Search

We consider the lattice formulation of SO(10) chiral gauge theory with left-handed Weyl fermions in the 16-dimensional spinor representation ($\underline{16}$) within the framework of the overlap fermion/Ginsparg–Wilson relation. We define a manifestly gauge-invariant path-integral measure for the left-handed Weyl field using all the components of the Dirac field, but the right-handed part of it is just saturated completely by inserting a suitable product of the SO(10)-invariant ’t Hooft vertices in terms of the right-handed field. The definition of the measure applies to all possible topological sectors of admissible link fields. The measure possesses all required transformation properties under lattice symmetries and the induced effective action is CP invariant. The global U(1) symmetry of the left-handed field is anomalous due to the non-trivial transformation of the measure, while that of the right-handed field is explicitly broken by the ’t Hooft vertices. There remains the issue of smoothness and locality in the gauge-field dependence of the Weyl fermion measure, but the question is well defined and the necessary and sufficient condition for this property is formulated in terms of the correlation functions of the right-handed auxiliary fields. In the weak gauge-coupling limit at least, all the auxiliary fields have short-range correlations and the question can be addressed further by Monte Carlo methods without encountering the sign problem. We also discuss the relations of our formulation to other approaches/proposals to decouple the species doubling/mirror degrees of freedom. These include the Eichten–Preskill model, the mirror-fermion model with overlap fermions, the domain-wall fermion model with the boundary Eichten–Preskill term, 4D topological insulator/superconductor with a gapped boundary phase, and the recent studies on the PMS phase/“mass without symmetry breaking”. We clarify the similarities and differences in the technical details and show that our proposal is a unified and well defined testing ground for that basic question.

We study $3$rd family Yukawa unification in the context of supersymmetric (SUSY) $\mathrm{SO}(10)$ GUTs and $\mathrm{SO}(10)$-motivated boundary conditions for the SUSY-breaking soft terms. We consider $\mu, Comment: 39 pages, 13 figures, 1 table, 2 appendices

In the minimal SUSY SU(5) GUT with $O(1)$ TeV SUSY particles and $O(1)$ or below self-coupling for the GUT-breaking Higgs field, the width of the dimension-6 proton decay is suppressed below the reach of Hyper-Kamiokande. In this paper, we point out that a SUSY SO(10) GUT which adopts only ${\bf 45}_{\rm H}+{\bf 16}_{\rm H}+{\bf \overline{16}}_{\rm H}$ GUT-breaking Higgs fields leads to an enhanced dimension-6 proton decay width detectable at Hyper-Kamiokande. The enhancement is because the SU(5)-breaking VEV of ${\bf 45}_{\rm H}$ arises due to Planck-suppressed terms, $W\propto ({\bf 45}_{\rm H}^2)^2/M_*+{\bf 45}_{\rm H}^4/M_*$, and is therefore substantially larger than the other VEVs that conserve SU(5). As a result, the $({\bf 3},{\bf 2},1/6)$ GUT gauge boson mass is about $1/5$ smaller than the $({\bf 3},{\bf 2},-5/6)$ GUT gauge boson mass and can induce a fast dimension-6 proton decay. Through a numerical analysis on threshold corrections of the GUT gauge bosons and the physical components of the GUT-breaking Higgs fields, we confirm that the dimension-6 proton decay can be within the reach of Hyper-Kamiokande., 15 pages

Here we correct some typesetting errors in affiliations.

The grand-unification gauge group SO(10) contains matter parity as a discrete subgroup. This symmetry could be at the origin of dark matter stability. The properties of the dark matter candidates depend on the path along which SO(10) is broken, in particular through Pati-Salam or left-right symmetric subgroups. We systematically determine the nonsupersymmetric dark matter scenarios that can be realized along the various paths. We emphasize that the dark matter candidates may have colored or electrically charged partners at low scale that belong to the same SO(10) multiplet. These states, which in many cases are important for coannihilation, could be observed more easily than the dark matter particle. We determine the structure of the tree-level and loop-induced mass splittings between the dark matter candidate and their partners and discuss the possible phenomenological implications.

A new solution is presented where the right-handed neutrino ν R in S O ( 10 ) pairs up with ν L to form a naturally light Dirac neutrino. It is based on the framework of E 6 → S O ( 10 ) × U ( 1 ) ψ , then S O ( 10 ) → S U ( 5 ) × U ( 1 ) χ .

We investigate the possibility of TeV-scale scalars as low energy remnants arising in the nonsupersymmetric SO(10) grand unification framework where the field content is minimal. We consider a scenario where the SO(10) gauge symmetry is broken into the gauge symmetry of the Standard Model (SM) through multiple stages of symmetry breaking, and a colored and hypercharged scalar χ picks a TeV-scale mass in the process. The last stage of the symmetry breaking occurs at the TeV-scale where the left-right symmetry, that is, SU(2)L⊗SU(2)R⊗U(1)B-L⊗SU(3)C, is broken into that of the SM by a singlet scalar field S of mass MS~1 TeV, which is a component of an SU(2)R-triplet scalar field, acquiring a TeV-scale vacuum expectation value. For the LHC phenomenology, we consider a scenario where S is produced via gluon-gluon fusion through loop interactions with χ and also decays to a pair of SM gauge bosons through χ in the loop. We find that the parameter space is heavily constrained from the latest LHC data. We use a multivariate analysis to estimate the LHC discovery reach of S into the diphoton channel.

We present in this paper the SO S pin library, which calculates an analytic decomposition of the Yukawa interactions invariant under SO(2N) in terms of an SU(N) basis. We make use of the oscillator expansion formalism, where the SO(2N) spinor representations are expressed in terms of creation and annihilation operators of a Grassmann algebra acting on a vacuum state. These noncommutative operators and their products are simulated in SO S pin through the implementation of doubly-linked-list data structures. These data structures were determinant to achieve a higher performance in the simplification of large products of creation and annihilation operators. We illustrate the use of our library with complete examples of how to decompose Yukawa terms invariant under SO(2N) in terms of SU(N) degrees of freedom for N = 2 and 5. We further demonstrate, with an example for SO(4), that higher dimensional field-operator terms can also be processed with our library. Finally, we describe the functions available in SO S pin that are made to simplify the writing of spinors and their interactions specifically for SO(10) models.

We study the flavour aspects of proton lifetime estimates in simple Grand unified models paying particular attention to their inherent fragility due to the notorious lack of control of some of the key parameters governing the relevant hard-process amplitudes. Among these, the theoretical uncertainties in the flavour structure of the baryon and lepton number violating charged currents due to the potential higher-order effects afflicting the matching of the underlying Yukawa couplings to the low-energy data often play a prominent role. Focusing on the minimal variants of the most popular unified models we study the potential instabilities of the corresponding proton lifetime estimates based on the renormalizable-level Yukawa fits with respect to the Planck-scale induced flavour effects. In particular, we perform a detailed numerical analysis of all minimal $SO(10)$ Yukawa sector fits available in the literature and show that the proton lifetime estimates based on these inputs exhibit a high degree of robustness with respect to moderate-size perturbations, well within the expected "improvement window" of the upcoming proton decay searches., Comment: 14 pages, 5 figures, major update focusing on comprehensibility, extended numerical analysis

Der erste Teil dieser Arbeit untersucht den Yukawa Sektor eines minimalen supersymmetrischen SO($_{10}$) Modells. Eine globale Analyse ergibt, dass die GUT Vorhersagen für Fermionmassen und deren Minschungsobservablen von jüngsten Daten aus Neutrinoexperimenten und Gittersimulationen angefochten werden. Weiterhin zeigt sich, dass die möglichen Werte für SUSY Schwellenkorrekturen zu den Yukawa Kopplungen erheblich eingeschränkt sind. Der zweite Teil befasst sich mit den Quantenkorrekturen von schweren Gluinos zum MSSM-Higgspotenzial. Die ausdrückliche Resummierung dieser Effekte zu allen Ordnungen der Störungstheorie zeigt den Zusammenhang zum Renormierungsschema der Topsquarks mit dem Ergbnis, dass für Niederenergieobservablen das $\textit{on-shell}$ Schema angewandt werden sollte. Ferner kann das $\textit{fine-tuning}$ im MSSM, verglichen mit dem Ergebnis in führender Ordnung, weniger drastisch sein, wenn diese Beiträge berücksichtigt werden.

We investigate the decoupling of heavy right handed neutrinos in the context of an SO(10) GUT model, where a remnant anomalous symmetry is $U(1)_{X}$. In this model the see-saw mechanism which generates the neutrino masses is intertwined with the Stueckelberg mechanism, which leaves the CP-odd phase of a very heavy Higgs in the low energy spectrum as an axion-like particle. Such pseudoscalar is predicted to be ultralight, in the $10^{-20}$ eV mass range. In this scenario, the remnant anomalous $X$ symmetry of the particles of the Standard Model is interpreted as due to the incomplete decoupling of the right handed neutrino sector. We illustrate this scenario including its realisation in the context of SO(10)., 18 pages, revised final version, acepted for pubblication on Physics Letters B

Publisher's version (útgefin grein), We present a minimal non-supersymmetric SO(10) GUT breaking directly to the Standard Model gauge group. Precise gauge coupling unification is achieved due to the presence of two color-octet scalars, one of which is accessible to LHC searches. Proton lifetime is predicted to be below 4.5 × 1034 years, which is within the projected five-year sensitivity of the proposed Hyper-Kamiokande experiment. We find that the Standard Model observables are reproduced to a reasonable accuracy in a numerical fit, which also predicts the unknown neutrino parameters. Finally, the two scalar representations stabilize the electroweak vacuum and the dark matter is comprised of axions, S.M.B. thanks the “Roland Gustafssons Stiftelse för teoretisk fysik” for partial financial support. T.O. acknowledges support by the Swedish Research Council (Vetenskapsrådet) through contract No. 2017-03934 and the KTH Royal Institute of Technology for a sabbatical period at the University of Iceland. M.P. thanks “Stiftelsen Olle Engkvist Byggmästare” for financial support through contract No. 2017/85 (179) as well as “Roland Gustafssons Stiftelse för teoretisk fysik”. Numerical computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC Center for High Performance Computing (PDC-HPC) at KTH Royal Institute of Technology in Stockholm, Sweden under project numbers PDC-2018-49 and SNIC 2018/3-559.

We explore the implications of LHC and cold dark matter searches for supersymmetric particle mass spectra in two different grand unified models with left-right symmetry, SO(10) and SU(4)c × SU(2)L × SU(2)R (4-2-2). We identify characteristic differences between the two scenarios, which imply distinct correlations between experimental measurements and the particular structure of the GUT group. The gauge structure of 4-2-2 enhances significantly the allowed parameter space as compared to SO(10), giving rise to a variety of coannihilation scenarios compatible with the LHC data, LSP dark matter and the ongoing muon g-2 experiment., The research of MG was supported by the Spanish MINECO, under grants FPA2014-53631- C-2-P and FPA2017-86380-P. RR is supported by the Ramon y Cajal program of the Spanish MICINN, the Elusives European ITN project (H2020-MSCA-ITN-2015//674896- ELUSIVES), the SOM Sabor y origen de la Materia (PROMETEOII/2014/050) and Centro de excelencia Severo Ochoa Program under grant SEV-2014-0398. QS acknowledges support by the DOE grant No. DE-SC0013880.

The classification method of the free fermionic heterotic string vacua is extended to models where the $SO(10)$ GUT symmetry is broken directly at the string scale to the Left-Right Symmetric subgroup. Our method involves using a fixed set of basis vectors which are defined by the boundary conditions assigned to the free fermions before enumerating the string vacua by varying the Generalised GSO (GGSO) projection coefficients. It allows the derivation of algebraic expressions for the GGSO projections for each sector that generates massless states in the models. This enables a computerised analysis of the entire massless spectrum of a given choice of GGSO projection coefficients. The total number of vacua in the class of models chosen is $2^{66}\approx 7.38 \times 10^{19}$. A statistical sampling is performed and a sample size of $10^{11}$ vacua with the Left-Right Symmetric gauge group is extracted. We present the results of the classification, noting that contrary to the previous classification of Pati-Salam models, no three generation exophobic models were found. The results obtained demonstrate the existence of three generation models with the necessary Higgs representations needed for viable spontaneous symmetry breaking, and with a leading top quark Yukawa coupling., 37 pages. 6 figures. Minor typographical corrections. Published version

In multi-field reheating after modular $j$-inflation we investigate the conditions under which baryogenesis via non-thermal leptogenesis can be successfully realized. We introduce three heavy right-handed neutrinos to the non-supersymmetric Standard Model of particle physics, assuming hierarchical neutrino masses. Considering a typical mass for the first right-handed neutrino of the order of $10^{11}~GeV$, suggested from the seesaw mechanism and also from concrete $SO(10)$ grand unification models, we obtain the allowed parameter space for viable baryogenesis. An upper bound for the inflaton mass as well as a lower bound for its branching ratio to the pair of lightest right-handed neutrinos are found and reported., 6 pages, 4 figures, current version accepted for publication in Eur. Phys. J. C

A $Z'$ gauge boson with mass around the (few) TeV scale is a popular example of physics beyond the Standard Model (SM) and can be a fascinating remnant of a Grand Unified Theory (GUT). Recently, $Z'$ models with non-universal couplings to the SM fermions due to extra vector-like states have received attention as potential explanations of the present $R_K$, $R_{K^{\ast}}$ anomalies; this includes GUT model proposals based on the $\mathrm{SO}(10)$ group. In this paper we further develop GUT models with a flavour non-universal low scale $Z'$ and clarify several outstanding issues within them. First, we successfully incorporate a realistic neutrino sector (with linear and/or inverse low scale seesaw mechanism), which was so far a missing ingredient. Second, we investigate in detail their compatibility with the $R_K$, $R_{K^{\ast}}$ anomalies; we find that the anomalies do not have a consistent explanation within such models. Third, we demonstrate that these models have other compelling phenomenological features; we study the correlations between the flavour violating processes of $\mu\to 3e$ and $\mu$-$e$ conversion in a muonic atom, showing how a GUT imprint could manifest itself in experiments., Comment: Revised version, published in NPB. New material, general conclusions unchanged. 30 pages, 4 figures, 2 tables

Gauge coupling unification and the stability of the Higgs vacuum are among two of the cherished features of low-energy supersymmetric models. Putting aside questions of naturalness, supersymmetry might only be realised in nature at very high energy scales. If this is the case, the preservation of gauge coupling unification and the stability of the Higgs vacuum would certainly require new physics, but it need not necessarily be at weak scale energies. New physics near the unification scale could in principle ensure Grand Unification, while new physics below $\mu \sim 10^{10}$ GeV could ensure the stability of the Higgs vacuum. Surprisingly however, we find that in the context of a supersymmetric SO(10) Grand Unified Theory, gauge coupling unification and the Higgs vacuum stability, when taken in conjunction with existing phenomenological constraints, require the presence of $\mathcal{O}$(TeV)-scale physics. This weak-scale physics takes the form of a complex scalar SU(2)$_L$ triplet with zero hypercharge, originating from the $\mathbf{210}$ of SO(10)., Comment: 30 pages, 20 figures

We study and compare various Z′ models arising from SO(10), focusing in particular on the Abelian subgroup U(1)R×U(1)B-L, broken at the TeV scale to Standard Model hypercharge U(1)Y. The gauge group U(1)R×U(1)B-L, which is equivalent to the U(1)Y×U(1)χ in a different basis, is well motivated from SO(10) breaking and allows neutrino mass via the linear seesaw mechanism. Assuming supersymmetry, we first consider single step gauge unification to predict the gauge couplings, then we consider the detection and characterization prospects of the resulting Z′ at the LHC by studying its possible decay modes into di-leptons as well as into Higgs bosons. The main new result here is to analyse in detail the expected leptonic forward-backward asymmetry at the high luminosity LHC and show that it may be used to discriminate the U(1)R×U(1)B-L model from the usual B-L model based on U(1)Y×U(1)B-L.

Supersymmetric $SO(10)$ models with Yukawa coupling matrices involving only a $10_H$ and a $\overline{126}_H$ of Higgs fields can lead to a predictive and consistent scenario for fermion masses and mixings, including the neutrino sector. However, when coupled minimally to a symmetry breaking sector that includes a $210_H$ and a $126_H$, these models lead either to an unacceptably small neutrino mass scale, or to non-perturbative values of the gauge couplings. Here we show that with the addition of a $54_H$ to the symmetry breaking sector, the successful predictions of these models for fermion masses and mixings can be maintained. The $54_H$ enables a reduction of the $B-L$ symmetry breaking scale to an intermediate value of order $10^{12}$ GeV, consistent with the observed neutrino mass spectrum, while preserving perturbative gauge coupling unification. We obtain an excellent fit to all fermion masses and mixings in this framework. We analyze carefully the prediction of the model for CP violation in neutrino oscillations. Consistency with proton lifetime, however, requires a mini-split SUSY spectrum with the squarks and sleptons having masses of order 100 TeV, accompanied by TeV scale gauginos and Higgsinos. Such a spectrum may arise from pure gravity mediation, which would predict the partial lifetime for the decay $p \rightarrow \overline{\nu} K^+$ to be an order of magnitude above the current experimental limit., Comment: 29 pages, 3 figures, replacement to match the published version

The relation between the mixing matrices of leptons and quarks: $U_{\rm{PMNS}} \approx V_{\rm{CKM}}^\dagger U_0$, where $U_0$ is a matrix of special forms (e.g. BM, TBM), can be a clue for understanding the lepton mixing and neutrino masses. It may imply the Grand unification and existence of a hidden sector with certain symmetry which generates $U_0$ and leads to the smallness of neutrino masses. We apply the residual symmetry approach to obtain $U_0$. The residual symmetries of both the visible and hidden sectors are $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$. Their embedding in a unified flavor group is considered. We find that there are only several possible structures of $U_0$, including the BM mixing and matrices with elements determined by the golden ratio. Realization of the BM scenario based on the $SO(10)$ GUT with the $S_4$ flavor group is presented. Generic features of this scenario are discussed, in particular, the prediction of CP phase $144^{\circ}\lesssim\delta_{\rm CP}\lesssim 210^{\circ}$ in the minimal version., Comment: 19 pages, 1 figure, Consideration of the CKM mixing in sect. V modified, references added

We study the correlation between proton lifetime and leptonic CP violation in a class of renormalizable supersymmetric SO(10) grand unified theories (GUTs) with {\bf 10}, {\bf 126} and {\bf 120} Higgs fields, which provides a unified description of all fermion masses and possibly resolution of the strong CP problem. This specific model is unique in that it can readily be compatible with current proton lifetime limits for a supersymmetry (SUSY) breaking scale as low as 5 TeV due to the presence of a specific Yukawa texture. Our investigation here reveals that proton partial lifetimes predicted by this class of models will be tested by forthcoming proton decay searches; furthermore, a discovery of leptonic CP violation in neutrino oscillations would also lead to substantial reduction of the parameter space of the model., 28 pages, 12 figures. arXiv admin note: text overlap with arXiv:1506.08468, arXiv:1601.06478

We solve the Goldstone modes in the renormalizable SUSY SO(10) model with general couplings. The Goldstones are expressed by the Vacuum Expectation Values and the Clebsch-Gordan coefficients of relevant symmetries without explicit dependence on the parameters of the model., 27 pages. Only arXiv number for [38] added

The grand unification theories based on SO(10) gauge group have been at the centre of attraction to beyond Standard Model phenomenology. The SO(10) gauge symmetry may pass through several intermediate symmetries before breaking to Standard Model. Therefore some higher symmetries may occur at the experimentally reachable scales. This feature flourishes easily in non-supersymmetric models compared to supersymmetric ones. We find that certain breaking chains give tremendous predictions for the physics being explored at various particle physics experiments. Explanation to neutrino masses through TeV scale inverse see-saw is the driving theme of the models studied.

Let $G$ be a compact connected Lie group and $p : E\to \Sigma A$ be a principal G-bundle with a characteristic map $\alpha : A\to G$, where $A=\Sigma A_{0}$ for some $A_{0}$. Let $\{K_{i}{\to} F_{i-1}{\hookrightarrow} F_{i} \,|\, 1{\le} i {\le} n,\, F_{0}{=} \{\ast\} \; F_{1}{=} \Sigma{K_{1}} \; \text{and}\; F_{n}{\simeq} G \}$ be a cone-decomposition of $G$ of length $m$ and $F'_{1}=\Sigma{K'_{1}} \subset F_{1}$ with $K'_{1} \subset K_{1}$ which satisfy $F_{i}F'_{1} \subset F_{i+1}$ up to homotopy for any $i$. Our main result is as follows: we have $\operatorname{cat}(X) \le m{+}1$, if firstly the characteristic map $\alpha$ is compressible into $F'_{1}$, secondly the Berstein-Hilton Hopf invariant $H_{1}(\alpha)$ vanishes in $[A, \Omega F'_1{\ast}\Omega F'_1]$ and thirdly $K_{m}$ is a sphere. We apply this to the principal bundle $\mathrm{SO}(9)\hookrightarrow\mathrm{SO}(10)\to S^{9}$ to determine L-S category of $\mathrm{SO}(10)$.

We show that a supersymmetric renormalizable theory based on gauge group SO(10) and Higgs system {\bf {10 $\oplus$ 210 $\oplus$ 126 $\oplus$ $\overline{\bf 126}$}} with no scale supergravity can lead to a Starobinsky kind of potential for inflation. Successful inflation is possible in the cases where the potential during inflation corresponds to $SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$, $SU(5)\times U(1)$ and flipped $SU(5)\times U(1)$ intermediate symmetry with a suitable choice of superpotential parameters. The reheating in such a scenario can occur via non perturbative decay of inflaton i.e. through "preheating". After the end of reheating, when universe cools down, the finite temperature potential can have a minimum which corresponds to MSSM., Comment: 6 pages, 2 figures, Replaced with version to appear in Phys Lett B

Using characters of finite group representations and monodromy of matter curves in F-GUT, we complete partial results in literature by building SO10 models with dihedral D 4 discrete symmetry. We first revisit the S 4 -and S 3 -models from the discrete group character view; then we extend the construction to D 4 . We find that there are three types of SO 10 × D 4 models depending on the ways the S 4 -triplets break down in terms of irreducible D 4 -representations: (α) as 1 + , − ⊕ 1 + , − ⊕ 1 − , + ; or ( β ) 1 + , + ⊕ 1 + , − ⊕ 1 − , − ; or also (γ) 1 + , − ⊕ 2 0 , 0 . Superpotentials and other features are also given.

We consider six-dimensional supergravity with gauge group $SO(10)\times U(1)_A$, compactified on the orbifold $T^2 / \mathbb{Z}_2$. Three quark-lepton generations arise as zero modes of a bulk $\bf16$-plet due to magnetic flux of the anomalous $U(1)_A$. Boundary conditions at the four fixed points break $SO(10)$ to subgroups whose intersection is the Standard Model gauge group. The gauge and Higgs sector consist of "split" $SO(10)$ multiplets. As consequence of the $U(1)_A$ flux, squarks and sleptons are much heavier than gauge bosons, Higgs bosons, gauginos and higgsinos. We thus obtain a picture similar to "split supersymmetry." The flavor structure of the quark and lepton mass matrices is determined by the symmetry breaking at the orbifold fixed points., Comment: 14 pages, 1 figure, clarifying paragraph added, to appear in PLB

We propose an SO ( 10 ) supersymmetric grand unified theory (SUSY GUT), where the SO ( 10 ) gauge symmetry breaks down to SU ( 3 ) c × SU ( 2 ) L × U ( 1 ) Y × U ( 1 ) X at the GUT scale and U ( 1 ) X is radiatively broken at the SUSY-braking scale. In order to achieve the observed Higgs mass around 126 GeV and also to satisfy constraints on flavor- and/or CP-violating processes, we assume that the SUSY-breaking scale is O ( 100 ) TeV , so that the U ( 1 ) X breaking scale is also O ( 100 ) TeV . One big issue in the SO ( 10 ) GUTs is how to realize realistic Yukawa couplings. In our model, not only 16-dimensional but also 10-dimensional matter fields are introduced to predict the observed fermion masses and mixings. The Standard-Model quarks and leptons are linear combinations of the 16- and 10-dimensional fields so that the U ( 1 ) X gauge interaction may be flavor-violating. We investigate the current constraints on the flavor-violating Z ′ interaction from the flavor physics and discuss prospects for future experiments.

Non-supersymmetric Grand Unified SO(10) × U(1)PQ models have all the ingredients to solve several fundamental problems of particle physics and cosmology — neutrino masses and mixing, baryogenesis, the non-observation of strong CP violation, dark matter, inflation — in one stroke. The axion — the pseudo Nambu-Goldstone boson arising from the spontaneous breaking of the U(1)PQ Peccei-Quinn symmetry — is the prime dark matter candidate in this setup. We determine the axion mass and the low energy couplings of the axion to the Standard Model particles, in terms of the relevant gauge symmetry breaking scales. We work out the constraints imposed on the latter by gauge coupling unification. We discuss the cosmological and phenomenological implications.

Alternative renormalizable minimal non-SUSY SO(10) GUT model is proposed. Instead of a ${\bf 126}$-dimensional Higgs field, a ${\bf 120}$-dimensional Higgs filed is ntroducedin addition to a ${\bf 10}$-dimensional Higgs field and plays a crucial role to reproduce the realistic charged fermion mass matrices. With contributions of ${\bf 120}$ Higgs field, the original Witten's scenario of inducing the right-handed Majorana neutrino mass through 2-loop diagrams becomes phenomenologically viable. This model inherits the nice features of the conventional renormalizable minimal SO(10) GUT model with ${\bf 10}+{\bf \overline{126}}$ Higgs fields, while supplemented with a low scale seesaw mechanism due to the 2-loop induced right-handed Majorana neutrino mass. %, Comment: 12 pages, 1 figure, errors are corrected and references are added

We suggest simple ways of implementing Peccei-Quinn (PQ) symmetry to solve the strong CP problem in renormalizable SUSY $SO(10)$ models with a minimal Yukawa sector. Realistic fermion mass generation requires that a second pair of Higgs doublets survive down to the PQ scale. We show how unification of gauge couplings can be achieved in this context. Higgsino mediated proton decay rate is strongly suppressed by a factor of $(M_{\rm PQ}/M_{\rm GUT})^2$, which enables all SUSY particles to have masses of order TeV. With TeV scale SUSY spectrum, $p \rightarrow \overline{\nu} K^+$ decay rate is expected to be in the observable range. Lepton flavor violating processes $\mu \rightarrow e\gamma$ decay and $\mu-e$ conversion in nuclei, induced by the Dirac neutrino Yukawa couplings, are found to be within reach of forthcoming experiments., Comment: 38 pages, 4 figures, replacement to match with the published version

We consider the minimal supersymmetric grand unified model (MSGUT) based on the group $\mathrm{SO}(10)$, and study conditions leading to possible domain wall (DW) formation. It has been shown earlier that the supersymmetry preserving vacuum expectation values (vev's) get mapped to distinct but degenerate set of vev's under action of $D$ parity, leading to formation of domain walls as topological pseudo-defects. The metastability of such walls can make them relatively long lived and contradict standard cosmology. Thus we are led to consider adding a nonrenormalisable Planck scale suppressed operator, that breaks $\mathrm{SO}(10)$ symmetry but preserves Standard Model symmetry. For a large range of right handed breaking scales $M_R$, this is shown to give rise to the required pressure difference to remove the domain walls without conflicting with consistent big bang nucleosynthesis (BBN) while avoiding gravitino overproduction. However, if the walls persist till the onset of weak (thermal) inflation, then a low $\sim 10 - 100$ TeV $M_R$ becomes problematic., Comment: 20 pages, 2 tables

We confront recent experimental results on neutrino mixing parameters with the requirements from strong thermal $SO(10)$-inspired leptogenesis, where the asymmetry is produced from next-to-lightest right-handed neutrinos $N_2$ independently of the initial conditions. There is a nice agreement with latest global analyses supporting $\sin\delta < 0$ and normal ordering at $ \sim 95\%$ C.L. On the other hand, the more stringent experimental lower bound on the atmospheric mixing angle starts to corner strong thermal $SO(10)$-inspired leptogenesis. Prompted and encouraged by this rapid experimental advance, we obtain a precise determination of the allowed region in the plane $\delta$ versus $\theta_{23}$. We confirm that for the benchmark case $\alpha_2 \equiv m_{D2} / m_{\rm charm}= 5 \, $, where $m_{D2}$ is the intermediate neutrino Dirac mass setting the $N_2$ mass, and initial pre-existing asymmetry $N_{B-L}^{\rm p, i} = 10^{-3}$, the bulk of solutions lies in the first octant. Though most of the solutions are found outside the $95\%$ C.L. experimental region, there is still a big allowed fraction that does not require a too fine-tuned choice of the Majorana phases so that the neutrinoless double beta decay effective neutrino mass allowed range is still $m_{ee}\simeq [10,30]\,{\rm meV}$. We also show how the constraints depend on $N_{B-L}^{\rm p, i}$ and $\alpha_2$. In particular, we show that the current best fit, ($\theta_{23},\delta)\simeq (47^{\circ}, -130^{\circ})$, can be reproduced for $N_{B-L}^{\rm p, i} = 10^{-3}$ and $\alpha_2 = 6$. Such large values for $\alpha_2$ have been recently obtained in a few realistic fits within $SO(10)$-inspired models. Finally, we also obtain that current neutrino data rule out $N_{B-L}^{\rm p, i} \gtrsim 0.1$ for $\alpha_2 \lesssim 4.7$., Comment: 21 pages, 5 figures. v2: matching version to be published in JHEP. arXiv admin note: text overlap with arXiv:1705.01935

In this talk, we investigate predictions of the SO(10) Grand Unified Theory (GUT), where an extra U(1)' gauge symmetry remains up to the supersymmetry (SUSY) breaking scale. The minimal setup of SO(10) GUT unifies quarks and leptons into a 16-representational field in each generations. The setup, however, suffers from the realization of the realistic Yukawa couplings at the electroweak scale. In order to solve this problem, we introduce 10-representational matter fields, and then the two kinds of matter fields mix with each other at the SUSY breaking scale, where the extra U(1)' gauge symmetry breaks down radiatively. One crucial prediction is that the Standard Model quarks and leptons are given by the linear combinations of the fields with two different U(1)' charges. The mixing also depends on the flavor. Consequently, the U(1)' interaction becomes flavor violating, and the flavor physics is the smoking-gun signal of our GUT model. The flavor violating Z' couplings are related to the fermion masses and the CKM matrix, so that we can derive some explicit predictions in flavor physics. We especially discuss $K$-$\overline{K}$ mixing, $B_{(s)}$-$\overline{B_{(s)}}$ mixing and the (semi)leptonic decays of $K$ and $B$ in our model. We also study the flavor violating $\mu$ and $\tau$ decays and discuss the correlations among the physical observables in this SO(10) GUT framework.

We apply the perturbative grand unification due to renormalization to distinguish TeV-scale relics of supersymmetric $\rm{SO}(10)$ scenarios. With rational theoretical constraints taken into account, we find that for the breaking pattern of either $\rm{SU}(5)$ or Pati-Salam only extra matter $\mathbf{16}$ supermultiplet of $SO(10)$ can appear at TeV scale, apart from MSSM spectrum., Typos corrected, Refs added, to match the published version

We examine a renormalizable SUSY SO(10) model without fine-tuning. We show how to construct MSSM doublets and to predict proton decay. We find that in the minimal set of Yukawa couplings the model is consistent with the experiments, while including $120_H$ to fit the data there are inconsistencies., Comment: 18 pages

We show that a renormalizable theory based on gauge group SO(10) and Higgs system 10 $$\oplus $$ 210 $$\oplus $$ 126 $$\oplus $$ $${\overline{\mathbf{126}}}$$ with no scale supergravity can lead to a Starobinsky kind of potential for inflation. Successful inflation is possible in cases where the potential during inflation corresponds to $$SU(3)_\mathrm {C} \times SU(2)_\mathrm {L} \times SU(2)_\mathrm {R} \times U(1)_{\mathrm {B-L}}$$ , $$SU(5)\times U(1)$$ and flipped $$SU(5)\times U(1)$$ symmetries with suitable choice of superpotential parameters. The reheating in such a scenario can occur via non-perturbative decay of inflaton, i.e. through ‘preheating’. After the end of reheating, when Universe cools down, the finite-temperature potential can have a minimum which corresponds to MSSM.

We propose a natural S 4 × SO(10) supersymmetric grand unified theory of flavour with an auxiliary $$ {\mathbb{Z}}_4^2\times {\mathbb{Z}}_4^R $$ symmetry, based on small Higgs representations (nothing larger than an adjoint) and hence a type-I seesaw mechanism. The Yukawa structure of all fermions is determined by the hierarchical vacuum expectation values of three S 4 triplet flavons, with CSD3 vacuum alignments, where up-type quarks and neutrinos couple to one Higgs 10, and the down-type quarks and charged leptons couple to a second Higgs 10. The Yukawa matrices are obtained from sums of low-rank matrices, where each matrix in the sum naturally accounts for the mass of a particular family, as in sequential dominance in the neutrino sector, which predicts a normal neutrino mass hierarchy. The model accurately fits all available quark and lepton data, with predictions for the leptonic CP phase in 95% credible intervals given by 281° < δ l < 308° and 225° < δ l < 253°. The model reduces to the MSSM, with the two Higgs doublets emerging from the two Higgs 10s without mixing, and we demonstrate how a μ term of $$ \mathcal{O}\left(\mathrm{T}\mathrm{e}\mathrm{V}\right) $$ can be realised, as well as doublet-triplet splitting, with Planck scale operators controlled by symmetry, leading to acceptable proton decay.

Grand Unified Theories (GUTs) are a very well motivated extensions of the Standard Model (SM), but the landscape of models and possibilities is overwhelming, and different patterns can lead to rather distinct phenomenologies. In this work we present a way to automatise the model building process, by considering a top to bottom approach that constructs viable and sensible theories from a small and controllable set of inputs at the high scale. By providing a GUT scale symmetry group and the field content, possible symmetry breaking paths are generated and checked for consistency, ensuring anomaly cancellation, SM embedding and gauge coupling unification. We emphasise the usefulness of this approach for the particular case of a non-supersymmetric SO(10) model with an intermediate left-right symmetry and we analyse how low-energy observables such as proton decay and lepton flavour violation might affect the generated model landscape., 36 pages, 6 figures

A multiplicity of quark-lepton families can naturally arise as zero-modes in flux compactifications. The flavour structure of quark and lepton mass matrices is then determined by the wave function profiles of the zero-modes. We consider a supersymmetric $SO(10)\times U(1)$ model in six dimensions compactified on the orbifold $T^2/{\mathbb Z_2}$ with Abelian magnetic flux. A bulk $\mathbf{16}$-plet charged under the $U(1)$ provides the quark-lepton generations whereas two uncharged $\mathbf{10}$-plets yield two Higgs doublets. Bulk anomaly cancellation requires the presence of additional $\mathbf{16}$- and $\mathbf{10}$-plets. The corresponding zero-modes form vectorlike split multiplets that are needed to obtain a successful flavour phenomenology. We analyze the pattern of flavour mixings for the two heaviest families of the Standard Model and discuss possible generalizations to three and more generations., Comment: 28 pages, 3 figures, 3 tables

We discuss gauge coupling unification of the SM descending directly from SO(10) while providing solutions to the three outstanding problems: neutrino masses, dark matter, and the baryon asymmetry of the universe. Conservation of matter parity as gauged discrete symmetry 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. The seesaw formula predicts two distinct patterns of RH$\nu$ 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 RH$\nu$ masses. A complete flavor analysis has been carried out to compute CP-asymmetries and solutions to Boltzmann equations have been utilized 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 RH$\nu$ masses. The 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 $\sim 10^7$ GeV to achieve precision gauge coupling unification. Threshold corrections due to superheavy components of ${126}_H$ 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., Comment: 58 pages PDFLATEX, 19 Figures, Revised as suggested by JHEP Review

We calculate the prominent perturbative contributions shaping the one-loop scalar spectrum of the minimal non-supersymmetric renormalizable $SO(10)$ Higgs model whose unified gauge symmetry is spontaneously broken by an adjoint scalar. Focusing on its potentially realistic $45\oplus 126$ variant in which the rank is reduced by a VEV of the 5-index self-dual antisymmetric tensor, we provide a thorough analysis of the corresponding one-loop Coleman-Weinberg potential, paying particular attention to the masses of the potentially tachyonic pseudo-Goldstone bosons (PGBs) transforming as $(8,1,0)$ and $(1,3,0)$ under the Standard Model gauge group. The results confirm the assumed existence of extended regions in the parameter space supporting a locally stable SM-like quantum vacuum inaccessible at the tree-level. The effective potential (EP) tedium is compared to that encountered in the previously studied $45\oplus 16$ $SO(10)$ Higgs model where the polynomial corrections to the relevant pseudo-Goldstone masses turn out to be easily calculable within a very simplified purely diagrammatic approach.

We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an ${\it extended}$ non-supersymmetric SO(10) model, where the Higgs sector contains the ${\bf 10}_{\rm H}$, ${\bf 120}_{\rm H}$, and ${\bf 126}_{\rm H}$ representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale $M_{\rm I}$. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80 %. Furthermore, a similar evolution can be performed for a ${\it minimal}$ SO(10) model, where the Higgs sector consists of the ${\bf 10}_{\rm H}$ and ${\bf 126}_{\rm H}$ representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters., Comment: 24 pages, 3 figures, 3 tables. Final version published in JHEP

We implement type-II seesaw dominance for neutrino mass and baryogenesis through heavy scalar triplet leptogenesis in a class of minimal non-supersymmetric SO(10) models where matter parity as stabilising discrete symmetry as well as WIMP dark matter (DM) candidates are intrinsic predictions of the GUT symmetry. We also find modifications of relevant CP-asymmetry formulas in such minimal models. Baryon asymmetry of the universe as solutions of Boltzmann equations is further shown to be realized for both normal and inverted mass orderings in concordance with cosmological bound and best fit values of the neutrino oscillation data including $\theta_{23}$ in the second octant and large values of leptonic Dirac CP-phases. Type-II seesaw dominance is at first successfully implemented in two cases of spontaneous SO(10) breakings through SU(5) route where the presence of only one non-standard Higgs scalar of intermediate mass $\sim 10^9-10^{10}$ GeV achieves unification. Lower values of the SU(5) unification scales $\sim 10^{15}$ GeV are predicted to bring proton lifetimes to the accessible ranges of Super-Kamiokande and Hyper-Kamiokande experiments. Our prediction of WIMP DM relic density in each model is due to a $\sim$ TeV mass matter-parity odd real scalar singlet ($\subset {16}_H \subset$ SO(10)) verifiable by LUX and XENON1T experiments. This DM is also noted to resolve the vacuum stability issue of the standard scalar potential. When applied to the unification framework of M. Frigerio and T. Hambye, in addition to the minimal fermionic triplet DM solution of $2.7$ TeV mass, this procedure of type-II seesaw dominance and triplet leptogenesis is also found to make an alternative prediction of triplet fermion plus real scalar singlet DM at the TeV scale., Comment: 65 pages, 20 figures; version accepted by JCAP

We discuss a class of left–right symmetric models where the light neutrino masses originate dominantly from type-I seesaw mechanism along with a sub-dominant type-II seesaw contribution. The dominant type-I seesaw gives rise to tri-bimaximal type neutrino mixing, whereas sub-dominant type-II seesaw acts as a small perturbation giving rise to non-zero θ 13 in our model which also has TeV scale right-handed neutrinos and Z ′ gauge boson thereby making the model verifiable at current accelerator experiments. Sub-dominant type-II and dominant type-I seesaw can be naturally accommodated by allowing spontaneous breaking of D-parity and SU ( 2 ) R gauge symmetry at high scale and allowing TeV scale breaking of U ( 1 ) R × U ( 1 ) B − L into U ( 1 ) Y . We also embed the left–right model in a non-supersymmetric SO ( 10 ) grand unified theory (GUT) with verifiable TeV scale Z ′ gauge boson. Drawing it to an end, we scrutinize in detail the evaluation of one-loop renormalization group evolution for relevant gauge couplings and estimation of the proton life time which can be accessible to the foreseeable experiments. And in the aftermost part we make an estimation of branching ratio for lepton flavor violating process μ → e + γ as a function of type-II seesaw strength due to doubly charged component of the right-handed Higgs triplet with mass at the TeV scale, which can be accessible at ongoing experiments.

An analysis is given of B − L violating interactions in SO(10) arising from the integration of 10 + 10 ¯ of SU(5) of heavy Higgs. The analysis is done within the well defined missing partner model where the doublet-triplet splitting arises naturally. The Higgs representations of the model consist of two 10-plets, one 120, one 210 plet and a 126 + 126 ¯ representations of SO(10). The SO(10) symmetry is spontaneously broken by the singlet in the 126 + 126 ¯ and 210. In this work we focus on the B−L interactions arising from the elimination of 10 + 10 ¯ plets of SU(5). We compute five field and six field B−L violating operators. The analysis extends previous analyses where B−L violating interactions arising from the elimination of 5 + 5 ¯ and 45 + 45 ¯ were computed. Specifically we compute dimension 6, 7 and 9 operators. These interactions can generate GUT scale baryogengesis, proton decay, and n − n ¯ oscillations.

A mechanism to generate flavour hierarchy via five dimensional wave-function localization is revisited in the context of an SO(10) grand unified theory. An extra dimension compactified on an orbifold together with SO(10) breaking generates different profiles for massless modes of fermions of different charges. Utilizing a suitable scalar content, a predictive model of fermion masses and mixing is constructed and shown to be viable with the current data through a detailed numerical analysis. All the Yukawa couplings in the model are of order unity while the hierarchies among different fermions result from the wave-function profiles. The naturalness of anarchical Yukawa couplings is studied and the predictions for various observables in the lepton sector are derived. The scalar field content of the model is suitable to solve the doublet-triplet splitting problem through the missing partner mechanism.

We show that, within SO(10)SO(10)-inspired leptogenesis, there exists a solution, with definite constraints on neutrino parameters, able simultaneously to reproduce the observed baryon asymmetry and to satisfy the conditions for the independence of the final asymmetry of the initial conditions (strong thermal leptogenesis). We find that the wash-out of a pre-existing asymmetry as large as O(0.1)O(0.1) requires: (i) reactor mixing angle 2°??13?20°2°??13?20°, in agreement with the experimental result ?13=8°–10°?13=8°–10°; (ii) atmospheric mixing angle 16°??23?41°16°??23?41°, compatible only with current lowest experimentally allowed values; (iii) Dirac phase in the range ??/2????/5??/2????/5, with the bulk of the solutions around ????/5????/5 and such that sign(JCP)=?sign(?B)sign(JCP)=?sign(?B); (iv) neutrino masses mimi normally ordered; (v) lightest neutrino mass in the range m1?15–25 meVm1?15–25 meV, corresponding to ?imi?85–105 meV?imi?85–105 meV; (vi) neutrinoless double beta decay (0???0???) effective neutrino mass mee?0.8m1mee?0.8m1. All together this set of predictive constraints characterises the solution quite distinctively, representing a difficultly forgeable, fully testable, signature. In particular, the predictions mee?0.8m1?15 meVmee?0.8m1?15 meV can be tested by cosmological observations and (ultimately) by 0???0??? experiments. We also discuss different interesting aspects of the solution such as theoretical uncertainties, stability under variation of the involved parameters, forms of the orthogonal and RH neutrino mixing matrices.

Although SO(10) Supersymmetric (SUSY) Grand Unification Theories (GUTs) are very attractive for neutrino mass and mixing, it is often quite difficult to achieve successful leptogenesis from the lightest right-handed neutrino N 1 due to the strong relations between neutrino and up-type quark Yukawa couplings. We show that in a realistic model these constraints are relaxed, making N 1 leptogenesis viable. To illustrate this, we calculate the baryon asymmetry of the Universe Y B from flavoured N 1 leptogenesis in a recently proposed Δ(27) × SO(10) SUSY GUT. The flavoured Boltzmann equations are solved numerically, and comparison with the observed Y B places constraints on the allowed values of right-handed neutrino masses and neutrino Yukawa couplings. The flavoured SO(10) SUSY GUT is not only fairly complete and predictive in the lepton sector, but can also explain the BAU through leptogenesis with natural values in the lepton sector albeit with some tuning in the quark sector.