Search

We consider a class of $\text{SO}(10)$ models with flavor symmetries in the Yukawa sector and investigate their viability by performing numerical fits to the fermion masses and mixing parameters. The fitting procedure involves a top-down approach in which we solve the renormalization group equations from the scale of grand unification down to the electroweak scale. This allows the intermediate scale right-handed neutrinos and scalar triplet, involved in the type I and II seesaw mechanisms, to be integrated out at their corresponding mass scales, leading to a correct renormalization group running. The result is that, of the 14 models considered, only two are able to fit the known data well. Both these two models correspond to $\mathbb{Z}_2$ symmetries. In addition to being able to fit the fermion masses and mixing parameters, they provide predictions for the sum of light neutrino masses and the effective neutrinoless double beta decay mass parameter, which are both within current observational bounds., Comment: 19 pages, 4 tables. Final version published in JHEP

We study the connection between absolute neutrino mass and neutrino mixing parameters within $SO(10)$-inspired leptogenesis. We show that current favoured values of the unknown neutrino mixing parameters point toward values of the absolute neutrino mass scale that will be fully tested by cosmological observations and neutrinoless double beta decay experiments during next years. In particular, for $m_{D2}/m_{\rm charm} \leq 5$, where $m_{D2}$ is the intermediate Dirac neutrino mass, and for current best fit values of the Dirac phase $\delta$ and the atmospheric neutrino mixing angle $\theta_{23}$, we derive a lower bound on the neutrinoless double beta decay effective neutrino mass $m_{ee} \gtrsim 31\,{\rm meV}$ and on the sum of the neutrino masses $\sum_i m_i \gtrsim 125\,{\rm meV}$. These lower bounds hold for normally ordered neutrino masses, as currently favoured by global analyses and approximately for $\delta \in [155^\circ,240^\circ]$ and $\theta_{23}$ in the second octant. If values in this region will be confirmed by future planned long baseline experiments, then a signal at next generation neutrinoless double beta decay experiments is expected, despite neutrino masses being normally ordered. Outside the region, the lower bounds strongly relax but a great fraction of the allowed range of values still allows a measurement of the lightest neutrino mass. Therefore, in the the next years low energy neutrino experiments will provide a very stringent test of $SO(10)$-inspired leptogenesis, resulting either in severe constraints or in a strong evidence., Comment: 35 pages, 6 figures; v2: matching version submitted and to be published in JHEP

Since $\mathrm{SO}(10)$ GUTs unify all fermions of the Standard Model plus a right-chiral neutrino in a representation $\mathbf{16}$ per family, they have the potential to be maximally predictive regarding the ratios between the masses (or Yukawa couplings) of different fermion types, i.e.~the up-type quarks, down-type quarks, charged leptons and neutrinos. We analyze the predictivity of classes of $\mathrm{SO}(10)$ (SUSY) GUT models for the fermion mass ratios, where the Yukawa couplings for each family are dominated by a single effective GUT operator of the schematic form $\mathbf{16}^2\cdot\mathbf{45}^n\cdot\mathbf{210}^{m}\cdot\mathbf{H}$, for $\mathbf{H}\in\{\mathbf{10},\mathbf{120},\mathbf{\overline{126}}\}$. This extends previous works to general vacuum expectation value directions for GUT-scale VEVs and to larger Higgs representations. In addition, we show that the location of the MSSM Higgses in the space of all doublets is a crucial aspect to consider. We discuss highly predictive cases and illustrate the predictive power in toy models consisting of masses for the 3rd and 2nd fermion family., Comment: 47 pages, 12 figures, 12 tables

We explicitly test the asymptotic grand unification of a minimal 5-dimensional model with SO(10) gauge theory compactified on an $S^{1}/Z_{2}\times Z^{\prime}_{2}$ orbifold. We consider all matter fields as propagating in the bulk and show that the gauge couplings asymptotically run to a fixed point in the UV. However, the Yukawa couplings will typically hit a Landau pole right above the compactification scale in this class of SO(10) models., 6 pages, 1 figure, submitted to the PACP2022 conference proceedings

We combine $SO(10)$ Grand Unified Theories (GUTs) with $A_4$ modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. We focus on the case where the three fermion families in the 16 dimensional spinor representation form a triplet of $\Gamma_3\simeq A_4$, with a Higgs sector comprising a single Higgs multiplet $H$ in the ${\mathbf{10}}$ fundamental representation and one Higgs field $\overline{\Delta}$ in the ${\mathbf{\overline{126}}}$ for the minimal models, plus and one Higgs field $\Sigma$ in the ${\mathbf{120}}$ for the non-minimal models, all with specified modular weights. The neutrino masses are generated by the type-I and/or type II seesaw mechanisms and results are presented for each model following an intensive numerical analysis where we have optimized the free parameters of the models in order to match the experimental data. For the phenomenologically successful models, we present the best fit results in numerical tabular form as well as showing the most interesting graphical correlations between parameters, including leptonic CP phases and neutrinoless double beta decay, which have yet to be measured, leading to definite predictions for each of the models., Comment: 36 pages, 10 figures

We employ a variety of symmetry breaking patterns in $SO(10)$ and $E_6$ Grand Unified Theories to demonstrate the appearance of topological defects including magnetic monopoles, strings, and necklaces. We show that independent of the symmetry breaking pattern, a topologically stable superheavy monopole carrying a single unit of Dirac charge as well as color magnetic charge is always present. Lighter intermediate mass topologically stable monopoles carrying two or three quanta of Dirac charge can appear in $SO(10)$ and $E_6$ models respectively. These lighter monopoles as well as topologically stable intermediate scale strings can survive an inflationary epoch. We also show the appearance of a novel necklace configuration in $SO(10)$ broken to the Standard Model via $SU(4)_c\times SU(2)_L\times SU(2)_R$. It consists of $SU(4)_c$ and $SU(2)_R$ monopoles connected by flux tubes. Necklaces consisting of monopoles and antimonopoles joined together by flux tubes are also identified. Even in the absence of topologically stable strings, a monopole-string system can temporarily appear. This system decays by emitting gravity waves and we provide an example in which the spectrum of these waves is strongly peaked around $10^{-4}~{\rm Hz}$ with $\Omega_{\rm gw}h^2\simeq 10^{-12}$. This spectrum should be within the detection capability of LISA., Comment: 21 pages including 3 figures, major revision, version to be published in JHEP

Publisher's version (útgefin grein), We consider numerical fits to non-supersymmetric SO(10)-based models in which neutrino mass is generated by the type-I or type-II seesaw mechanism or a combination of both. The fits are performed with a sophisticated top-down procedure, taking into account the renormalization group equations of the gauge and Yukawa couplings, integrating out relevant degrees of freedom at their corresponding mass scales, and using recent data for the Standard Model observables. We find acceptable fits for normal neutrino mass ordering only and with neutrino mass generated by either type-I seesaw only or a combination of types I and II seesaw in which type-I seesaw is dominant. Furthermore, we find predictions from the best fit regarding the small neutrino masses, the effective neutrinoless double beta decay mass, and the leptonic CP-violating phase. Finally, we show that the fits are rather insensitive to the chosen value of the unification scale., The authors wish to thank Sofiane M. Boucenna for collaboration in early stages of this project. T.O. acknowledges support by the Swedish Research Council (Vetenskapsr˚adet) 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 Byggm¨astare” and “Roland Gustafssons Stiftelse f¨or teoretisk fysik” for financial support. 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 investigate the Yukawa coupling unification for the third generation in a class of SO(10) unified models which are consistent with the 4.2 σ deviation from the standard model of the muon g − 2 seen by the Fermilab experiment E989. A recent analysis in supergravity grand unified models shows that such an effect can arise from supersymmetric loops correction. Using a neural network, we further analyze regions of the parameter space where Yukawa coupling unification consistent with the Fermilab result can appear. In the analysis we take into account the contributions to Yukawas from the cubic and the quartic interactions. We test the model at the high luminosity and high energy LHC and estimate the integrated luminosities needed to discover sparticles predicted by the model.

In a class of gauged $U(1)$ extended Standard Models (SMs), the breaking of the $U(1)$ symmetry is not only a source for Majorana masses of right-handed (RH) neutrinos crucial for the seesaw mechanism, but also a source of stochastic gravitational wave (GW) background. Such $U(1)$ extended models are well-motivated from the viewpoint of grand unification. In this paper, we discuss a successful ultraviolet completion of a $U(1)$ extended SM by an $SO(10)$ grand unified model through an intermediate step of $SU(5) \times U(1)$ unification. With a parameter set that is compatible with the $SO(10)$ grand unification, we find that a first-order phase transition associated with the $U(1)$ symmetry breaking can be strong enough to generate GWs with a detectable size of amplitude. We also find that the resultant GW amplitude reduces and its peak frequency becomes higher as the RH neutrino masses increase., Comment: 24 pages, 3 figures, discussion and references added, the final journal published version

We consider a class of unified models based on the gauge group $\mathsf{SO(10)}$ which with appropriate choice of Higgs representations generate in a natural way a pair of light Higgs doublets needed to accomplish electroweak symmetry breaking. In this class of models higher dimensional operators of the form matter-matter-Higgs-Higgs in the superpotential after spontaneous breaking of the GUT symmetry generate contributions to Yukawa couplings which are comparable to the ones from cubic interactions. Specifically we consider an $\mathsf{SO(10)}$ model with a sector consisting of $\mathsf{126+\overline{126} + 210}$ of heavy Higgs which breaks the GUT symmetry down to the standard model gauge group and a sector consisting of $2\times \mathsf{10+120}$ of light Higgs fields. In this model we compute the corrections from the quartic interactions to the Yukawa couplings for the top and the bottom quarks and for the tau lepton. It is then shown that inclusion of these corrections to the GUT scale Yukawas allows for consistency of the top, bottom and tau masses with experiment for low $\tan\beta$ with a value as low as $\tan\beta$ of 5$-$10. We compute the sparticle spectrum for a set of benchmarks and find that satisfaction of the relic density is achieved via a compressed spectrum and coannihilation and three sets of coannihilations appear: chargino-neutralino, stop-neutralino and stau-neutralino. We investigate the chargino-neutralino coannihilation in detail for the possibility of observation of the light chargino at the high luminosity LHC (HL-LHC) and at the high energy LHC (HE-LHC) which is a possible future 27 TeV hadron collider. It is shown that all benchmark models but one can be discovered at HL-LHC and all would be discoverable at HE-LHC. The ones discoverable at both machines require a much shorter time scale and a lower integrated luminosity at HE-LHC., Comment: 27 pages, 5 figures and 9 tables

Grand Unified Theories (GUT) predict proton decay as well as the formation of cosmic strings which can generate gravitational waves. We determine which non-supersymmetric $SO(10)$ breaking chains provide gauge unification in addition to a gravitational signal from cosmic string decay. We calculate the GUT and intermediate scales for these $SO(10)$ breaking chains by solving the renormalisation group equations at the two-loop level. This analysis predicts the GUT scale, hence the proton lifetime, in addition to the scale of cosmic string generation and thus the associated gravitational wave signal. We determine which $SO(10)$ breaking chains survive in the event of the null results of the next generation of gravitational waves and proton decay searches and determine the correlations between proton decay and gravitational waves scales if these observables are measured., Comment: 39 pages, 8 figures, 7 tables, discussions and refs added, published in JHEP

We thank Paco del Aguila, Renato Fonseca, Luca Marzola and Davide Meloni for discussions and comments on the manuscript, and Jérémie Quevillon for collaboration at an early stage of the study. This work was supported by the Estonian Research Council grants MOBTT86 , PRG803 and by the EU through the European Regional Development Fund CoE program TK133 “The Dark Side of the Universe.” A.D. is also supported by the Junta de Andalucía through the Talentia Senior program as well as by A-FQM-211-UGR18 , and P18-FR-4314 ( FEDER )., We discuss the possibility of unifying in a simple and economical manner the Yukawa couplings of third generation fermions in a non-supersymmetric SO(10) model with an intermediate symmetry breaking, focusing on two possible patterns with intermediate Pati-Salam and minimal left-right groups. For this purpose, we assume a minimal Yukawa sector at high energy, starting with two Higgs bi-doublets at the intermediate scale which then simply reduce to a two Higgs doublet model at the electroweak scale. We first enforce gauge coupling unification at the two-loop level by including the threshold corrections in the renormalizationgroup running which are generated by the heavy fields that appear at the intermediate symmetry breaking scale. We then study the running of the Yukawa couplings of the top quark, bottom quark and tau lepton at two-loops in these two breaking schemes, when the appropriate matching conditions are imposed. We find that the unification of the third family Yukawa couplings can be achieved while retaining a viable spectrum, provided that the ratio of the vacuum expectation values of the two Higgs doublet fields is large, tanβ≈60., European Commission, Eesti Teadusagentuur, European Regional Development Fund, Junta de Andalucía A-FQM-211-UGR18, P18-FR-4314

The minimal realistic SO(10) model with the adjoint representation causing the GUT symmetry breaking is an appealing candidate for a realistic Grand Unified Theory. Moreover, the model allows one to make significant improvement in the proton lifetime error estimates due to the suppression of the potential gravitational effects influencing the GUT scale physics. We performed a comprehensive numerical study of the proton decay width including one-loop quantum effects mandatory in the physically relevant scenarios. The model’s study was also extended by improved perturbativity constraints. We present a thorough discussion of various consistency constraints that were used to asses theory's viability.

We study a renormalizable supersymmetric (SUSY) $SO(10)$ grand unified theory model where the Yukawa couplings of single ${\bf 10}$, single ${\bf \overline{126}}$, and single ${\bf 120}$ fields ($Y_{10}$, $Y_{126}$, and $Y_{120}$) account for the quark and lepton Yukawa couplings and the neutrino mass. We pursue the possibility that $Y_{10}$, $Y_{126}$, and $Y_{120}$ reproduce the correct quark and lepton masses, Cabibbo–Kobayashi–Maskawa and Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrices and neutrino mass differences, and at the same time suppress dimension-5 proton decays (proton decays via colored Higgsino exchange) through their texture, so that the soft SUSY-breaking scale can be reduced as much as possible without conflicting the current experimental bound on proton decays. We perform a numerical search for such a texture, and investigate implications of that texture on unknown neutrino parameters, the Dirac CP phase of the PMNS matrix, the lightest neutrino mass, and the $(1,1)$-component of the neutrino mass matrix in the charged lepton basis. Here we concentrate on the case when the active neutrino mass is generated mostly by the Type-2 seesaw mechanism, in which case we can obtain predictions for the neutrino parameters from the condition that dimension-5 proton decays be suppressed as much as possible.

We derive the threshold corrections in $\mathrm{SO}(10)$ grand unified models with the intermediate symmetry being flipped $\mathrm{SU}(5)\times\mathrm{U}(1)$ or $\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)\times\mathrm{U}(1)$, with the masses of the scalar fields set by the survival hypothesis. These models do not achieve gauge coupling unification if the matching conditions do not take threshold corrections into account. We present results showing the required size of threshold corrections for any value of the intermediate and unification scales. In particular, our results demonstrate that both of these models are disfavored since they require large threshold corrections to allow for unification with a predicted proton lifetime above current experimental bounds., Comment: 6 pages, 5 figures. Final version published in Eur. Phys. J. C

Publisher's version (útgefin grein), Despite the successes of the Standard Model of particle physics, it is known to suffer from a number of deficiencies. Several of these can be addressed within non-supersymmetric theories of grand unification based on SO(10). However, achieving gauge coupling unification in such theories is known to require additional physics below the unification scale, such as symmetry breaking in multiple steps. Many such models are disfavored due to bounds on the proton lifetime. Corrections arising from threshold effects can, however, modify these conclusions. We analyze all seven relevant breaking chains with one intermediate symmetry breaking scale, assuming the “survival hypothesis” for the scalar masses. Two are allowed by proton lifetime and two are disfavored by a failure to unify the gauge couplings. The remaining three unify at a too low scale, but can be salvaged by various amounts of threshold corrections. We parametrize this and thereby rank the models by the size of the threshold corrections required to save them., The authors wish to thank Sofiane M. Boucenna for collaboration in early stages of this project and Erik Sönnerlind for pointing out errors and clarifying issues with numerics in a draft of this manuscript. 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” and “Roland Gustafssons Stiftelse för teoretisk fysik” for financial support. 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 SNIC 2018/3-559 and SNIC 2020/5-122.

We explore the stop mass and its possible probe through a set of three different signal processes within a class of SUSY GUTs with non-universal gaugino masses. The stop mass can be realized in a wide range (0.4–8 TeV) consistent with the current experimental constraints. We consider the decay processes; $$\tilde{t}_{1}\rightarrow t\tilde{\chi }_{1}^{0}$$ t ~ 1 → t χ ~ 1 0 , $$\tilde{t}_{1}\rightarrow b W^{\pm }\tilde{\chi }_{1}^{0}$$ t ~ 1 → b W ± χ ~ 1 0 and $$\tilde{t}_{1}\rightarrow b q{\bar{q}}^{\prime }\tilde{\chi }_{1}^{0}$$ t ~ 1 → b q q ¯ ′ χ ~ 1 0 to be possible signals, and explore the impact of the current experimental results as well as the possible mass scales of stop, which can be probed in the future collider experiments. We find that the first and third signal processes can be tested in the current experiments, and significantly probed in future, while the second signal process is not available for the current experiments in this class of SUSY GUTs. We also comment that the second signal process can be available to be tested when the collider experiments are conducted at high center of mass energies and luminosity.

The alternative renormalizable minimal SO(10) model is composed of the Yukawa couplings with 10⊕120 Higgs fields, whereas the right-handed (RH) neutrino Majorana masses are generated via the Witten mechanism. The gauge coupling unification is achieved together with a unique pattern of the fermion masses and mixing at the grand unification scale due to additional contributions of vector-like quarks to the standard model renormalization group equations. We perform the fitting of the model to the experimental data of charged fermion masses and the CKM matrix. The best fit point is obtained with large pulls for mc, ms, mb, and mτ. For the modifications to the minimal model by adding either 10′ or 120′, a large deviation for the tau mass rules out all these models. In the case with the bottom and vector-like quark mixing, the mass matrices are well fitted the charged fermions but the bound on the light neutrino mass scale excludes this scenario. To ameliorate this deficit, we consider the two-step symmetry breaking scenario, SO(10)→SU(5)→SU(3)C×SU(2)L×U(1)Y, with the SO(10) breaking at the Planck scale leading to the radiatively generated RH neutrino Majorana masses being at the ordinary seesaw scale. For this case, we find the best fit point with χ2=7.8 consistent with experimental results including the neutrino sector. The largest deviation is 2.3σ corresponding to the strange quark mass. Hence, a more precise determination of the strange quark mass can test this model. For the best fit point, we find the effective Majorana neutrino mass of mββ=0.22 meV and the sum of light neutrino masses as Σ=0.078 eV, which are consistent with the current constraints from the search for the neutrinoless double beta decay and the CMB anisotropy measurement.

The ratio of the partial widths of some dimension-5 proton decay modes can be predicted without detailed knowledge of SUSY particle masses, and thus allows us to experimentally test various SUSY GUT models without discovering SUSY particles. In this paper, we study the ratio of the partial widths of the $p\to K^0\mu^+$ and $p\to K^+\bar{\nu}_\mu$ decays in the minimal renormalizable SUSY $SO(10)$ GUT, under only a plausible assumption that the 1st and 2nd generation left-handed squarks are mass-degenerate. In the model, we expect that the Wilson coefficients of dimension-5 operators responsible for these modes are on the same order and that the ratio of $p\to K^0\mu^+$ and $p\to K^+\bar{\nu}_\mu$ partial widths is $O(0.1)$. Hence, we may be able to detect both $p\to K^0\mu^+$ and $p\to K^+\bar{\nu}_\mu$ decays at Hyper-Kamiokande, thereby gaining a hint for the minimal renormalizable SUSY $SO(10)$ GUT. Moreover, since this partial width ratio is quite suppressed in the minimal $SU(5)$ GUT, it allows us to distinguish the minimal renormalizable SUSY $SO(10)$ GUT from the minimal $SU(5)$ GUT. In the main body of the paper, we perform a fitting of the quark and lepton masses and flavor mixings with the Yukawa couplings of the minimal renormalizable $SO(10)$ GUT, and derive a concrete prediction for the partial width ratio based on the fitting results. We find that the partial width ratio generally varies in the range 0.05-0.6, confirming the above expectation., Comment: 27 pages, 3 figures. Version accepted for publication in PTEP

Publisher's version (útgefin grein)., We investigate the complete renormalization group running of fermion observables in two different realistic non-supersymmetric models based on the gauge group SO(10) with intermediate symmetry breaking for both normal and inverted neutrino mass orderings. Contrary to results of previous works, we find that the model with the more minimal Yukawa sector of the Lagrangian fails to reproduce the measured values of observables at the electroweak scale, whereas the model with the more extended Yukawa sector can do so if the neutrino masses have normal ordering. The difficulty in finding acceptable fits to measured data is a result of the added complexity from the effect of an intermediate symmetry breaking as well as tension in the value of the leptonic mixing angle θℓ23 ., We would like to thank Sofiane Boucenna, Davide Meloni, Stella Riad, and Shun Zhou for useful discussions. T.O. acknowledges support by the Swedish Research Council (Vetenskapsr˚adet) 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 Byggm¨astare” and “Roland Gustafssons Stiftelse f¨or teoretisk fysik” for financial support. 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 number PDC-2017-115.

A $Z_2$ symmetry that extends the weak interaction, $SU(2)_L \rightarrow SU(2)_L \times SU(2)'$, and the Higgs sector, $H(2) \rightarrow H(2,1) + H'(1,2)$, yields a Standard Model quartic coupling that vanishes at scale $v' = ~\gg~$. Near $v'$, theories either have a "prime" sector, or possess "Left-Right" (LR) symmetry with $SU(2)' = SU(2)_R$. If the $Z_2$ symmetry incorporates spacetime parity, these theories can solve the strong CP problem. The LR theories have all quark and lepton masses arising from operators of dimension 5 or more, requiring Froggatt-Nielsen structures. Two-loop contributions to $\bar{\theta}$ are estimated and typically lead to a neutron electric dipole moment of order $10^{-27}$e cm that can be observed in future experiments. Minimal models, with gauge group $SU(3) \times SU(2)_L \times SU(2)_L \times U(1)_{B-L}$, have precise gauge coupling unification for $v' = 10^{10\pm1}$ GeV, successfully correlating gauge unification with the observed Higgs mass of $125$ GeV. With $SU(3) \times U(1)_{B-L}$ embedded in $SU(4)$, the central value of the unification scale is reduced from $10^{16-17}$ GeV to below $10^{16}$ GeV, improving the likelihood of proton decay discovery. Unified theories based on $SO(10) \times CP$ are constructed that have $H+H'$ in a ${\bf 16}$ or ${\bf 144}$ and generate higher-dimensional flavor operators, while maintaining perturbative gauge couplings., Comment: 36 pages, 5 figures

We extend the free fermionic classification methodology to the class of standard-like heterotic-string vacua, in which the $SO(10)$ GUT symmetry is broken at the string level to $SU(3)\times SU(2)\times U(1)^2$. The space of GGSO free phase configurations in this case is vastly enlarged compared to the corresponding $SO(6)\times SO(4)$ and $SU(5)\times U(1)$ vacua. Extracting substantial numbers of phenomenologically viable models therefore requires a modification of the classification methods. This is achieved by identifying conditions on the GGSO projection coefficients, which are satisfied at the $SO(10)$ level by random phase configurations, and that lead to three generation models with the $SO(10)$ symmetry broken to the $SU(3)\times SU(2)\times U(1)^2$ subgroup. Around each of these fertile $SO(10)$ configurations, we perform a complete classification of standard-like models, by adding the $SO(10)$ symmetry breaking basis vectors, and scanning all the associated GGSO phases. Following this methodology we are able to generate some $10^7$ three generation Standard-like Models. We present the results of the classification and one exemplary model with distinct phenomenological properties, compared to previous SLM constructions., 37 pages. 3 figures. 9 tables. Minor corrections. Published version

Model building in SO(10), which is the leading grand unification framework, often involves large Higgs representations and their couplings. Explicit calculations of such couplings is a multi-step process that involves laborious calculations that are time consuming and error prone, an issue which only grows as the complexity of the coupling increases. Therefore, there exists an opportunity to leverage the abilities of computer software in order to algorithmically perform these calculations on demand. This paper outlines the details of such software, implemented in C++ using in-built libraries. The software is capable of accepting invariant couplings involving an arbitrary number of SO(10) Higgs tensors, each having up to five indices. The output is then produced in LaTeX, so that it is universally readable and sufficiently expressive. Through the use of this software, SO(10) coupling analysis can be performed in a way that minimizes calculation time, eliminates errors, and allows for experimentation with couplings that have not been computed before in the literature. Furthermore, this software can be expanded in the future to account for similar Higgs–Spinor coupling analysis, or extended to include further SO(N) invariant couplings.

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 .

Recent encouraging experimental results on neutrino mixing parameters prompt further investigation on $SO(10)$-inspired leptogenesis and on the associated strong thermal solution that has correctly predicted a non-vanishing reactor mixing angle, it further predicts $\sin\delta \lesssim 0$, now supported by recent results at $\sim 95\%$ C.L., normally ordered neutrino masses and atmospheric mixing angle in the first octant, best fit results in latest global analyses. Extending a recent analytical procedure, we account for the mismatch between the Yukawa basis and the weak basis, that in $SO(10)$-inspired models is described by a CKM-like unitary transformation $V_L$, obtaining a full analytical solution that provides useful insight and reproduces accurately all numerical results, paving the way for future inclusion of different sources of theoretical uncertainties and for a statistical analysis of the constraints. We show how muon-dominated solutions appear for large values of the lightest neutrino mass in the range $(0.01$--$1)\,{\rm eV}$ but also how they necessarily require a mild fine tuning in the seesaw relation. For the dominant (and untuned) tauon-dominated solutions we show how, turning on $V_L \simeq V_{CKM}$, some of the constraints on the low energy neutrino parameters get significantly relaxed. In particular we show how the upper bound on the atmospheric neutrino mixing angle in the strong thermal solution gets relaxed from $\theta_{23} \lesssim 41^{\circ}$ to $\theta_{23} \lesssim 44^{\circ}$, an important effect in the light of the most recent NO$\nu$A, T2K and IceCube results., Comment: 34 pages, 4 figures; v2: matches JHEP version; v3: simple typo corrected: right-hand sides of Eqs. (47) and (48) were swapped in the paper (not in the code)

We consider a simple extension of the minimal left-right symmetric model (LRSM) in order to explain the PeV neutrino events seen at the IceCube experiment from a heavy decaying dark matter. The dark matter sector is composed of two fermions: one at PeV scale and the other at TeV scale such that the heavier one can decay into the lighter one and two neutrinos. The gauge annihilation cross sections of PeV dark matter are not large enough to generate its relic abundance within the observed limit. We include a pair of real scalar triplets $\Omega_{L,R}$ which can bring the thermally overproduced PeV dark matter abundance into the observed range through late time decay and consequent entropy release thereby providing a consistent way to obtain the correct relic abundance without violating the unitarity bound on dark matter mass. Another scalar field, a bitriplet under left-right gauge group is added to assist the heavier dark matter decay. The presence of an approximate global $U(1)_X$ symmetry can naturally explain the origin of tiny couplings required for long-lived nature of these decaying particles. We also show, how such an extended LRSM can be incorporated within a non-supersymmetric $SO(10)$ model where the gauge coupling unification at a very high scale naturally accommodate a PeV scale intermediate symmetry, required to explain the PeV events at IceCube., Comment: 33 pages, 9 figures, 4 tables; error in relic density calculation fixed and discussion expanded for better clarity; matches published version

We extend the nonsupersymmetric SO(10) grand unification theories by adding a horizontal symmetry, which connects the three generations of fermions. Without committing to any specific symmetry group, we investigate the 1-loop renormalization group evolutions of the gauge couplings with one and two intermediate breaking scales. We find that depending on the SO(10) breaking chains, gauge coupling unification is compatible with only a handful of choices of representations of the Higgs bosons under the horizontal symmetry., 21 pages, 6 tables. v2: Further clarifications added primarily in Discussions Section, References updated, to be published in PRD

Motivated by the R-D(*) anomalies, we investigate an SO(10) grand unification scenario where a charge -1/3 scalar leptoquark (S-1) remains as the only new physics candidate at the TeV scale. This l ...

Physics letters / B B809, 1-5 (2020). doi:10.1016/j.physletb.2020.135764, The spontaneous breaking of U(1)$_{B−L}$ around the scale of grand unification can simultaneously account for hybrid inflation, leptogenesis, and neutralino dark matter, thus resolving three major puzzles of particle physics and cosmology in a single predictive framework. The $B−L$ phase transition also results in a network of cosmic strings. If strong and electroweak interactions are unified in an SO(10) gauge group, containing U(1)$_{B−L}$ as a subgroup, these strings are metastable. In this case, they produce a stochastic background of gravitational waves that evades current pulsar timing bounds, but features a flat spectrum with amplitude h$^2$Ω$_{GW}$∼10$^{−8}$ at interferometer frequencies. Ongoing and future LIGO observations will hence probe the scale of $B−L$ breaking., Published by North-Holland Publ., Amsterdam

We study the proton lifetime in the $SO(10)$ Grand Unified Theory (GUT), which has the left-right (LR) symmetric gauge theory below the GUT scale. In particular, we focus on the minimal model without the bi-doublet Higgs field in the LR symmetric model, which predicts the LR-breaking scale at around $10^{10\text{--}12}$ GeV. The Wilson coefficients of the proton decay operators turn out to be considerably larger than those in the minimal $SU(5)$ GUT model especially when the Standard Model Yukawa interactions are generated by integrating out extra vector-like multiplets. As a result, we find that the proton lifetime can be within the reach of the Hyper-Kamiokande experiment even when the GUT gauge boson mass is in the $10^{16\text{--}17}$ GeV range. We also show that the mass of the extra vector-like multiplets can be generated by the Peccei-Quinn symmetry breaking in a consistent way with the axion dark matter scenario., 20 pages, 3 figures (v1); Minor revision, references added (v2)

Journal of high energy physics 11(11), 074 (2020). doi:10.1007/JHEP11(2020)074, An accidental U(1) Peccei-Quinn (PQ) symmetry automatically arises in a class of SO(10) unified theories upon gauging the SU(3)f$_{f}$​ flavour group. The PQ symmetry is protected by the $\mathbb{Z}_4 \times \mathbb{Z}_3$ center of SO(10)×SU(3)$_f$ up to effective operators of canonical dimension nine (developing high-scale contributions to the axion potential). In the pre-inflationary PQ breaking scenario the axion mass window is predicted to be $m_a$∈[7×10$^{−8}$,10$^{−3}$] eV, where the lower end is bounded by the seesaw scale and the upper end by iso-curvature fluctuations. A high-quality axion, that is immune to the PQ quality problem, is obtained for $m_a$ ≳0.02 eV. We finally offer a general perspective on the PQ quality problem in 4D grand unified theories., Published by SISSA, [Trieste]

We propose a simple non-supersymmetric grand unified theory (GUT) based on the gauge group $SO(10) \times U(1)_\psi$. The model includes 3 generations of fermions in ${\bf 16}$ ($+1$), ${\bf 10}$ ($-2$) and ${\bf 1}$ ($+4$) representations. The ${\bf 16}$-plets contain Standard Model (SM) fermions plus right-handed neutrinos, and the ${\bf 10}$-plet and the singlet fermions are introduced to make the model anomaly-free. Gauge coupling unification at $M_{GUT} \simeq 5 \times 10^{15}-10^{16}$ GeV is achieved by including an intermediate Pati-Salam breaking at $M_{I} \simeq 10^{12}-10^{11}$ GeV, which is a natural scale for the seesaw mechanism. For $M_{I} \simeq 10^{12}-10^{11}$, proton decay will be tested by the Hyper-Kamiokande experiment. The extra fermions acquire their masses from $U(1)_\psi$ symmetry breaking, and a $U(1)_\psi$ Higgs field drives a successful inflection-point inflation with a low Hubble parameter during inflation, $H_{inf} \ll M_{I}$. Hence, cosmologically dangerous monopoles produced from $SO(10)$ and PS breakings are diluted away. The reheating temperature after inflation can be high enough for successful leptogenesis. With the Higgs field contents of our model, a ${\bf Z}_2$ symmetry remains unbroken after GUT symmetry breaking, and the lightest mass eigenstate among linear combinations of the ${\bf 10}$-plet and the singlet fermions serves as a Higgs-portal dark matter (DM). We identify the parameter regions to reproduce the observed DM relic density while satisfying the current constraint from the direct DM detection experiments. The present allowed region will be fully covered by the future direct detection experiments such as LUX-ZEPLIN DM experiment. In the presence of the extra fermions, the SM Higgs potential is stabilized up to $M_{I}$., Comment: 25 pages, 5 figures, new references added