VEV of triplet scalar There is the well known standard ansatz to t fermion masses in SO(10) along the line of [67]. To estimate the Dirac mass matrix in this work we have carried out one-loop renormalization group evolution of Yukawa couplings in the bottom-up approach using PDG values of all charged fermion masses. At the electroweak scale = MZ using experimental data on charged fermion masses we choose up-quark or down-quark mass diagonal bases in two di erent scenarios. We then evolve them upto the GUT scale = MU using bottom-up approach [71{73]. At this scale we assume equality of the up-quark and the Dirac neutrino mass matrices, MD ' Mu, which holds upto a very good approximation in SO(10) due to its underlying quark-lepton symmetry [23, 24]. As pointed out in section 1, 2 t to all fermion masses and mixings in SUSY SO(10) or in non-SUSY SO(10) with G224 intermediate symmetry requires a small departure from this assumption [69, 137, 139, 140]. On the other hand a very recent derivation of neutrino mass and mixing sum-rules has been found to require MD close to Mu [141] as in our Although in the present case of non-SUSY SO(10) breaking directly to the SM gauge theory, fermion mass t is not our goal in this paper, we have discussed the issue in We further assumed that MD(MMGUT ) MD( ) for all lower mass scales We could have done better to estimate the Dirac mass matrix at the electroweak scale by following the top- down approach but since it does not get appreciable correction due to the absence of the strong gauge coupling 3C [71{73] contribution, this approximation does not in uence our nal result substantially. Another reason is that for leptogenesis we need Dirac neutrino Yukawa couplings at intermediate scales, (106{1012) GeV where the renormalisation group (RG) running e ects are expected to be smaller in the top-down approach. Thus in the down quark diagonal basis under the assumption of negligible RG e ects = MZ 00:01832+0:00441i 0:65882+0:27319i 1 3:32785+0:00019i 81:8543 1:64 We repeat the above procedure in the up-quark diagonal basis at = MZ instead of the down quark diagonal basis leading to (1:5027+0:0038i)10 9 (7:51+3:19i)10 61 M D(u)(GeV) = B@(1:5027+0:0038i)10 9 (7:51+3:19i)10 6 For the sake of clarity it might be necessary to explain how the mass matrix structure given in eq. (2.4) emerges with very small non-diagonal elements. In the bottom-up approach for the RG evolution of Yukawa matrices, we have assumed the up-quark mass matrix Mu(MZ ) to be diagonal in one case at the electroweak scale which we designate as up-quark diagonal basis. In this case naturally all elements of the down quark mass matrix Md(MZ ) are non-vanishing. In the alternative case, called the d-quak diagonal basis, we have chosen Md(MZ ) diagonal for which all nine elements of Mu(MZ ) are non-vanishing. In the case of up-quark diagonal basis, however, the non-diagonal elements of Mu(MMGUT ) acquire non-vanishingly small corrections due to RG e ects in the bottom-up approach and this is approximated as the Dirac-neutino mass matrix M D(u)(MGUT). This explains the appearance of non-diagonal elements appearing in eq. (2.4). It may be noted further that the RG-corrections in the Dirac neutrino mass matrix M D(u) for evolutions from = MGUT down to relevant lower scales have been ignored as they are expected to be much smaller. The Dirac neutrino mass matrices given in eq. eq. (2.3) and eq. (2.4) are used in the second term of the right-hand side (r.h.s.) of eq. (2.2) where in the left-hand side (l.h.s.) we use the value of light neutrino mass matrix for the normally ordered case with that Majorana phases are zero at all mass scales. We then search for solutions for the Majorana coupling f or, equivalently, the values of RH neutrino masses. Due to strongly hierarchical structure of MD matrix, it is impractical to assume the dominance of the type-I or the type-II term in the hybrid seesaw formula of eq. (2.2). Since eq. (2.2) is quadratic in f , it has two solutions for every eigenvalue and should be only two distinct positive de nite solutions. We estimated these solutions for f using the neutrino oscillation data of ref. [191] as input and numerical iteration. A robust iterative numerical estimation of f matrix is performed to match the oscillation data. Thus by xing the lightest neutrino mass and the VEV vL in a chosen hierarchy of light neutrino masses, the precise forms of the two solutions with positive de nite f are evaluated upto the desired precision. These solutions are presented in gure 1 for two sets of values of = 0:1 and In gure 1 we have presented these solutions for the normally ordered values of active light neutrino masses. Solutions in the top row of the gure have strongly hierarchical heavy RH neutrino masses, lightest of them being MN1 collider experiments, and the heaviest MN3 O(1012) GeV. We call such solutions of RH O(103 5) GeV, testable in future neutrino masses to represent a hierarchical spectrum scenario. Solutions in the bottom row of the gure are not so hierarchical and the RH neutrinos only span three orders of magnitude of mass range. We call the solutions of this type given in the bottom row to represent a compact spectrum scenario. Lightest of RH neutrino in this scenario is O(109 11) GeV which is far away from direct detection limit of any collider experiment. masses increase with for the compact spectrum scenario while it almost stays una ected in the hierarchical spectrum scenario. Also the theory should continue to remain perturbative on the quartic coupling in the case when the three neutrino masses are normally ordered. The top row represents a hierarchical spectrum solution of RH neutrinos and the bottom row represents a not so hierarchical scenario which we call as compact spectrum solution. The values of M L = 1012 GeV and vR = 1015:5 GeV have been kept xed. The value of the quartic coupling used here has been = 0:1(0:001) for the left panel (right panel). acquiring N1-dominated leptogenesis because increasing ( 1) for the above value of M will make MN1 < 109 GeV and N1- dominated leptogenesis will not be possible. In the compact spectrum scenario we estimate the f matrix in the d-diagonal basis MD = M D(d) f = B@0:4617 0 0:385 + 0:1291i 0:4617 0:4922i 3:509 + 1:080i 1 0:4922i 4:626 + 0:1567i 22:80 + 0:3317iC For the same parameters in the compact spectrum scenario but with M D(u) in u-diagonal basis given in eq. (2.4), we derive MD = M D(u) 0 0:3175 + 0:0904i 0:1232 f = B@ 0:1232 1:587 + 0:2599i C 0:6918i 1:587 + 0:2599i In the hierarchical spectrum scenario, similarly, we have the two matrices for f MD = M D(d) MD = M D(u) f = B@ 4:0194 + 1:5783i 4:0194 + 1:5783i 1 0 0:000025 + 0:000008i 0:00019 f = B 0:56091 + 0:0092i 0:95702 0:00177i 0:95702 Despite widely varying magnitudes of di erent elements in the matrix, the mass eigenvalues quark and d quark diagonal bases are not very di erent in both the compact spectrum and the hierarchical spectrum scenarios. Therefore, we have presented only one set of solutions for the RH masses in gure 1. It is quite encouraging to note that despite the GUT scale value of vR, the type-II term does not upset the type-I seesaw term in the hybrid formula, rather both of them contribute signi cantly to the light neutrino mass matrix. We will explore the plausibility of su cient leptogenesis using the hybrid seesaw mechanism of this model to explain BAU. Baryon asymmetry of the Universe In this section at rst we estimate the leptonic CP- asymmetry generated in decays of both L. The dynamically generated lepton asymmetry gets converted into baryon asymmetry due to sphaleron interaction [192]. Leptogenesis is discussed in various papers [58, 160, 193{208]. The avour independent calculation of asymmetry is applicable at high temperatures when all the charged lepton mediated interactions are out of equilibrium i.e. T & 1012 GeV. Flavour dependent analysis [202] becomes necessary for leptogenesis at lower temperatures. In hierarchical spectrum scenarios we have MN1 which violates the Davidson-Ibarra bound [209] badly, therefore it can not produce required amount of avour independent lepton asymmetry. Instead it washes out the asymmetry produced at the early stage in N2;3 decays. In the recent studies [202, 210{213] it has been shown that under such circumstances the next heavy neutrino N2 can produce the required asymmetry, if MN2 & 1010 GeV and there exists a heavier N3. If the asymmetry produced by N2 is not completely washed out by lightest neutrino N1, it survives and gets converted to baryon asymmetry. On the other hand, in the compact spectrum scenario, the lightest RH neutrino is well within the Davidson-Ibarra bound, therefore the asymmetry can be produced in the lightest RH decay. Since for a large region of the parameter space we have shown that MN1 1012 GeV, the asymmetry will depend on avour dynamics. i = "iN + "i : iN = k6=i k6=i diagrams represent vertex corrections and the second diagram represents self-energy correction. The avoured CP-asymmetry in the decay of Ni to a lepton l is generated in the lepton avor generation , and is de ned as [216, 217, 229] i = (Ni ! l + H ) + (Ni ! l + H) gure 2. The total asymmetry is sum of the two contributions L [62] as shown in The rst line of this expression contains lepton number violating terms while the second line is the lepton number conserving but violates lepton avour. Here, Y^ = Y Uf is the Dirac Yukawa coupling in the right-handed neutrino diagonal mass basis and Uf is the unitary matrix diagonalizing f . The loop functions in the asymmetry expression are [217] g(x) = h(x) = p Here by retaining the Wigner-Eckart term in the loop function we can handle degenerate mass scenario without hitting singularity, which is possible in compact spectrum scenario in our model (see gure 1). Note that in the degenerate regime CP asymmetry gets largest contribution from self-energy term and may reach to a value of O(1). The CP -asymmetry produced in Ni decay from the L mediated diagram is [62] i = | Δiα10-6 ε top left(right)-panel correspond to d(u)-quark diagonal basis for = 0:1. The bottom left(right) panel correspond to d(u)-quark diagonal basis but for which gets contribution proportional to the trilinear coupling mass term . Its loop function is larger for smaller M L can not be made arbitrarily small without decreasing or increasing vL which is constrained to be below GeV from electroweak (EW) precision constraints. Decreasing would decrease CP asymmetry linearly. estimated the avored CP-asymmetry for di erent values of the lightest neutrino mass in the normally ordered hierachical case of light neutrino masses. Change in the mass of m 1 alters f and thus changes the masses and mixings of RH s. Flavour asymmetries for Ni avour are shown in gure 3 for compact spectrum case and in gure 4 for the hierarchical spectrum case of RH s. We note that variation in quartic coupling changes CP-asymmetry signi cantly, particularly in the hierarchical spectrum scenario. The tree level decay widths are una ected by the presence of the scalar triplet L in the scheme. The presence of the heavy scalar triplet L in our theory adds another source of CP ) which is produced by the decay of the triplet scalar itself into two like-sign or neutral leptons [62]. Though one triplet scalar is enough to generate the active neutrino masses and mixings through type-II seesaw, the asymmetry production in L decay needs either more than one triplet scalars [218{221] or combination of triplet scalar and right| Δiα10-6 ε masses. The top left (right)-panel correspond to d(u)-quark diagonal basis for = 0:1. The bottom left(right) panel correspond to d(u)-quark diagonal basis but for handed neutrinos [62] as shown in gure 5 for our model. The CP-asymmetry generated L decay and mediated by RH is written as [62] = 2 log(1 + M 2 =M N2k ) : We note that, since vR ' 1015:5 GeV and M L ' 1012 GeV, either of the two terms in the denominator of " is large enough to keep the CP -asymmetry fairly small for the parameters under consideration. For example, if three right-handed neutrino masses are MNk = (6:6990; 13:869; 1431) 109 GeV, the three CP-asymmetries due to Nk decays from CP-asymmetries from the third diagram are: j Nk j = (5:2 Compared to these numbers, the CP-asymmetry due to j j = 2:1 M1;2, the asymmetry generated at the early stage will be washed out at the production phase of lighter RH s. Henceforth, we will ignore the L asymmetry in our numerical estimations [219]. In the next subsection we will estimate the lepton asymmetry using Boltzmann equations for the system. Boltzmann equations The evolution of number density is obtained by solving the set of Boltzmann equations. The co-moving number density is YX nX =s. The Boltzmann equations for heavy neutrinos number density are [190] Ki(Di(z) + Si(z)) YNi (z) X Wi(z) A stands for the total asymmetry stored in the fermionic such that Ki = P Ki . In eq. (3.7) the equilibrium number density [190, 215] is de ned as Ki = YNeqi = 135 (3) R2z2K2(Riz) T Mi 135 (3) i ! requires the lightest right-handed neutrino to acquire mass MN1 & 4 decay rates are Di(z) = R2zK1(Riz)=K2(Riz) where K1 and K2 are the rst and the seci ond order modi ed Bessel functions [215, 222], respectively. The scattering terms Si(z) account for Higgs-mediated 108 GeV [179{181] inverse decay contribution is WiID(z) = 1 R4z3K1(Riz): The unit lepton number changing L = 1 scattering contributing to washout is WiS(z) = matrices are [213] scattering involving top quark are included in the evolution of asymmetry [222]. We have ignored the o -shell part of L = 2 process in the washout term which is a good approximation as long as MNi =1013 Ki [223]. We have also omitted the not contribute to the washout but can a ect the abundance of heavy neutrinos. When avor e ects are taken into account, they also tend to redistribute the lepton asymmetry among avors. These e ects are of higher order in the neutrino Yukawa couplings and are expected to have little impact on the nal baryon asymmetry. We further neglected the scalar triplet related washout processes, gauge scatterings, spectator processes, and the higher order processes like 1 ! 3 and 2 ! 3. The heavy gauge bosons processes such as Ni eR ! qR qR0 and NiNi ! f f tend to keep the heavy neutrinos in thermal equilibrium, thus reducing the generated lepton asymmetry. This e ect is practically negligible because RH s are much lighter than the RH gauge bosons. We also ignore such avour e ects [224] which are relevant for resonant leptogenesis. Baryon asymmetry in the compact scenario In this scenario the tau lepton avour state decouples while the electron and muon states are still coupled. Thus, a avour dependent analysis is necessary. In the two avour case = "ie + "i , Ki;e+ = Kie + Ki , and the avour coupling A = 417=589 120=589 ! ; C = 224=589 : In this case the baryon asymmetry is expressed as asymmetry in to baryon asymmetry by non-perturbative sphaleron process [225, 226]. The results of BBN [227] and PLANCK [11, 12] experiments are Y B = Y BBBN = (8:10 Y PBlanck = (8:58 Compared to these somewhat higher value of BAU obtained from WMAP 7 years' data has been reported in ref. [228]. The washout coe cients Ki in the compact spectrum scenario of RH neutrino masses for the lightest neutrino mass m 1 = 0:00127 eV and 2 [0:0001; 0:5] are plotted in gure 6. We see that there are two to four orders of variation in the washout for the above allowed in both the d-diagonal (left panel) and the u-diagonal (right panel) cases. We 0.0001 0.001 0.0001 0.001 Other parameters are kept xed as described in the text. list the washout parameters for = 0:1 in the case of the d-quark diagonal basis In the u-quark diagonal basis the washout parameters are K = B@2:77 K = B@1:46 Our observations in the two cases are summarized below. (a) The d-quark diagonal basis. We note that Ki = P the system is in strong washout regime for most of the parameter space. The asymmetry is determined by a balance between production and destruction. The nal asymmetry freeze occurs at the decoupling of washout with zf lepton asymmetry is approximated as [229] (7{10). In the single avour analysis the YNeq1 (z = 0) [229] gives Using the values of Ki from gure 6 and "1 = P "1 from gure 7 we can easily achieve the required lepton asymmetry. In fact it may lead to a constraint on quartic coupling . (b) The u-diagonal basis. We note that, since K1 = P 1, this is a very weak washout regime. Ignoring thermal e ect on CP-asymmetry and assuming zero initial 0.0001 0.001 0.0001 0.001 Other parameters are kept xed as described in the text. avours (double-dot-dashed blue curve) and dashed curve) for the u-quark diagonal basis and compact spectrum RH mass scenario. Left (right) panel correspond to non-zero (zero) initial thermal abundance. The quartic coupling If there is already an initial amount of asymmetry left over, say through N2 decay, it will not be washed out because the system is in weak washout regime. But with zero initial abundance, YN1 (z = 0) = 0 [229] We note that even if we assume initial thermal abundance Y eq(0) 0:0039, the CPasymmetry "1 10 6 ( gure 7) and K 10 3 ( gure 6). Therefore the generated asymmetry would be determined by initial abundance and, in the zero initial abundance scenario, the required lepton asymmetry can not be produced for any parameter value. Therefore the avour independent analysis in the u-quark diagonal scenario with zero initial abundance of YN1 fails to give the required asymmetry. On the other hand a avor dependent analysis can enhance the asymmetry. The avour dependent lepton asymmetry is analyzed using Boltzmann equations (3.7) and is shown in gure 8 for u-quark diagonal basis. Thus in avoured analysis we nd that nal lepton vR=1015.5 GeV spectrum scenario with Dirac neutrino mass matrix determined in the d-quark diagonal basis as described in the text. asymmetry is independent of initial abundance and is close to the experimental value for < 0:05. This explicitly shows that N2 decay contributes to lepton asymmetry which is not completely washed out in the N1 decay. The reason for doing avoured analysis is that there are enhancements in the nal asymmetry compared to the un avoured case. Using d-quark diagonal basis shows the variation of total asymmetry with respect to quartic coupling for a xed value of the scalar triplet mass M = 1012 GeV, vR = 1015:5 GeV, and the lightest neutrino Baryon asymmetry in the hierarchical scenario The Davidson-Ibarra bound is not respected in the hierarchical spectrum scenario of RH (see gure 1). In such a case there is the possibility of leptogenesis if asymmetry is produced by the decay of N2. Lower bound on the lightest RH is passed to MN2 & 1010 GeV. The N2-dominated leptogenesis can be successful if there is a heavy neutrino, or triplet scalar with MN3 ; M L > MN2 , and the washout from the lightest RH (N1) is circumvented. 109 GeV the lepton avour states become incoherent and the washout acts separately on each avour asymmetry. We need to solve Boltzmann equations at the i is very small compared to CP-asymmetry due to N2;3 decays. The decay and washout are also suppressed by a factor M12=M32( the scenario M3 & 1012 GeV 10 15) and M12=M22( M2 > 109 GeV 10 10). Also we note that in M1, the role of N3 becomes indistinct by 10 + 5y+ 1 10 + 10y + 1 + 24 24 + 15 + 15y 5 +5y+10y+45y +10 + 45 5y+ 45+15y +50y + 10 + 1 1+ 24 + 10y+ 10 + 40 + 40y + 75 + 5 +5y Energy Scale Particle content SM+(1; 3; 0)F SM + (1; 3; 0)F + (8; 1; 0)F SM + (1; 3; 0)F + (8; 1; 0)F + (1; 3; 1)H MZ MT MT MO 0 41=10 1 0 41=10 1 0 41=10 1 043=101 B 7=6 C 0199=50 27=10 44=51 B@ 9=10 0199=50 27=10 44=51 B@ 9=10 163=6 12 CA 0199=50 27=10 44=51 B@ 9=10 163=6 12 CA 083=10 171=10 44=51 B@57=10 275=6 Particle content and beta function coe cients In this subsection we present the particle content used in various ranges of mass scales as shown in table 2 and the corresponding beta-function coe cients which have contributed for the gauge coupling uni cation, leptogenesis, and dark matter as shown in table 3. SU(5) (3C ; 2L; 1Y ) SU(5) (3C ; 2L; 1Y ) (1, 3/2, 5/2) (1/2, 0, 1/5) (1, 3/2, 5/2) (1/2, 0, 1/5) (1, 3/2, 1/10) (1, 3/2, 1/10) the sake of convenience, the would-be goldstone modes of all super-heavy gauge bosons have been provided from the scalar representation 45H . Super-heavy particles and coe cients for threshold e ects In this subsection we identify the super-heavy particle contents of various SO(10) representations with their quantum numbers and beta function coe cients under the SM gauge group. These coe cients shown in table 4, table 5, and table 6 have been used for the estimation of threshold e ects on proton lifetime predictions. A discussion on charged fermion mass parametrization While all single step descents of SUSY GUTs leading to MSSM exhibit almost profound gauge coupling uni cation, there has been several attempts in SUSY SO(10) to explain fermion masses of three generations of quarks and leptons along with the attractive phenomena like b Yukawa uni cation. In certain other cases approximate SU(5) (3C ; 2L; 1Y ) (15, 24, 12/5) (12, 8, 24/5) (12, 8, 24/5) validity of some of the Georgi-Jarlskog [70] type mass relations have been found to hold at the GUT scale. While some recent works have presented very attractive details of data analysis with 2- t [69] as pointed out in section 1, a much larger number of other research papers have con ned to partially quantitative or qualitative representations of the charged fermion masses as these latter types of investigations focus on other challenging issues of particle physics. Compared to such interesing results on fermion mass ts in the direct breaking model of SUSY SO(10) [69], non-SUSY models need at least one intermediate gauge symmetry to ensure gauge coupling uni cation within the constraint of extended survival hypothesis [28, 29]. Also unlike the MSSM or SUSY SO(10), the RG extrapolated values of charged fermion masses through either SM or twoHiggs doublet model in the bottom-up approach [71{73] do not exhibit a precise b Yukawa uni cation at the scale 1016 GeV. Unlike the attempts to present all fermion masses in SUSY SO(10) through 2 t and non-SUSY case with SU(4)C intermediate symmetry [69], to our knowledge no such analysis appears to have been done so far in the direct breaking of non-SUSY SO(10) where gauge coupling uni cation itself under the minimal ne-tuning constraint [28, 29] is highly challenging. In attempts to confront more challenging problems in SUSY or non-SUSY SO(10), a number of recent works have ignored the question of tting the charged fermion masses while con ning mainly to only neutrino masses and mixings, or at most a qualitative presentation of charged fermion masses [39{42, 73, 79{88, 88{96, 98{104]. However, even though a present goal, we point out how the charged fermion masses may be parameterized within this direct breaking model of non-SUSY SO(10) while successfully encompassing standard model paradigm at lower scales, neutrino masses, baryon asymmetry, dark matter, gauge coupling uni cation, and GUT scale parity restoration. The Higgs representations 10H ; 126H , and 120H are known to contribute to fermion masses through the corresponding renormalizable Yukawa interactions. We include two copies of 10H elds in the corresponding renormalizable part of the Yukawa Lagrangian L(N1R) = L(N2R) = The Yukawa term f 16:16:126H has been found to be speci cally suitable in approximately satisfying the GJ type relations in the down quark and charged lepton sectors. Convenwhich plays a crucial role in the type-I and type-II seesaw components of the hybrid seesaw formula used in this work. Therefore, the prime concern for charged fermion mass t in the present model may be the smallness of the value of the matrix elements for successful predictions of baryon asymmetry in this model. We provide below how this di culty can be circumvented in two di erent ways: (i) Non-renormalizable, and (ii) Renormalizable; any one of these can be added to L(10) for charged fermion mass parametrization. (i). Non-renormalizable Yukawa correction. There have been attempts to represent fermion masses in SUSY SO(10) via non-renermalizable interactions with additional avor avon elds [282, 283]. Without introducing any such additional elds or symmetries, our attempt here is con ned to the non-SUSY SO(10) gauge symmetry and the Higgs representations of the model. We note that the following non-renormalizable Yukawa (NRY) interactions are allowed tions with mi0j and lepton mass matrices can be parameterized as: bution is suppressed by a factor MGUT . Noting that 10H (2; 2; 15), it contributes to non-diagonal elements of all Dirac type mass matrices antisymmetrically which we ignore in this qualitative explanation, but can be included if a 2 t is desired in future works. The second Yukawa interaction in eq. (A.3) containing 45H has an e ective (2; 2; 15)H component that is contained in 126 and its contribution is symmetric. It is important to note that at the GUT scale L(N2R) gives a suppressed factor that adequately quali es it to parameterize the needed additional correc10 5)vew. Thus, at the GUT scale the quark Mu = Gu + Fu; MD = Gu Md = Gd + Fd; Ml = Gd where Gu = Y (u) < 10Hu >, Gd = Y (d) < 10Hd >, Fp F(2)10 4: < 10Hp >, p = u; d. Details of fermion mass parametrization goes in a manner similar to those discussed in [94{96, 142, 144{147]. (ii). Renormalizable correction. Through renormalizable interaction, the improvement of fermion mass parametrization is also suggested by the introduction of a second 126H representation [144, 146, 147]. We denote this and its corresponding components under G224 as 1260H 0R(1; 3; 10); 0(2; 2; 15); : : :. In contrast to the 126H whose mass has been ne tuned to be at M L 1012 GeV for the implementation of the type-II seesaw component of the hybrid seesaw formula, leptogenesis, and coupling uni cation, all the components of 1260H are naturally assigned masses near the GUT scale consistent with extended survival hypothesis [28, 29]. Also no VEV is needed to be assigned to 0R >= 0, since the corresponding role of gauge symmetry breaking has been taken over by < R(1; 3; 10) >= vR 126H . Thus the presence of the second Higgs representation 1260H does not a ect the type-II seesaw and the RH neutrino masse parameters of type-I in the hybrid seesaw formula of eq. (2.2). Even upto the two-loop level it does not a ect the gauge coupling uni cation of the present model. Denoting the corresponding SO(10) invariant Yukawa term as f 016:16:(126)0, we have renorIt is well known that such corrections provide reasonable parameterization of the fermion masses of the rst and second generations. With degeneracy of all superheavy components of 1260H , its threshold corrections to uni cation scale and proton lifetime are vanishingly small [281]. Similarly, if the renormalizable antisymmetric contributions to fermion mass matrices due to Yukawa interaction of a 120H SO(10) are included, its threshold e ects on uni cation scale and proton lifetime would be also vanishingly small due to degeneracy of the components. Alternatively the fermion mass parametrization may be improved further by including both the renormalizable and non-renormalizable contributions in eq. (A.4). In addition, the antisymmetric contribution through the rst nonrenormalizable term in L(N1R) may be can be very well replaced by renormalizable Yukawa contribution h(120)16:16:120H . also included for still further improvement. Further, the antisymmetric NRY due to LNR The next question is whether this parametrization signi cantly a ects the predicted In SO(10) there are two maximal subgroups of rank 5: the Pati-Salam group G224 and the Gfl). When SU(4)C G224 is unbroken, the assumed boundary condition is exact. Similarly it is well known that in the presence of Gfl symmetry gauge symmetries are also broken and the boundary condition is approximate to the extent MD = 4Fu. This suggests that u 4Fu=mtop should be a small number in case fermion mass t is also included as a required ingredient in this model. For a very is almost exactly satis ed near the GUT scale bottom-up approach within the SM paradigm [71{73]: 1015:56 GeV by values obtained in the With the dominance of the element (Fd)22 in the (22) elements of down-quark and charged lepton mass matrices, j(Fd)22j j(Gd)22j, gives (Fd)22 30 MeV and a fractional change We have checked that even afte applying these corrections satisfying the rst of GJ relation in eq. (A.1), our solutions and predictions on baryon asymmetry made in this work are not signi cantly a ected. Also they remain largely una ected as long as the corrections to the elements of the Dirac neutrino mass matrix MD are either less or at most of the same order as those given in section 2. After the GUT symmetry breaking to the SM gauge theory we have assumed only one linear combination of di erent up type and down type doublets to remain massless to form the standard Higgs doublet. M.K.P. acknowledges nancial support through the research project SB/S2/HEP-011/2013 awarded by the Department of Science and Technology, Government of India. R.L.A. acknowledges the award of a Post-Doctoral Fellowship by Siksha 'O' Ausandhan University where this work was carried out. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. [arXiv:1207.7214] [INSPIRE]. experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE]. analysis of neutrino masses, mixings and phases: entering the era of leptonic CP-violation searches, Phys. Rev. D 86 (2012) 013012 [arXiv:1205.5254] [INSPIRE]. [arXiv:1103.0734] [INSPIRE]. (2014) 093006 [arXiv:1405.7540] [INSPIRE]. Experiments, Nucl. Phys. B 908 (2016) 199 [arXiv:1512.06856] [INSPIRE]. Probe (WMAP) observations: Determination of cosmological parameters, Astrophys. J. Suppl. 148 (2003) 175 [astro-ph/0302209] [INSPIRE]. in the fermion triplet seesaw model, Phys. Rev. D 78 (2008) 033007 [arXiv:0803.0481] Probe (WMAP) Observations: Data Processing, Sky Maps and Basic Results, Astrophys. J. Suppl. 180 (2009) 225 [arXiv:0803.0732] [INSPIRE]. Probe (WMAP) Observations: Cosmological Interpretation, Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538] [INSPIRE]. 110 [INSPIRE]. parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE]. 377 [astro-ph/0603449] [INSPIRE]. [arXiv:1211.7090] [INSPIRE]. (1974) 438 [INSPIRE]. 93 (1975) 193 [INSPIRE]. Large Scale Structure with Cold Dark Matter, Nature 311 (1984) 517 [INSPIRE]. Theories, Phys. Rev. Lett. 33 (1974) 451 [INSPIRE]. [Erratum ibid. D 11 (1975) 703] [INSPIRE]. 2558 [INSPIRE]. of Parity, Phys. Rev. D 12 (1975) 1502 [INSPIRE]. B 153 (1979) 334 [INSPIRE]. B 177 (1981) 60 [INSPIRE]. Rev. D 27 (1983) 1601 [INSPIRE]. Rev. D 24 (1981) 1681 [INSPIRE]. Phys. Rev. D 25 (1982) 3092 [INSPIRE]. Conf. Proc. C 910725v1 (1991) 690 [INSPIRE]. sin2 W and grand uni cation, Phys. Rev. D 44 (1991) 817 [INSPIRE]. [hep-ph/0204097] [INSPIRE]. 035007 [hep-ph/0402122] [INSPIRE]. uni cation and large atmospheric mixing: A case for noncanonical seesaw, Phys. Rev. Lett. 90 (2003) 051802 [hep-ph/0210207] (1982) 287 [INSPIRE]. 36 [INSPIRE]. uni cation and large neutrino mixings, Phys. Lett. B 570 (2003) 215 [hep-ph/0303055] [INSPIRE]. grand uni ed theory, Phys. Lett. B 588 (2004) 196 [hep-ph/0306242] [INSPIRE]. [hep-ph/0308197] [INSPIRE]. model for neutrino mixings, Phys. Lett. B 587 (2004) 105 [hep-ph/0311330] [INSPIRE]. supersymmetric SO(10) model with Type-III see-saw mechanism, JHEP 06 (2005) 016 [hep-ph/0503114] [INSPIRE]. minimal SUSY SO(10) GUT, Phys. Rev. D 72 (2005) 051701 [hep-ph/0412348] [INSPIRE]. Relations, Phys. Lett. B 67 (1977) 193 [INSPIRE]. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE]. U(1) Theories, Phys. Rev. D (1979) 95 [INSPIRE]. Phys. Rev. Lett. 44 (1980) 912 [INSPIRE]. 22 (1980) 2227 [INSPIRE]. (1980) 61 [INSPIRE]. SO(10) Model, Nucl. Phys. B 181 (1981) 287 [INSPIRE]. Spontaneous Parity Violation, Phys. Rev. D 23 (1981) 165 [INSPIRE]. High-resolution inelastic electron scattering on 208 Pb at 50 and 63.5 MeV and fragmentation of the magnetic quadrupole strength, Phys. Lett. B 74 (1978) 45 [INSPIRE]. matter, Phys. Rev. D 66 (2002) 063002 [hep-ph/0111381] [INSPIRE]. B 582 (2004) 73 [hep-ph/0307237] [INSPIRE]. Theories, Phys. Rev. D 34 (1986) 3457 [INSPIRE]. Lett. 62 (1989) 1221 [INSPIRE]. [hep-ph/9207218] [INSPIRE]. [hep-ph/0605006] [INSPIRE]. 095002 [arXiv:1102.5148] [INSPIRE]. Lett. B 86 (1979) 297 [INSPIRE]. higher scales in MSSM, Eur. Phys. J. C 14 (2000) 159 [hep-ph/9902374] [INSPIRE]. a heavier gluino, Phys. Rev. D 86 (2012) 035019 [arXiv:1206.3910] [INSPIRE]. SO(10), JHEP 09 (2011) 137 [arXiv:1105.5943] [INSPIRE]. neutrinos in SO(10), AIP Conf. Proc. 1382 (2011) 115 [INSPIRE]. JHEP 03 (2011) 133 [arXiv:1012.2697] [INSPIRE]. Phys. Proc. 265-266 (2015) 317 [INSPIRE]. ve-dimensional SO(10) model, JHEP 09 (2015) 040 [arXiv:1507.00669] [INSPIRE]. model, Phys. Lett. B 767 (2017) 295 [arXiv:1611.08341] [INSPIRE]. masses in SUSY SO(10) S4, Phys. Rev. D 78 (2008) 053004 [arXiv:0804.4571] M(R), Phys. Rev. Lett. 70 (1993) 3189 [hep-ph/9211310] [INSPIRE]. forces., Phys. Rev. D 57 (1998) 2736 [hep-ph/9710246] [INSPIRE]. Lopsided SO(10) Flavor Structure in B physics, Phys. Rev. D 75 (2007) 055016 [hep-ph/0612114] [INSPIRE]. Models, Phys. Lett. B 651 (2007) 195 [hep-ph/0605088] [INSPIRE]. framework, Phys. Rev. D 68 (2003) 072002 [INSPIRE]. Stabilized Doublet-Triplet Splitting, JHEP 06 (2010) 084 [arXiv:1003.2625] [INSPIRE]. avor violation within a realistic seesaw and neutrino mixing, JHEP 07 (2005) 048 [hep-ph/0505067] [INSPIRE]. Stabilized Doublet-Triplet Splitting, JHEP 06 (2010) 084 [arXiv:1003.2625] [INSPIRE]. SO(10) model, JHEP 05 (2005) 017 [hep-ph/0412373] [INSPIRE]. from SO(10) GUT, JHEP 11 (2016) 018 [arXiv:1607.05437] [INSPIRE]. mass from M-theory SO(10), JHEP 11 (2016) 173 [arXiv:1607.06741] [INSPIRE]. in aton mass in a supersymmetric SO(10) model, JCAP 06 (2005) 005 [hep-ph/0503201] [arXiv:1609.05849] [INSPIRE]. In ation and Neutrino Masses in a No-Scale SO(10) Model, JCAP 11 (2016) 018 SO(10), Phys. Lett. B 765 (2017) 256 [arXiv:1611.10196] [INSPIRE]. (2016) 954 [arXiv:1605.07955] [INSPIRE]. University Press, Cambridge (2007), pg. 29. Phys. Rev. D 82 (2010) 055010 [arXiv:1007.3488] [INSPIRE]. in SU(5) With Higher Dimensional Operators, Phys. Rev. D 39 (1989) 316 [INSPIRE]. rescue of minimal SU(5), Mod. Phys. Lett. A 8 (1993) 1487 [INSPIRE]. Mod. Phys. Lett. A 7 (1992) 559 [INSPIRE]. predictions in SU(5) with split multiplets, Phys. Rev. D 49 (1994) 3711 [INSPIRE]. 476 [hep-ph/0403286] [INSPIRE]. (2005) 367 [hep-ph/0409190] [INSPIRE]. [hep-ph/0410198] [INSPIRE]. 055011 [hep-ph/0703080] [INSPIRE]. Phys. Lett. A 24 (2009) 583 [arXiv:0809.0942] [INSPIRE]. [arXiv:1411.6044] [INSPIRE]. Phys. Rev. D 80 (2009) 085020 [Erratum ibid. D 81 (2010) 029903] [arXiv:0907.1894] Phys. Rev. D 81 (2010) 015002 [arXiv:0903.2475] [INSPIRE]. Phys. Rev. D 81 (2010) 075002 [arXiv:0912.1545] [INSPIRE]. [arXiv:1106.4137] [INSPIRE]. Pramana 79 (2012) 1271 [INSPIRE]. [127] M.K. Parida, Radiative see-saw formula in nonsupersymmetric SO(10) with dark matter, Radiative Neutrino Mass Models, JHEP 09 (2016) 111 [arXiv:1605.03986] [INSPIRE]. [hep-ph/9404238] [INSPIRE]. uni cation, Phys. Rev. D 46 (1993) 2261 [INSPIRE]. (2017) 136 [arXiv:1612.04329] [INSPIRE]. 015013 [arXiv:0903.4049] [INSPIRE]. breaking from strong dynamics, Nucl. Phys. B 905 (2016) 73 [arXiv:1507.04467] running of fermion observables in an SO(10) model, JHEP 12 (2014) 052 [arXiv:1409.3730] [INSPIRE]. Observables in an Extended Non-Supersymmetric SO(10) Model, JHEP 03 (2017) 045 [arXiv:1612.07973] [INSPIRE]. mass-mixing sum rule from SO(10) and neutrinoless double beta decay, arXiv:1701.00491 SO(10), Proton Lifetime, Nonunitarity E ects and a Low-mass Z0 Boson, Phys. Rev. D 86 (2012) 093004 [arXiv:1112.1826] [INSPIRE]. [143] M.K. Parida and S. Patra, Left-right models with light neutrino mass prediction and dominant neutrinoless double beta decay rate, Phys. Lett. B 718 (2013) 1407 [arXiv:1211.5000] [INSPIRE]. beta decay and observable lepton avor violation in left-right models and SO(10) grand uni cation with low mass WR; ZR bosons, JHEP 08 (2013) 122 [arXiv:1302.0672] with low-mass Z0, RH neutrinos and veri able LFV, LNV and proton decay, Eur. Phys. J. C 75 (2015) 183 [arXiv:1312.3185] [INSPIRE]. decay in SO(10) with low-mass Z' boson, observable n n oscillation, lepton and rare kaon decay, JHEP 01 (2015) 045 [arXiv:1401.1412] [INSPIRE]. inverse see-saw motivated SO(10) GUT, Pramana 86 (2016) 223. resonances at the LHC, Phys. Rev. Lett. 115 (2015) 181803 [arXiv:1508.02277] [INSPIRE]. experimental tests, Nucl. Phys. B 906 (2016) 77 [arXiv:1411.6748] [INSPIRE]. theories, Nucl. Part. Phys. Proc. 273-275 (2016) 2642 [arXiv:1510.01096] [INSPIRE]. Mass WR Gauge Bosons Without Observable Parity Restoration, Phys. Lett. B 234 (1990) 45 [INSPIRE]. 4023493 [arXiv:1607.07236] [INSPIRE]. Eur. Phys. J. C 74 (2014) 3107 [arXiv:1407.6908] [INSPIRE]. coupling uni cation in nonsupersymmetric SO(10) grand uni ed models, Phys. Rev. D 91 (2015) 095010 [arXiv:1502.06929] [INSPIRE]. Uni ed Models, PoS(PLANCK 2015)088 [arXiv:1510.03509] [INSPIRE]. Non-supersymmetric SO(10) Grand Uni ed Models, JHEP 10 (2015) 193 [arXiv:1509.00809] [INSPIRE]. (2017) 016 [arXiv:1611.04693] [INSPIRE]. Lett. B 383 (1996) 405 [hep-ph/9605353] [INSPIRE]. 56 (1997) 5431 [hep-ph/9707235] [INSPIRE]. uni cation, Phys. Rev. D 89 (2014) 035002 [arXiv:1311.3228] [INSPIRE]. GUTs, Phys. Rev. D 93 (2016) 013012 [arXiv:1509.06313] [INSPIRE]. supersymmetric SO(10), Phys. Rev. D 48 (1993) 5354 [hep-ph/9306242] [INSPIRE]. Phys. B 259 (1985) 175 [INSPIRE]. 075011 [hep-ph/0701104] [INSPIRE]. a testable SUSY SO(10) model, Phys. Lett. B 668 (2008) 299 [arXiv:0807.3959] [INSPIRE]. in SUSY SO(10) with heavy WR, Phys. Rev. D 82 (2010) 093017 [arXiv:1007.5085] [INSPIRE]. Lett. B 100 (1981) 403 [INSPIRE]. From SO(10) Grand Uni cation With Low Mass Right-handed Gauge Bosons, Phys. Rev. D 40 (1989) 3074 [INSPIRE]. [175] M.K. Parida and P.K. Patra, Useful theorem on vanishing threshold contribution to sin**2-Theta-W in a class of grand uni ed theories, Phys. Rev. Lett. 66 (1991) 858 sin2 W in grand uni ed theories at high mass scales, Phys. Rev. Lett. 68 (1992) 754 neutrino data and leptogenesis, JHEP 09 (2003) 021 [hep-ph/0305322] [INSPIRE]. Phys. Rev. Lett. 96 (2006) 061802 [hep-ph/0509299] [INSPIRE]. neutrino mass, JHEP 01 (2007) 043 [hep-ph/0609046] [INSPIRE]. Matter, Nucl. Phys. B 787 (2007) 152 [arXiv:0706.4071] [INSPIRE]. 112001 [arXiv:1203.4030] [INSPIRE]. Report: Neutrinos, arXiv:1310.4340 [INSPIRE]. [arXiv:1305.4391] [INSPIRE]. (2014) 253 [arXiv:1307.0162] [INSPIRE]. + in Super-Kamiokande, Phys. Rev. Lett. 113 (2014) 121802 SO(10) Uni cation with a Left-Right Symmetric Seesaw Mechanism, Nucl. Phys. B 809 (2009) 183 [arXiv:0808.2058] [INSPIRE]. [arXiv:1312.2878] [INSPIRE]. Number Nonconservation and GUT Mechanism for Baryogenesis, Phys. Lett. B 191 (1987) 171 [INSPIRE]. 48 (1993) 5006 [hep-ph/9305290] [INSPIRE]. Phys. Lett. B 345 (1995) 248 [Erratum ibid. B 384 (1996) 487] [hep-ph/9411366] Majorana neutrinos, Phys. Lett. B 389 (1996) 693 [hep-ph/9607310] [INSPIRE]. Nucl. Phys. B 504 (1997) 61 [hep-ph/9702393] [INSPIRE]. 389 (1996) 73 [hep-ph/9608308] [INSPIRE]. Lett. B 431 (1998) 354 [hep-ph/9710460] [INSPIRE]. baryogenesis, Phys. Lett. B 547 (2002) 128 [hep-ph/0209301] [INSPIRE]. Nucl. Phys. B 575 (2000) 61 [hep-ph/9911315] [INSPIRE]. universe, Phys. Rev. D 65 (2002) 043512 [hep-ph/0109030] [INSPIRE]. low-energies, Nucl. Phys. B 643 (2002) 229 [hep-ph/0206174] [INSPIRE]. Minimal scenarios for leptogenesis and CP-violation, Phys. Rev. D 67 (2003) 073025 [hep-ph/0211001] [INSPIRE]. Lett. B 458 (1999) 73 [hep-ph/9812276] [INSPIRE]. matter in hybrid seesaw, Phys. Rev. D 79 (2009) 033010 [arXiv:0811.0953] [INSPIRE]. leptogenesis, Phys. Lett. B 535 (2002) 25 [hep-ph/0202239] [INSPIRE]. [hep-ph/0502082] [INSPIRE]. right-handed neutrino mass hierarchy, Phys. Rev. D 73 (2006) 073006 [hep-ph/0512160] leptogenesis and the tauon N2-dominated scenario, Nucl. Phys. B 849 (2011) 521 [arXiv:1007.1641] [INSPIRE]. N2-dominated leptogenesis, Nucl. Phys. B 856 (2012) 180 [arXiv:1003.5132] [INSPIRE]. avours: from density matrix to Boltzmann equations, JCAP 01 (2013) 041 Rev. Lett. 80 (1998) 5716 [hep-ph/9802445] [INSPIRE]. systematic approach, JCAP 08 (2014) 003 [arXiv:1401.4347] [INSPIRE]. and leptogenesis, Nucl. Phys. B 602 (2001) 23 [hep-ph/0011192] [INSPIRE]. Phys. Rev. D 49 (1994) 2118 [hep-ph/9307279] [INSPIRE]. 315 (2005) 305 [hep-ph/0401240] [INSPIRE]. Matters in Leptogenesis, JHEP 09 (2006) 010 [hep-ph/0605281] [INSPIRE]. Equations: an Application to Resonant Leptogenesis, Nucl. Phys. B 886 (2014) 569 [arXiv:1404.1003] [INSPIRE]. Number Nonconservation, Nucl. Phys. B 308 (1988) 885 [INSPIRE]. electroweak fermion number violation, Phys. Rev. D 42 (1990) 3344 [INSPIRE]. from precision cosmology to fundamental physics, Phys. Rept. 472 (2009) 1 [arXiv:0809.0631] [INSPIRE]. Observations: Power Spectra and WMAP-Derived Parameters, Astrophys. J. Suppl. 192 (2011) 16 [arXiv:1001.4635] [INSPIRE]. 2012 (2012) 158303 [arXiv:1301.3062] [INSPIRE]. Dominance, JCAP 11 (2006) 011 [hep-ph/0609038] [INSPIRE]. other observable predictions with low-scale S4 symmetry, Phys. Rev. D 83 (2011) 093004 [arXiv:1011.4577] [INSPIRE]. Breaking, in proceedings of The 1979 Cargese Summer Institute on Recent Developments in Gauge Theories, G. 't Hooft et al. eds., Plenum Press, New York (1980), NATO Sci. Ser. B 59 (1980) 135 [INSPIRE]. 178 [hep-ph/0512090] [INSPIRE]. Wino Dark Matter Case Study, JCAP 07 (2014) 031 [arXiv:1401.6212] [INSPIRE]. parameters, Astron. Astrophys. 571 (2014) A16 [arXiv:1303.5076] [INSPIRE]. JHEP 10 (2014) 033 [Erratum ibid. 01 (2015) 041] [arXiv:1407.7058] [INSPIRE]. [arXiv:1009.5058] [INSPIRE]. experiment, Phys. Rev. Lett. 101 (2008) 091301 [arXiv:0805.2939] [INSPIRE]. Electroweak-Interacting Dark Matter with Higgs Boson and Its Phenomenology, Phys. Lett. B 742 (2015) 80 [arXiv:1410.3569] [INSPIRE]. (2008) 033002 [arXiv:0805.1613] [INSPIRE]. multi-lepton signals, Nucl. Phys. B 813 (2009) 22 [arXiv:0808.2468] [INSPIRE]. Rev. D 82 (2010) 053004 [arXiv:0904.2390] [INSPIRE]. [arXiv:0909.3240] [INSPIRE]. operation, J. Phys. Conf. Ser. 110 (2008) 062002 [INSPIRE]. rays with energies 1.5-100 GeV, Nature 458 (2009) 607 [arXiv:0810.4995] [INSPIRE]. Measured by PAMELA, Phys. Rev. Lett. 111 (2013) 081102 [arXiv:1308.0133] [INSPIRE]. spectrum from 20 GeV to 1 TeV with the Fermi Large Area Telescope, Phys. Rev. Lett. 102 in Primary Cosmic Rays of 0:5{500 GeV with the Alpha Magnetic Spectrometer on the International Space Station, Phys. Rev. Lett. 113 (2014) 121101 [INSPIRE]. emission from galaxy clusters, arXiv:1201.1003 [INSPIRE]. Perseus Cluster of Galaxies: Implications for Cosmic Rays, Dark Matter and NGC 1275, the Fermi Large Area Telescope, JCAP 05 (2010) 025 [arXiv:1002.2239] [INSPIRE]. [258] Fermi-LAT collaboration, S. Zimmer, J. Conrad and A. Pinzke, A Combined Analysis of Clusters of Galaxies | Gamma Ray Emission from Cosmic Rays and Dark Matter, with Fermi LAT Observations of Nearby Galaxy Clusters, JCAP 01 (2012) 042 Probe (WMAP) Observations: Cosmological Interpretation, Astrophys. J. Suppl. 180 (2009) [261] Atacama Cosmology Telescope collaboration, J.L. Sievers et al., The Atacama Cosmology Telescope: Cosmological parameters from three seasons of data, JCAP 10 (2013) [262] K.T. Story et al., A Measurement of the Cosmic Microwave Background Damping Tail from the 2500-square-degree SPT-SZ survey, Astrophys. J. 779 (2013) 86 [arXiv:1210.7231] Probe (WMAP) Observations: Cosmological Parameter Results, Astrophys. J. Suppl. 208 [264] N. Arkani-Hamed and S. Dimopoulos, Supersymmetric uni cation without low energy supersymmetry and signatures for ne-tuning at the LHC, JHEP 06 (2005) 073 [265] M. Cirelli and A. Strumia, Cosmology of neutrinos and extra light particles after WMAP3, Uni cation of Strong, Weak and Electromagnetic Interactions, Nucl. Phys. B 135 (1978) 66 Wess-Zumino Gauge, Nucl. Phys. B 245 (1984) 425 [INSPIRE]. With Super eld Techniques, Phys. Lett. B 177 (1986) 55 [INSPIRE]. branes, Phys. Rept. 441 (2007) 191 [hep-ph/0601023] [INSPIRE]. + 0 in a Large Water Cherenkov Detector, Phys. Rev. Lett. 102 [281] R.N. Mohapatra, A theorem on the threshold corrections in grand uni ed theories, Phys. GUT for fermion masses, Phys. Lett. B 622 (2005) 327 [hep-ph/0507045] [INSPIRE]. [1] ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [2] CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS [3] G.L. Fogli, E. Lisi, A. Marrone, D. Montanino, A. Palazzo and A.M. Rotunno, Global [4] T. Schwetz, M. Tortola and J.W.F. Valle, Global neutrino data and recent reactor uxes: status of three- avour oscillation parameters, New J. Phys. 13 (2011) 063004 [5] D.V. Forero, M. Tortola and J.W.F. Valle, Neutrino oscillations re tted, Phys. Rev. D 90 [6] M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Global Analyses of Neutrino Oscillation [7] WMAP collaboration, D.N. Spergel et al., First year Wilkinson Microwave Anisotropy [8] A. Abada, C. Biggio, F. Bonnet, M.B. Gavela and T. Hambye, [9] WMAP collaboration, G. Hinshaw et al., Five-Year Wilkinson Microwave Anisotropy [10] WMAP collaboration, E. Komatsu et al., Seven-Year Wilkinson Microwave Anisotropy [11] R. Kalita, D. Borah and M.K. Das, Corrections to Scaling Neutrino Mixing: Non-zero 13; CP and Baryon Asymmetry, Nucl. Phys. B 894 (2015) 307 [arXiv:1412.8333] [12] Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological [13] F. Zwicky, Die Rotverschiebung von extragalaktischen Nebeln, Helv. Phys. Acta 6 (1933) [14] WMAP collaboration, D.N. Spergel et al., Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology, Astrophys. J. Suppl. 170 (2007) [16] G.R. Blumenthal, S.M. Faber, J.R. Primack and M.J. Rees, Formation of Galaxies and [17] XENON10 collaboration, J. Angle et al., A search for light dark matter in XENON10 data, Phys. Rev. Lett. 107 (2011) 051301 [Erratum ibid. 110 (2013) 249901] [arXiv:1104.3088] [18] L.E. Strigari, Galactic Searches for Dark Matter, Phys. Rept. 531 (2013) 1 [19] H. Georgi, H.R. Quinn and S. Weinberg, Hierarchy of Interactions in Uni ed Gauge [20] H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 [21] H. Georgi, The State of the Art | Gauge Theories, AIP Conf. Proc. 23 (1975) 575 [22] H. Fritzsch and P. Minkowski, Uni ed Interactions of Leptons and Hadrons, Annals Phys. [23] J.C. Pati and A. Salam , Uni ed Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions , Phys. Rev . D 8 ( 1973 ) 1240 [INSPIRE]. [24] J.C. Pati and A. Salam , Lepton Number as the Fourth Color , Phys. Rev . D 10 ( 1974 ) 275 [25] R.N. Mohapatra and J.C. Pati , A Natural Left-Right Symmetry , Phys. Rev . D 11 ( 1975 ) [26] G. Senjanovic and R.N. Mohapatra , Exact Left-Right Symmetry and Spontaneous Violation [27] G. Senjanovic , Spontaneous Breakdown of Parity in a Class of Gauge Theories, Nucl . Phys. [28] F. del Aguila and L.E. Iban~ez, Higgs Bosons in SO(10) and Partial Uni cation, Nucl . Phys. [29] R.N. Mohapatra and G. Senjanovic , Higgs Boson E ects in Grand Uni ed Theories, Phys. [30] S. Dimopoulos , S. Raby and F. Wilczek , Supersymmetry and the Scale of Uni cation , Phys. [31] W.J. Marciano and G. Senjanovic , Predictions of Supersymmetric Grand Uni ed Theories, [32] U. Amaldi , U. De Boer and H. Furstenau , Consistency checks of GUTs with LEP data , [33] U. Amaldi , W. de Boer and H. Furstenau , Comparison of grand uni ed theories with electroweak and strong coupling constants measured at LEP , Phys. Lett . B 260 ( 1991 ) 447 [34] P. Langacker and M.-x. Luo, Implications of precision electroweak experiments for Mt , 0 , [35] J.R. Ellis , S. Kelley and D.V. Nanopoulos , A Detailed comparison of LEP data with the predictions of the minimal supersymmetric SU(5) GUT, Nucl . Phys . B 373 ( 1992 ) 55 [36] T. Fukuyama , A. Ilakovac , T. Kikuchi , S. Meljanac and N. Okada , SO(10) group theory for the uni ed model building , J. Math. Phys. 46 ( 2005 ) 033505 [hep-ph/0405300] [INSPIRE]. [37] B. Bajc , A. Melfo , G. Senjanovic and F. Vissani , The minimal supersymmetric grand uni ed theory . 1. Symmetry breaking and the particle spectrum , Phys. Rev. D 70 ( 2004 ) [38] C.S. Aulakh and A. Girdhar , SO(10) a la Pati-Salam , Int. J. Mod . Phys . A 20 ( 2005 ) 865 [39] B. Bajc , G. Senjanovic and F. Vissani , b [40] H.S. Goh , R.N. Mohapatra and S.-P. Ng , Minimal SUSY SO ( 10 ), b [41] C.S. Aulakh , B. Bajc , A. Melfo , G. Senjanovic and F. Vissani , The minimal supersymmetric [42] H.S. Goh , R.N. Mohapatra and S.-P. Ng , Minimal SUSY SO(10) model and predictions for neutrino mixings and leptonic CP-violation , Phys. Rev. D 68 (2003) 115008 [43] H.S. Goh , R.N. Mohapatra , S. Nasri and S.-P. Ng , Proton decay in a minimal SUSY SO(10) [44] T. Fukuyama , A. Ilakovac , T. Kikuchi and K. Matsuda , Neutrino oscillations in a [45] T. Fukuyama , A. Ilakovac , T. Kikuchi , S. Meljanac and N. Okada , Higgs masses in the [46] E. Witten , Mass Hierarchies in Supersymmetric Theories, Phys. Lett . B 105 ( 1981 ) 267 [47] S. Dimopoulos and H. Georgi , Solution of the Gauge Hierarchy Problem, Phys. Lett. B 117 [48] R.K. Kaul , Supersymmetric solution of gauge hierarchy problem , Pramana 19 ( 1982 ) 183. [49] R.K. Kaul , Gauge Hierarchy in a Supersymmetric Model , Phys. Lett . B 109 ( 1982 ) 19 [50] R.K. Kaul and P. Majumdar , Cancellation of Quadratically Divergent Mass Corrections in Globally Supersymmetric Spontaneously Broken Gauge Theories, Nucl . Phys . B 199 ( 1982 ) [51] E.B. Bogomolny , Calculation of the Green Functions by the Coupling Constant Dispersion [52] M. Gell-Mann , P. Ramond and R. Slansky , Complex Spinors and Uni ed Theories, Conf. [53] S.L. Glashow , The Future of Elementary Particle Physics, NATO Sci. Ser . B 61 ( 1980 ) 687 [54] T. Yanagida , Horizontal Symmetry And Masses Of Neutrinos, Conf. Proc. C 7902131 [55] R.N. Mohapatra and G. Senjanovic , Neutrino Mass and Spontaneous Parity Violation, [56] J. Schechter and J.W.F. Valle , Neutrino Masses in SU(2) [57] M. Magg and C. Wetterich , Neutrino Mass Problem and Gauge Hierarchy, Phys. Lett. B 94 [58] G. Lazarides , Q. Sha and C. Wetterich , Proton Lifetime and Fermion Masses in an [59] R.N. Mohapatra and G. Senjanovic , Neutrino Masses and Mixings in Gauge Models with [60] R. Frey , A. Richter , A. Schwierczinski , E. Spamer , O. Titze and W. Knu pfer, [61] R.N. Mohapatra , S. Nussinov and V.L. Teplitz , Mirror matter as sel nteracting dark [62] T. Hambye and G. Senjanovic , Consequences of triplet seesaw for leptogenesis , Phys. Lett. [64] L.M. Krauss and F. Wilczek , Discrete Gauge Symmetry in Continuum Theories, Phys. Rev. [65] S.P. Martin , Some simple criteria for gauged R-parity , Phys. Rev. D 46 ( 1992 ) R2769 [66] C.S. Aulakh , A. Melfo , A. Rasin and G. Senjanovic , Supersymmetry and large scale left-right symmetry , Phys. Rev. D 58 ( 1998 ) 115007 [hep-ph/9712551] [INSPIRE]. [67] K.S. Babu and R.N. Mohapatra , Predictive neutrino spectrum in minimal SO(10) grand uni cation , Phys. Rev. Lett . 70 ( 1993 ) 2845 [hep-ph/9209215] [INSPIRE]. [68] S. Bertolini , T. Schwetz and M. Malinsky , Fermion masses and mixings in SO(10) models and the neutrino challenge to SUSY GUTs, Phys . Rev . D 73 ( 2006 ) 115012 [69] A.S. Joshipura and K.M. Patel , Fermion Masses in SO(10) Models, Phys. Rev. D 83 ( 2011 ) [70] H. Georgi and C. Jarlskog , A New Lepton-Quark Mass Relation in a Uni ed Theory, Phys. [71] C.R. Das and M.K. Parida , New formulas and predictions for running fermion masses at higher scales in SM, 2 HDM and MSSM, Eur . Phys. J. C 20 ( 2001 ) 121 [hep-ph/0010004] [73] M.K. Parida and N.N. Singh , Low-energy formulas for neutrino masses with tan beta dependent hierarchy , Phys. Rev. D 59 ( 1999 ) 032002 [hep-ph/9710328] [INSPIRE]. [74] A.S. Joshipura and K.M. Patel , Yukawa coupling uni cation in SO(10) with positive [75] A.S. Joshipura and K.M. Patel , Viability of the exact tri-bimaximal mixing at MGUT in [76] A.S. Joshipura and K.M. Patel , Uni ed description of fermion masses with quasi-degenerate [77] G. Altarelli and G. Blankenburg , Di erent SO(10) Paths to Fermion Masses and Mixings, [78] P.M. Ferreira , W. Grimus , D. Jurciukonis and L. Lavoura , Flavour symmetries in a renormalizable SO(10) model, Nucl . Phys . B 906 ( 2016 ) 289 [arXiv:1510.02641] [INSPIRE]. [79] F. Feruglio , K.M. Patel and D. Vicino , An ordered anarchy from 5D SO(10), Nucl . Part. [80] F. Feruglio , K.M. Patel and D. Vicino , A realistic pattern of fermion masses from a [81] T. Fukuyama , N. Okada and H.M. Tran , Sparticle spectroscopy of the minimal SO( 10 ) [82] M.K. Parida , Intermediate left-right gauge symmetry, uni cation of couplings and fermion [83] N.G. Deshpande , E. Keith and T.G. Rizzo , SO(10) grand uni cation with a low -energy [84] M.K. Parida , Vanishing corrections on intermediate scale and implications for uni cation of [85] X. Ji , Y. Li and Y. Zhang , Atmospheric Neutrino Mixing and b ! s Transitions: Testing [86] X.-d. Ji, Y. -c . Li, R.N. Mohapatra , S. Nasri and Y. Zhang , Leptogenesis in Realistic SO( 10 ) [87] J.C. Pati , Leptogenesis and neutrino oscillations within a predictive G(224)=SO(10) [88] K.S. Babu , J.C. Pati and Z. Tavartkiladze , Constraining Proton Lifetime in SO(10) with [89] K.S. Babu , J.C. Pati and P. Rastogi , Lepton [90] M. Lindner , M.A. Schmidt and A. Yu . Smirnov, Screening of Dirac avor structure in the [91] B. Dutta , Y. Mimura and R.N. Mohapatra , Neutrino masses and mixings in a predictive SO(10) model with CKM CP-violation , Phys. Lett . B 603 ( 2004 ) 35 [hep-ph/0406262] [92] B. Dutta , Y. Mimura and R.N. Mohapatra , CKM CP-violation in a minimal SO(10) model for neutrinos and its implications , Phys. Rev. D 69 ( 2004 ) 115014 [hep-ph/0402113] [93] M. Malinsky , J.C. Romao and J.W.F. Valle , Novel supersymmetric SO(10) seesaw mechanism , Phys. Rev. Lett . 95 ( 2005 ) 161801 [hep-ph/0506296] [INSPIRE]. [94] P.S.B. Dev and R.N. Mohapatra , TeV Scale Inverse Seesaw in SO(10) and Leptonic Non-Unitarity E ects , Phys . Rev . D 81 ( 2010 ) 013001 [arXiv:0910.3924] [INSPIRE]. [95] K.S. Babu and R.N. Mohapatra , Determining Majorana Nature of Neutrino from Nucleon n oscillations , Phys. Rev. D 91 ( 2015 ) 013008 [arXiv:1408.0803] [96] S. Blanchet , P.S.B. Dev and R.N. Mohapatra , Leptogenesis with TeV Scale Inverse Seesaw in SO(10), Phys . Rev . D 82 ( 2010 ) 115025 [arXiv:1010.1471] [INSPIRE]. [97] K.S. Babu , J.C. Pati and Z. Tavartkiladze , Constraining Proton Lifetime in SO(10) with [98] T. Fukuyama and T. Kikuchi , Axion and right-handed neutrino in the minimal SUSY [99 ] M.C. Romao , SO(10) SUSY GUTs from M theory , PoS(PLANCK 2015)028 [INSPIRE]. [100] J. Hisano , Y. Muramatsu , Y. Omura and Y. Shigekami , Flavor physics induced by light Z0 [101] B.S. Acharya , K. Boz_ek , M. Crispim Rom~ao, S.F. King and C. Pongkitivanichkul , Neutrino [102] T. Fukuyama , T. Kikuchi and T. Osaka , Non-thermal leptogenesis and a prediction of [103] J. Ellis , M.A.G. Garcia , N. Nagata , D.V. Nanopoulos and K.A. Olive , Starobinsky-Like [104] G.K. Leontaris , N. Okada and Q. Sha , Non-minimal quartic in ation in supersymmetric [105] B. Bajc and A. Yu . Smirnov, Hidden avor symmetries of SO(10) GUT, Nucl . Phys . B 909 [106] S. Weinberg , Living in the Universe , in Universe or Multiverse, B.J. Carr ed., Cambridge [107] S.M. Barr , A New Approach to Flavor Symmetry and an Extended Naturalness Principle , [108] M.K. Parida , P.K. Patra and A.K. Mohanty , Gravity Induced Large Grand Uni cation Mass [109] B. Brahmachari , U. Sarkar , K. Sridhar and P.K. Patra , Higher dimensional operators to the [110] P.H. Frampton , Light leptoquarks as possible signature of strong electroweak uni cation , [111] P.H. Frampton , J.T. Liu and M. Yamaguchi , Bottom quark mass predictions in nonsupersymmetric SU(5) uni cation , Phys. Lett . B 277 ( 1992 ) 130 [INSPIRE]. [112] M.L. Kynshi and M.K. Parida , Higgs scalar in the grand desert with observable proton lifetime in SU(5) and small neutrino masses in SO(10), Phys . Rev . D 47 ( 1993 ) R4830 [113] M.L. Kynshi and M.K. Parida , Threshold e ects on intermediate mass and proton lifetime [114] P. Fileviez Perez , Fermion mixings versus D = 6 proton decay , Phys. Lett . B 595 ( 2004 ) [115] I. Dorsner and P. Fileviez Perez , Could we rotate proton decay away? , Phys. Lett. B 606 [116] I. Dorsner and P. Fileviez Perez , How long could we live? , Phys. Lett . B 625 ( 2005 ) 88 [117] I. Dorsner and P. Fileviez Perez , Uni cation without supersymmetry: Neutrino mass, proton decay and light leptoquarks, Nucl . Phys . B 723 ( 2005 ) 53 [hep-ph/0504276] [INSPIRE]. [118] B. Bajc and G. Senjanovic , Seesaw at LHC, JHEP 08 ( 2007 ) 014 [hep-ph/0612029] [119] B. Bajc , M. Nemevsek and G. Senjanovic , Probing seesaw at LHC, Phys. Rev . D 76 ( 2007 ) [120] E. Ma and D. Suematsu , Fermion Triplet Dark Matter and Radiative Neutrino Mass, Mod. [121] T. Aizawa , M. Ibe and K. Kaneta , Coupling Uni cation and Dark Matter in a Standard Model Extension with Adjoint Majorana Fermions , Phys. Rev . D 91 ( 2015 ) 075012 [122] M. Kadastik , K. Kannike and M. Raidal , Dark Matter as the signal of Grand Uni cation , [123] M. Kadastik , K. Kannike and M. Raidal , Matter parity as the origin of scalar Dark Matter , [124] T. Hambye , On the stability of particle dark matter, PoS(IDM2010)098 [arXiv:1012 .4587] [125] M. Frigerio and T. Hambye , Dark matter stability and uni cation without supersymmetry , [126] M.K. Parida , Radiative Seesaw in SO(10) with Dark Matter , Phys. Lett . B 704 ( 2011 ) 206 [128] C. Hagedorn , T. Ohlsson , S. Riad and M.A. Schmidt , Uni cation of Gauge Couplings in [129] D. Chang , R.N. Mohapatra and M.K. Parida , Decoupling Parity and SU(2)R Breaking Scales: A New Approach to Left-Right Symmetric Models , Phys. Rev. Lett . 52 ( 1984 ) 1072 [130] D. Chang , R.N. Mohapatra and M.K. Parida , A New Approach to Left-Right Symmetry Breaking in Uni ed Gauge Theories , Phys. Rev . D 30 ( 1984 ) 1052 [INSPIRE]. [131] D. Chang , R.N. Mohapatra and M.K. Parida , New Mechanism for Baryon Generation in SO(10) Models With Low Mass Wr Boson , Phys. Lett . B 142 ( 1984 ) 55 [INSPIRE]. [132] D. Chang , R.N. Mohapatra , J. Gipson , R.E. Marshak and M.K. Parida , Experimental Tests of New SO(10) Grand Uni cation, Phys. Rev. D 31 ( 1985 ) 1718 [INSPIRE]. [133] R.N. Mohapatra and M.K. Parida , Threshold e ects on the mass scale predictions in SO(10) models and solar neutrino puzzle , Phys. Rev. D 47 ( 1993 ) 264 [hep-ph/9204234] [INSPIRE]. [134] D.-G. Lee, R.N. Mohapatra, M.K. Parida and M. Rani, Predictions for proton lifetime in minimal nonsupersymmetric SO(10) models: An update, Phys. Rev. D 51 (1995) 229 [135] N.G. Deshpande, E. Keith and P.B. Pal, Implications of LEP results for SO(10) grand [136] S. Bertolini, L. Di Luzio and M. Malinsky, Intermediate mass scales in the non-supersymmetric SO(10) grand uni cation: A Reappraisal, Phys. Rev. D 80 (2009) [137] K.S. Babu, K. Schmitz and T.T. Yanagida, Pure gravity mediation and spontaneous B [138] K.S. Babu, B. Bajc and S. Saad, Yukawa Sector of Minimal SO(10) Uni cation, JHEP 02 [139] D. Meloni, T. Ohlsson and S. Riad, E ects of intermediate scales on renormalization group [140] D. Meloni, T. Ohlsson and S. Riad, Renormalization Group Running of Fermion [141] F. Buccella, M. Chianese, G. Mangano, G. Miele, S. Morisi and P. Santorelli, A neutrino [142] R. Lal Awasthi and M.K. Parida, Inverse Seesaw Mechanism in Nonsupersymmetric [144] R.L. Awasthi, M.K. Parida and S. Patra, Neutrino masses, dominant neutrinoless double [146] M.K. Parida, R.L. Awasthi and P.K. Sahu, Proton decay and new contribution to 0 2 [147] R.L. Awasthi, Prospects of experimentally reachable beyond Standard Model physics in [148] P.S. Bhupal Dev and R.N. Mohapatra, Uni ed explanation of the eejj, diboson and dijet [149] M.K. Parida and B. Sahoo, Planck-scale induced left-right gauge theory at LHC and [150] B. Sahoo and M.K. Parida, Low-mass right-handed gauge bosons from minimal grand uni ed [151] M.K. Parida and P.K. Patra, Spontaneous Compacti cation E ects in SO(10) With Low [152] M.K. Parida and B.P. Nayak, Singlet Fermion Assisted Dominant Seesaw with Lepton Flavor and Number Violations and Leptogenesis, Adv. High Energy Phys. 2017 (2017) [153] M. Heikinheimo, M. Raidal and C. Spethmann, Testing Right-Handed Currents at the LHC, [154] K.A. Olive, Supersymmetric Dark Matter or not, PoS(DSU2015)035 [arXiv:1604.07336] [155] Y. Mambrini, N. Nagata, K.A. Olive, J. Quevillon and J. Zheng, Dark matter and gauge [156] N. Nagata, Dark Matter and Gauge Coupling Uni cation in non-SUSY SO(10) Grand [157] N. Nagata, K.A. Olive and J. Zheng, Weakly-Interacting Massive Particles in [158] N. Nagata, K.A. Olive and J. Zheng, Asymmetric Dark Matter Models in SO(10), JCAP 02 [159] M. Lindner and M. Weiser, Gauge coupling uni cation in left-right symmetric models, Phys. [160] A. Pilaftsis , CP violation and baryogenesis due to heavy Majorana neutrinos , Phys. Rev . D [161] C. Arbelaez , M. Hirsch , M. Malinsky and J.C. Rom~ao, LHC-scale left-right symmetry and [162] C. Arbelaez , R. Longas , D. Restrepo and O. Zapata , Fermion dark matter from SO ( 10 ) [163] K.S. Babu and S.M. Barr , Natural suppression of Higgsino mediated proton decay in [164] J.R. Ellis , D.V. Nanopoulos and S. Sarkar , The Cosmology of Decaying Gravitinos, Nucl. [165] J. Ellis , D.V. Nanopoulos , K.A. Olive and S.-J. Rey , On the thermal regeneration rate for light gravitinos in the early universe, Astropart . Phys. 4 ( 1996 ) 371 [hep-ph/9505438] [166] V.S. Rychkov and A. Strumia , Thermal production of gravitinos , Phys. Rev. D 75 ( 2007 ) [167] S.K. Majee , M.K. Parida and A. Raychaudhuri , Neutrino mass and low-scale leptogenesis in [168] S.K. Majee , M.K. Parida , A. Raychaudhuri and U. Sarkar , Low intermediate scales for leptogenesis in SUSY SO(10) GUTs , Phys . Rev . D 75 ( 2007 ) 075003 [hep-ph/0701109] [169] M.K. Parida and A. Raychaudhuri , Inverse see-saw , leptogenesis, observable proton decay [170] S. Weinberg , E ective Gauge Theories , Phys. Lett . B 91 ( 1980 ) 51 [INSPIRE]. [171] L.J. Hall , Grand Uni cation of E ective Gauge Theories, Nucl . Phys . B 178 ( 1981 ) 75 [172] B.A. Ovrut and H.J. Schnitzer , The Decoupling Theorem and Minimal Subtraction , Phys. [173] M.K. Parida , Heavy Particle E ects in Grand Uni ed Theories With Fine Structure Constant Matching, Phys. Lett . B 196 ( 1987 ) 163 [INSPIRE]. [174] M.K. Parida and C.C. Hazra , Superheavy Higgs Scalar E ects in E ective Gauge Theories [176] M.K. Parida and P.K. Patra , Theorem on vanishing multiloop radiative corrections to [177] M.K. Parida , Threshold and compacti cation e ects in GUTS, Pramana 41 (Suppl.1) [178] A.E. Faraggi and E. Halyo , Cabibbo-Kobayashi-Maskawa mixing in superstring derived Standard-like Models, Nucl . Phys . B 416 ( 1994 ) 63 [hep-ph/9306235] [INSPIRE]. [179] E.K. Akhmedov , M. Frigerio and A. Yu . Smirnov, Probing the seesaw mechanism with [180] E.K. Akhmedov and M. Frigerio , Duality in Left-Right Symmetric Seesaw Mechanism , [182] M. Cirelli , A. Strumia and M. Tamburini , Cosmology and Astrophysics of Minimal Dark [183] Super-Kamiokande collaboration , H. Nishino et al., Search for Nucleon Decay into Charged Anti-lepton plus Meson in Super-Kamiokande I and II, Phys . Rev . D 85 ( 2012 ) [184] Super-Kamiokande collaboration , J.L. Raaf, Recent Nucleon Decay Results from Super-Kamiokande, Nucl. Phys. Proc. Suppl . 229 - 232 ( 2012 ) 559 [INSPIRE]. [185] J.L. Hewett et al., Fundamental Physics at the intensity frontier, arXiv:1205. 2671 [186] K.S. Babu et al., Working Group Report: Baryon Number Violation, arXiv:1311. 5285 [187] Intensity Frontier Neutrino Working Group, A. de Gouv^ea et al., Working Group [188] Super-Kamiokande collaboration , K. Abe et al., Search for Nucleon Decay via n ! [189] K. Abe et al., Calibration of the Super-Kamiokande Detector, Nucl. Instrum. Meth. A 737 [190] A. Abada , P. Hosteins , F.-X. Josse-Michaux and S. Lavignac , Successful Leptogenesis in [191] F. Capozzi , G.L. Fogli , E. Lisi , A. Marrone , D. Montanino and A. Palazzo , Status of three-neutrino oscillation parameters , circa 2013 , Phys. Rev . D 89 ( 2014 ) 093018 [192] V.A. Kuzmin , V.A. Rubakov and M.E. Shaposhnikov , Anomalous Electroweak Baryon [193] M.A. Luty , Baryogenesis via leptogenesis, Phys. Rev. D 45 ( 1992 ) 455 [INSPIRE]. [194] A. Acker , H. Kikuchi , E. Ma and U. Sarkar , CP violation and leptogenesis , Phys. Rev . D [195] M. Flanz , E.A. Paschos and U. Sarkar , Baryogenesis from a lepton asymmetric universe , [196] M. Flanz , E.A. Paschos , U. Sarkar and J. Weiss , Baryogenesis through mixing of heavy [197] A. Pilaftsis , Resonant CP-violation induced by particle mixing in transition amplitudes , [198] W. Buchmu ller and M. Plu macher, Baryon asymmetry and neutrino mixing , Phys. Lett . B [200] W. Buchmuller , P. Di Bari and M. Plumacher , A bound on neutrino masses from [201] W. Buchmuller , P. Di Bari and M. Plu macher, Cosmic microwave background, matter-antimatter asymmetry and neutrino masses, Nucl . Phys . B 643 ( 2002 ) 367 [Erratum ibid . B 793 ( 2008 ) 362] [hep-ph/0205349] [INSPIRE]. [202] R. Barbieri , P. Creminelli , A. Strumia and N. Tetradis , Baryogenesis through leptogenesis, [203] K. Hamaguchi , H. Murayama and T. Yanagida , Leptogenesis from N dominated early [204] T. Hambye , Leptogenesis at the TeV scale, Nucl . Phys . B 633 ( 2002 ) 171 [hep-ph/0111089] [205] J.R. Ellis and M. Raidal , Leptogenesis and the violation of lepton number and CP at [206] G.C. Branco , R. Gonzalez Felipe , F.R. Joaquim , I. Masina , M.N. Rebelo and C.A. Savoy , [207] E. Ma , S. Sarkar and U. Sarkar , Scale of SU(2)R symmetry breaking and leptogenesis , Phys. [208] P.-H. Gu , M. Hirsch , U. Sarkar and J.W.F. Valle , Neutrino masses, leptogenesis and dark [209] S. Davidson and A. Ibarra , A lower bound on the right-handed neutrino mass from [210] P. Di Bari , Seesaw geometry and leptogenesis, Nucl . Phys . B 727 ( 2005 ) 318 [211] O. Vives , Flavor dependence of CP asymmetries and thermal leptogenesis with strong [212] E. Bertuzzo , P. Di Bari and L. Marzola , The problem of the initial conditions in avoured [213] S. Antusch , P. Di Bari , D.A. Jones and S.F. King , A fuller avour treatment of [214] S. Blanchet , P. Di Bari , D.A. Jones and L. Marzola , Leptogenesis with heavy neutrino [215] S. Davidson , E. Nardi and Y. Nir , Leptogenesis, Phys. Rept. 466 ( 2008 ) 105 [216] L. Covi , E. Roulet and F. Vissani , CP violating decays in leptogenesis scenarios , Phys. Lett. [217] F. Buccella , D. Falcone , C.S. Fong , E. Nardi and G. Ricciardi , Squeezing out predictions with leptogenesis from SO(10), Phys . Rev . D 86 ( 2012 ) 035012 [arXiv:1203.0829] [218] E. Ma and U. Sarkar , Neutrino masses and leptogenesis with heavy Higgs triplets , Phys. [219] D. Aristizabal Sierra , M. Dhen and T. Hambye , Scalar triplet avored leptogenesis: a [220] T. Hambye , E. Ma and U. Sarkar , Supersymmetric triplet Higgs model of neutrino masses [221] P .J. O'Donnell and U. Sarkar , Baryogenesis via lepton number violating scalar interactions , [222] W. Buchmuller , P. Di Bari and M. Plu macher, Leptogenesis for pedestrians, Annals Phys. [223] A. Abada , S. Davidson , A. Ibarra , F.X. Josse-Michaux , M. Losada and A. Riotto , Flavour [224] P.S. Bhupal Dev , P. Millington , A. Pilaftsis and D. Teresi , Flavour Covariant Transport [225] S. Yu . Khlebnikov and M.E. Shaposhnikov , The Statistical Theory of Anomalous Fermion [226] J.A. Harvey and M.S. Turner , Cosmological baryon and lepton number in the presence of [227] F. Iocco , G. Mangano , G. Miele , O. Pisanti and P.D. Serpico , Primordial Nucleosynthesis : [228] D. Larson et al., Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) [229] C.S. Fong , E. Nardi and A. Riotto , Leptogenesis in the Universe , Adv. High Energy Phys. [230] S. Antusch , S.F. King and A. Riotto , Flavour-Dependent Leptogenesis with Sequential [231] M.K. Parida , P.K. Sahu and K. Bora , Flavor uni cation, dark matter, proton decay and [232] G. 't Hooft, Naturalness, Chiral Symmetry Breaking and Spontaneous Chiral Symmetry [233] M. Cirelli , N. Fornengo and A. Strumia , Minimal dark matter, Nucl . Phys . B 753 ( 2006 ) [235] Planck collaboration , P. A.R. Ade et al., Planck 2013 results. XVI. Cosmological [236] J. Hisano , S. Matsumoto , M. Nagai , O. Saito and M. Senami , Non-perturbative e ect on thermal relic abundance of dark matter , Phys. Lett . B 646 ( 2007 ) 34 [hep-ph/0610249] [237] M. Cirelli , F. Sala and M. Taoso , Wino-like Minimal Dark Matter and future colliders , [238] S. Mohanty , S. Rao and D.P. Roy , Relic density and PAMELA events in a heavy wino dark matter model with Sommerfeld e ect , Int. J. Mod. Phys. A 27 (2012) 1250025 [239] J. Angle et al., Limits on spin-dependent WIMP-nucleon cross-sections from the XENON10 [240] J. Hisano , D. Kobayashi , N. Mori and E. Senaha , E ective Interaction of [241] R. Franceschini , T. Hambye and A. Strumia , Type-III see-saw at LHC , Phys. Rev . D 78 [242] F. del Aguila and J.A. Aguilar-Saavedra , Distinguishing seesaw models at LHC with [243] A. Arhrib et al., Collider Signatures for Heavy Lepton Triplet in Type I+III Seesaw , Phys. [244] A. De Roeck et al., From the LHC to Future Colliders , Eur. Phys. J. C 66 ( 2010 ) 525 [245] A. De Roeck and R. Ent , Future Facilities Summary, arXiv:0910 .4753 [INSPIRE]. [246] PAMELA collaboration, M. Boezio et al., The PAMELA space experiment: First year of [247] PAMELA collaboration , O. Adriani et al., An anomalous positron abundance in cosmic [248] PAMELA collaboration , O. Adriani et al., Cosmic-Ray Positron Energy Spectrum [249] Fermi-LAT collaboration, A.A. Abdo et al., Measurement of the Cosmic Ray e+ + e [250] AMS collaboration, L. Accardo et al., High Statistics Measurement of the Positron Fraction [251] C.- H. Chen and T. Nomura , Inert Higgs Doublet Dark Matter in Type-II Seesaw, Nucl . [252] J. Han , C.S. Frenk , V.R. Eke , L. Gao and S.D.M. White , Evidence for extended gamma-ray [253] Z. Qin , H. Xu , J. Wang , Y. Wang , J. Gu and X.-p. Wu, Chandra Observation of a Weak Shock in the Galaxy Cluster A2556, Astrophys . J. 762 ( 2013 ) 22 [arXiv:1211.1134] [254] T. Andrade and D. Marolf , No chiral truncation of quantum log gravity? , JHEP 03 ( 2010 ) [255] MAGIC collaboration , J. Aleksic et al., MAGIC Gamma-Ray Telescope Observation of the [256] M. Ackermann et al., Constraints on Dark Matter Annihilation in Clusters of Galaxies with [257] L. Dugger , T.E. Jeltema and S. Profumo , Constraints on Decaying Dark Matter from Fermi Observations of Nearby Galaxies and Clusters , JCAP 12 ( 2010 ) 015 [arXiv:1009.5988] [259] X. Huang , G. Vertongen and C. Weniger , Probing Dark Matter Decay and Annihilation [260] WMAP collaboration, E. Komatsu et al., Five-Year Wilkinson Microwave Anisotropy [263] WMAP collaboration, G. Hinshaw et al., Nine-Year Wilkinson Microwave Anisotropy [266] Particle Data Group collaboration , K.A. Olive et al., Review of Particle Physics, Chin. [267] S.R. Coleman and E.J. Weinberg , Radiative Corrections as the Origin of Spontaneous Symmetry Breaking , Phys. Rev . D 7 ( 1973 ) 1888 [INSPIRE]. [268] Y. Aoki , C. Dawson , J. Noaki and A. Soni , Proton decay matrix elements with domain-wall [269] RBC-UKQCD collaboration, Y . Aoki et al., Proton lifetime bounds from chirally symmetric lattice QCD , Phys. Rev . D 78 ( 2008 ) 054505 [arXiv:0806.1031] [INSPIRE]. [270] Y. Aoki , E. Shintani and A. Soni , Proton decay matrix elements on the lattice , Phys. Rev. [271] A.J. Buras , J.R. Ellis , M.K. Gaillard and D.V. Nanopoulos , Aspects of the Grand [272] J.T. Goldman and D.A. Ross , How Accurately Can We Estimate the Proton Lifetime in an SU(5) Grand Uni ed Model?, Nucl . Phys . B 171 ( 1980 ) 273 [INSPIRE]. [273] J.R. Ellis , D.V. Nanopoulos and S. Rudaz , GUTs 3: SUSY GUTs 2, Nucl . Phys . B 202 [274] L.E. Iban ~ez and C. Mun~oz, Enhancement Factors for Supersymmetric Proton Decay in the [275] C. Mun ~oz, Enhancement Factors for Supersymmetric Proton Decay in SU(5) and SO ( 10 ) [276] B. Bajc , I. Dorsner and M. Nemevsek , Minimal SO ( 10 ) splits supersymmetry , JHEP 11 [277] P. Nath and P. Fileviez Perez , Proton stability in grand uni ed theories , in strings and in [278] Super-Kamiokande collaboration , H. Nishino et al., Search for Proton Decay via [279] S. Raby et al., DUSEL Theory White Paper, arXiv:0810 .4551 [INSPIRE]. [280] M. Shiozawa , Nucleon Decay Searches, talk presented at TAUP, Asilomar, CA, U.S.A., [282] M.-C. Chen , S. Dawson and T. Krupovnickas , Higgs triplets and limits from precision [283] R. Dermisek and S. Raby , Bi-large neutrino mixing and CP-violation in an SO(10) SUSY


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Standard coupling unification in SO(10), hybrid seesaw neutrino mass and leptogenesis, dark matter, and proton lifetime predictions, Journal of High Energy Physics, 2017, DOI: 10.1007/JHEP04(2017)075