Search

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 ...

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.

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

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.

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 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 propose a renormalizable model based on Δ(27) family symmetry with an SO(10) grand unified theory leading to a novel form of spontaneous geometrical CP violation. The symmetries, including Δ(27) and Z9×Z12×ZR4, are broken close to the grand unified theory breaking scale to yield the minimal supersymmetric standard model with the standard R parity. SO(10) is broken via SU(5) with doublet-triplet splitting achieved by a version of the Dimopoulos-Wilczek (missing vacuum expectation value) mechanism. Low-scale Yukawa structure is dictated by the coupling of matter to Δ(27) antitriplets ¯ϕ of which the vacuum expectation values are aligned in the constrained sequential dominance 3 directions by the superpotential. Light physical Majorana neutrinos masses emerge from a specific implementation of the seesaw mechanism within SO(10). The model predicts a normal neutrino mass hierarchy with the best-fit lightest neutrino mass between 0.32 and 0.38 meV, CP-violating oscillation phase δl≈(275–280)°, and the remaining neutrino parameters all within 1σ of their best-fit experimental values.

We present a new class of unified models based on SO(10) symmetry which provides insights into the masses and mixings of quarks and leptons, including the neutrinos. The key feature of our proposal is the absence of Higgs boson 10_H belonging to the fundamental representation that is normally employed. Flavor mixing is induced via vector-like fermions in the 16 + 16-bar representation. A variety of scenarios, both supersymmetric and otherwise, are analyzed involving a 126_H along with either a 45_H or a 210_H of Higgs boson employed for symmetry breaking. It is shown that this framework, with only a limited number of parameters, provides an excellent fit to the full fermion spectrum, utilizing either type-I or type-II seesaw mechanism. These flavor models can be potentially tested and distinguished in their predictions for proton decay branching ratios, which are analyzed., 40 pages, Latex, 1 figure

In this paper, an extension of the classification of flipped SU(5) heterotic-string vacua from Faraggi, Rizos and Sonmez [Nucl. Phys. B886, 202 (2014)] with a variation of the SO(10) breaking α basis vector is presented. A statistical sampling in the space of 245 flipped SU(5) vacua is explored, where 1011 distinct GGSO projection configurations are scanned in comparison to the 1012 GGSO distinct coefficients scanned in the space of 244 vacua in Faraggi, Rizos and Sonmez. A JAVA code, akin to the one used for the classification in Faraggi, Rizos and Sonmez, was implemented to explore these. Results presented here indicate that no three-generation exophobic vacua exist, which was also found to be the case in Faraggi, Rizos and Sonmez as all odd generations were projected out. This paper will also study the details on the comparison between the two classifications achieved and reflect on the future directions in the quest for finding three-generation exophobic flipped SU(5) heterotic-string models.

Recently interest in GUT baryogenesis has been resurrected due to the observation that B-violating dimension seven operators that arise in grand unified theories that also violate B-L produce baryon asymmetry that cannot be wiped out by sphaleron processes. While a general analysis of such higher dimensional operators from a bottom up approach exists in the literature, a full analysis of them derived from grand unification does not exist. In this work we present a complete analysis of B-L=-2 operators within a realistic SO(10) grand unification where the doublet-triplet splitting is automatic via a missing partner mechanism. Specifically we compute all allowed dimension five, dimension seven and dimension nine operators arising from matter-Higgs interactions. The relative strength of all the allowed B-L=-2 operators is given. Such interactions are useful in the study of neutrino masses, baryogenesis, proton decay and $n-\bar n$ oscillations within a common realistic grand unification framework.

We construct and analyze nonsupersymmetric SO(10) standard model extensions which explain dark matter (DM) through the fermionic Higgs portal. In these SO(10)-based models the DM particle is naturally stable since a ${Z}_{2}$ discrete symmetry, the matter parity, is left at the end of the symmetry breaking chain to the standard model. Potentially realistic models contain the $\mathbf{10}$ and $\mathbf{45}$ fermionic representations from which a neutralino-like mass matrix with arbitrary mixings can be obtained. Two different SO(10) breaking chains will be analyzed in light of gauge coupling unification: the standard path $\mathrm{SU}(5)\ifmmode\times\else\texttimes\fi{}U(1{)}_{X}$ and the left-right symmetry intermediate chain. The former opens the possibility of a split supersymmetric-like spectrum with an additional (inert) scalar doublet, while the later requires additional exotic scalar representations associated to the breaking of the left-right symmetry.

In this work I present a complete analysis of proton decay in an $SO(10)$ model previously proposed by Dutta, Mimura, and Mohapatra. The $\mathbf{10}$, $\overline{\mathbf{126}}$, and $\mathbf{120}$ Yukawa couplings contributing to fermion masses in this model have well-motivated restrictions on their textures intended to give favorable results for proton lifetime as well as a realistic fermion sector without the need for fine-tuning and for either type-I or type-II dominance in the neutrino mass matrix. I obtain a valid fit for the entire fermion sector for both types of seesaw dominance, including ${\ensuremath{\theta}}_{13}$ in good agreement with the most recent data. For the case with type-II seesaw, I find that using the Yukawa couplings fixed by the successful fermion sector fit, proton partial lifetime limits are satisfied for nearly every pertinent decay mode, even for nearly arbitrary values of the triplet Higgs mixing parameters, with only the ${K}^{+}\overline{\ensuremath{\nu}}$ mode requiring a minor $\mathcal{O}(1{0}^{\ensuremath{-}1})$ cancellation in order to satisfy the experimental limit. I also find a maximum lifetime for that mode of $\ensuremath{\tau}({K}^{+}\overline{\ensuremath{\nu}})\ensuremath{\sim}{10}^{36}\text{ }\text{ }\mathrm{yr}$, which should be tested by forthcoming experiments. For the type-I seesaw case, I find that all six pertinent decay modes of interest are satisfied for values of the triplet mixing parameters giving no major enhancement, with modes other than ${K}^{+}\overline{\ensuremath{\nu}}$ easily satisfied for arbitrary mixing values, and with a maximum lifetime for ${K}^{+}\overline{\ensuremath{\nu}}$ of nearly ${10}^{38}\text{ }\text{ }\mathrm{yr}$.

We consider grand unified theories based on $SO(10)$ which originate from $\text{string}/M$ theory on ${G}_{2}$ manifolds or Calabi-Yau spaces with discrete symmetries. In this framework we are naturally led to a novel solution of the doublet-triplet splitting problem previously considered by Dvali which involves an extra vectorlike Standard Model family and light but weakly coupled color triplets. These additional states are predicted to be accessible at the LHC and also induce R-parity violation. Gauge coupling unification occurs with a larger GUT coupling.

In this paper we analyze Yukawa unification in a three family SO(10) SUSY GUT. We perform a global $\chi^2$ analysis and show that SUSY effects do not decouple even though the universal scalar mass parameter at the GUT scale, $m_{16}$, is found to lie between 15 and 30 TeV with the best fit given for $m_{16} \approx 25$ TeV. Note, SUSY effects don't decouple since stops and bottoms have mass of order 5 TeV, due to RG running from $M_{GUT}$. The model has many testable predictions. Gauginos are the lightest sparticles and the light Higgs boson is very much Standard Model-like. The model is consistent with flavor and CP observables with the $BR(\mu \to e\gamma)$ close to the experimental upper bound. With such a large value of $m_{16}$ we clearly cannot be considered "natural" SUSY nor are we "Split" SUSY. We are thus in the region in between or "SUSY on the Edge.", Comment: 23 pages, 3 figures, 9 tables; Changed title, added references for Section 3.2; Typos corrected

Unlike minimal SU(5), SO(10) provides a straightforward path towards gauge coupling unification by modifying the renormalization group evolution of the gauge couplings above some intermediate scale which may also be related to the seesaw mechanism for neutrino masses. Unification can be achieved for several different choices of the intermediate gauge group below the SO(10) breaking scale. In this work, we consider in detail the possibility that SO(10) unification may also provide a natural dark matter candidate, stability being guaranteed by a leftover $Z_2$ symmetry. We systematically examine the possible intermediate gauge groups which allow a non-degenerate, fermionic, Standard Model singlet dark matter candidate while at the same time respecting gauge coupling unification. Our analysis is done at the two-loop level. Surprisingly, despite the richness of SO(10), we find that only two models survive the analysis of phenomenological constraints, which include suitable neutrino masses, proton decay, and reheating., 39 pages, 8 figures. Version accepted for publication in Physical Review D

The free fermionic construction of the heterotic string in four dimensions produced a large space of three-generation models with the underlying $SO(10)$ embedding of the Standard Model states. The $SO(10)$ symmetry is broken to a subgroup directly at the string scale. Over the past few years free fermionic models with the Pati-Salam and flipped $SU(5)$ subgroups have been classified. In this paper we extend this classification program to models in which the $SO(10)$ symmetry is broken at the string level to the $SU(4)\ifmmode\times\else\texttimes\fi{}SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1{)}_{R}$ (SU421) subgroup. The subspace of free fermionic models that we consider corresponds to symmetric ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ orbifolds. We provide a general argument that shows that this class of SU421 free fermionic models cannot produce viable three-generation models.

We review the current status of the minimal non-supersymmetric SO(10) grand unified theory and perform a detailed next-to-leading-order analysis of the gauge unification and proton lifetime constraints on the part of its parameter space supporting a ZeV-scale color sextet scalar. This, together with a TeV-scale color octet studied in detail in a preceding work, represents one of the two minimally fine-tuned settings compatible with all the relevant consistency and phenomenology limits. Both these scenarios can be extensively tested at the future megaton-scale proton-decay facilities. On top of that, the light octet solution can be accessible in the TeV-scale collider searches.

Renormalizable SO(10) grand unified theories (GUTs), extended by $O(N_g)_F$ family gauge symmetry, generate minimal supersymmetric Standard Model flavour structure dynamically via vacuum expectation values of "Yukawon" Higgs multiplets. For concrete illustration and calculability, we work with the fully realistic minimal supersymmetric GUTs based on the $\bf{210 \oplus {\overline{126}}\oplus 126} $ GUT Higgs system - which were already parameter counting minimal relative to other realistic models. $SO(10)$ fermion Higgs channels $\bf{\overline{126},10}$($\mathbf{120}$) extend to symmetric(antisymmetric) representations of $O(N_g)_F$, while $\mathbf{210,126}$ are symmetric. $N_g=3$ dynamical Yukawa generation reduces the matter fermion Yukawas from 15 to 3 (21 to 5) without (with) the $\bf{120}$ Higgs. Yukawon GUTs are thus ultraminimal in parameter counting terms. Consistent symmetry breaking is ensured by a hidden sector Bajc-Melfo(BM) superpotential with a pair of symmetric $O(N_g)$ multiplets $\phi,S $, of which the latter's singlet part $S_s$ breaks supersymmetry and the traceless part $\hat S $ furnishes flat directions to cancel the $O(N_g)$ D-term contributions of the visible sector. Novel dark matter candidates linked to flavour symmetry arise from both the BM sector and GUT sector minimal supersymmetric Standard Model singlet pseudo-Goldstones. These relics may be viable light($< 50 $ GeV) cold dark matter as reported by DAMA/LIBRA. In contrast to the new minimal supersymmetric SO(10) grand unified theory (NMSGUT) even sterile neutrinos can appear in certain branches of the flavour symmetry breaking without the tuning of couplings.

We present the results of a numerical search for the Dirac Yukawa matrices of the Standard Model, consistent with the quark and lepton masses and their mixing angles. We assume a diagonal up-quark matrix, natural in ${\mathsc{Z}}_{\mathbf{7}}\ensuremath{\rtimes}{\mathsc{Z}}_{\mathbf{3}}$, bimaximal or tribimaximal seesaw mixing, and $SU(5)$ unification to relate the down-quark and charged lepton Dirac Yukawa matrices using Georgi-Jarlskog mechanisms. The measured value of ${\ensuremath{\theta}}_{13}$ requires an asymmetric down-quark Yukawa matrix. Satisfying the measured values of both ${\ensuremath{\theta}}_{13}$ and the electron mass restricts the number of solutions, underlying the importance of the recent measurement of the reactor angle.

We present a new mechanism for doublet-triplet splitting in supersymmetric SO(10) models using a missing vev pattern which is different from the one used in the currently popular Dimopoulos-Wilczek method. In our method, the doublets in a {$\bf 16,\bar{16}$} pair are the ones split from the rest of the multiplet and are then mixed with the doublets from one or two {\bf 10}'s giving rise to the doublets {$\bf H_u$} and {$\bf H_d$} of the standard model. This approach provides a natural way to understand why top quark is so much heavier than the bottom quark. It also enables us to generate both hierarchical and nonhierarchical pattern for neutrino masses, the latter being of interest if neutrino is the hot component of the dark matter of the universe. We construct a simple, realistic model based on this idea. The model uses only simple representations, has no unwanted flat directions and maintains coupling constant unification as a prediction., Comment: 5 pages Revtex, preprint no. UMD-PP-99-031; a new reference added

It is shown that the doublet-triplet splitting problem can be solved in SO(10) using the Dimopoulos-Wilczek mechanism with a very economical Higgs content and simple structure. Only one adjoint Higgs field is required, together with spinor and vector fields. The successful SUSY GUT prediction of gauge coupling unification is preserved. Higgsino-mediated proton decay can be suppressed below (but not far below) present limits without fine-tuning., Comment: 11 pages, LaTeX. Discussion at end of section 3 of stability of gauge hierarchy and higher-dimension operators has been substantially revised and extended. Minor modification of model, with certain coefficients replaced by VEVs of singlet fields. N.B. Changed author list

We present the details of a global ${\ensuremath{\chi}}^{2}$ analysis of electroweak data, including fermion masses and mixing angles, in SO(10) SUSY GUTs. Just as precision electroweak data are used to test the standard model, the well-determined standard model parameters are the precision electroweak data for testing theories beyond the standard model. In this paper we use the latest experimentally measured values for these parameters. We study several models discussed in the literature. One of these models provides an excellent fit to the low energy data with ${\ensuremath{\chi}}^{2}\ensuremath{\sim}1$ for three degrees of freedom. We present graphs of constant ${\ensuremath{\chi}}^{2}$ contours as functions of position in soft SUSY-breaking parameter space, as well as our predictions for a few selected points in parameter space. We also study the sensitivity of our results to changes in various parameters. Finally, we discuss the consequences of our work in the context of a general MSSM analysis at the $Z$ scale.

We uncover a rich microphysical structure for SO(10) cosmic strings. For the abelian string the electroweak symmetry is restored around it in a region depending on the electroweak scale. A rich structure of nonabelian strings is found. Some of these also restore the electroweak symmetry. We investigate the zero mode structure of our strings. Whilst there are right handed neutrino zero modes for the abelian string, they do not survive the electroweak phase transition. In general the nonabelian strings do not have fermion zero modes. We consider the generalisation of our results to other theories and consider cosmological consequences of them., Comment: 34 pages, LATEX. Replaced version is restructured, and has small correction to fermion zero mode analysis. To be published in Physical Review D

Nucleon lifetimes for various decay modes via dimension-6 operators are calculated in the anomalous $U(1{)}_{A}$ grand unified theory (GUT) scenario, in which the unification scale ${\ensuremath{\Lambda}}_{u}$ becomes smaller than the usual supersymmetric (SUSY) unification scale ${\ensuremath{\Lambda}}_{G}=2\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\text{ }\mathrm{GeV}$ in general. Since the predicted lifetime $\ensuremath{\tau}(p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{e}^{c})$ falls around the experimental lower bound, though it is strongly dependent on the explicit models, the discovery of the this nucleon decay can be expected in the near future. We explain why the two ratios ${R}_{1}\ensuremath{\equiv}\frac{{\ensuremath{\Gamma}}_{n\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{\ensuremath{\nu}}^{c}}}{{\ensuremath{\Gamma}}_{p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{e}^{c}}}$ and ${R}_{2}\ensuremath{\equiv}\frac{{\ensuremath{\Gamma}}_{p\ensuremath{\rightarrow}{K}^{0}+{\ensuremath{\mu}}^{c}}}{{\ensuremath{\Gamma}}_{p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{e}^{c}}}$ are important in identifying the grand unification group, and we show that three anomalous $U(1{)}_{A}$ SUSY GUT models, with $SU(5)$, $SO(10)$ and ${E}_{6}$ grand unification groups, can be identified by measuring the two ratios. If ${R}_{1}$ is larger than 0.4, the grand unification group is not $SU(5)$, and moreover, if ${R}_{2}$ is larger than 0.3, the grand unification group is implied to be ${E}_{6}$.

We analyze the relation between the present (and foreseen) bounds on matter stability and the presence of TeV-scale color octet scalar states in nonsupersymmetric $SO(10)$ grand unification with one adjoint Higgs representation triggering the symmetry breaking. This scenario, discarded long ago due to tree-level tachyonic instabilities appearing in all phenomenologically viable breaking patterns, has been recently revived at the quantum level. By including the relevant two-loop corrections we find a tight correlation between the octet mass and the unification scale which either requires a light color octet scalar within the reach of the LHC or, alternatively, a proton lifetime accessible to the forthcoming megaton-scale facilities.

Supersymmetric SO(10) grand unified models with renormalizable Yukawa couplings involving 10, 126, and 120 Higgs fields have been shown to give a very economical theory for understanding quark-lepton flavor in a unified framework. In previous papers, we showed how nucleon decay can be suppressed in these models without invoking cancellation, by choice of Yukawa flavor texture within a type II seesaw framework for neutrinos that explains all mixings and masses including the recently observed ``large'' ${\ensuremath{\theta}}_{13}$. In this followup paper, we extend our earlier work to the case of type I seesaw and show that the recently measured large ${\ensuremath{\theta}}_{13}$ can be accommodated in this case while suppressing proton decay. We then point out that the two cases (type I and II) lead to different testable predictions for $B(\ensuremath{\mu}\ensuremath{\rightarrow}e+\ensuremath{\gamma})$ and $B(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}(e)+\ensuremath{\gamma})$ as well as different flavor final states in nucleon decay. In particular, we find that for the type I seesaw case, $B(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}+\ensuremath{\gamma})$ can be observable while at the same time suppressing $B(\ensuremath{\mu}\ensuremath{\rightarrow}e+\ensuremath{\gamma})$, whereas in the type II seesaw case, $B(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}+\ensuremath{\gamma})$ is always suppressed whereas $B(\ensuremath{\mu}\ensuremath{\rightarrow}e+\ensuremath{\gamma})$ is observable.

We propose a unified model of elementary particles based on a supersymmetric SO(10){sub GUT}{times} SO(6){sub {ital H}} gauge theory. This model completely achieves natural unification of the strong and electroweak interactions without any fine tunings. The masslessness of Higgs doublets is guaranteed by a chiral U(1){sub {ital A}} symmetry. On the other hand, the Higgs triplets have a GUT-scale mass invariant under the chiral U(1){sub {ital A}}. {copyright} {ital 1996 The American Physical Society.}

We show that one-loop GUT scale threshold corrections to gauge couplings are a significant constraint on the GUT symmetry-breaking sector of the theory. The one-loop threshold corrections relate the prediction for {alpha}{sub {ital s}}({ital M}{sub {ital Z}}) to the proton lifetime. We have calculated these corrections in a new complete SO(10) SUSY GUT. The results are consistent with the low-energy measurement of {alpha}{sub {ital s}}({ital M}{sub {ital Z}}). We have also calculated the proton lifetime and branching ratios in this model. We show that proton decay rates provide a powerful test for theories of fermion masses. {copyright} {ital 1996 The American Physical Society.}

The flat-space limit of the one-loop effective potential for SO(10) GUT{close_quote}s in spatially flat Friedmann-Robertson-Walker cosmologies is applied to study the dynamics of the early universe. The numerical integration of the corresponding field equations shows that, for such grand unified theories, a sufficiently long inflationary stage is achieved for suitable choices of the initial conditions. However, a severe fine-tuning of these initial conditions is necessary to obtain a large {ital e}-fold number. In the direction with residual symmetry SU(4){sub PS}{circle_times}SU(2){sub {ital L}}{circle_times}SU(2){sub {ital R}}, one eventually finds parametric resonance for suitable choices of the free parameters of the classical potential. This phenomenon leads in turn to the end of inflation. {copyright} {ital 1996 The American Physical Society.}

We analyze the scalar lepton mass matrices in a supersymmetric SO(10) grand unified model with soft SUSY breaking terms generated at Planck scale and a Georgi-Jarslkog Yukawa texture at GUT scale induced by higher dimensional operators. This model predicts lepton flavor violation. The predictive features of the Georgi-Jarlskog texture are used to estimate branching ratios for the radiative decays $e_{a} \rightarrow e_{b}+\gamma,$ and we find rates that could provide an experimental test for this kind of model., Comment: uudecoded figure file replaced; text of paper and figures unchanged

Fermion masses and mixing angles are studied in an SUSY SO(10){times}{Delta}(48){times}U(1) model with small tan{beta}. Thirteen parameters involving masses and mixing angles in the quark and charged lepton sector are successfully predicted by a single Yukawa coupling and three ratios of VEV{close_quote}s caused by necessary symmetry breaking. Ten relations among the low energy parameters have been found with four of them free from renormalization modifications. They could be tested directly by low energy experiments. {copyright} {ital 1996 The American Physical Society.}

We construct a supersymmetric SO(10){times}U(1){sub {ital F}} model of the Yukawa interactions at the grand unification scale from knowledge of a phenomenological set of mass matrices obtained by a previous bottom-up approach. The U(1){sub {ital F}} family symmetry determines the textures for the Majorana and generic Dirac mass matrices, while the SO(10) symmetry relates each particular element of the up, down, neutrino, and charged lepton Dirac matrices. The dominant second and third family contributions in the Dirac sector are renormalizable, while the remaining contributions to the Dirac mass matrices are of higher order, restricted by the U(1){sub {ital F}} family symmetry to a small set of tree diagrams, and mainly complex symmetric. The tree diagrams for the Majorana mass matrix are all nonrenormalizable and of progressively higher order, leading to a nearly geometrical structure. Pairs of {bold 1}, {bold 45}, {bold 10}, and {bold 126} Higgs representations enter with those having large vacuum expectation values breaking the symmetry down to SU(3){sub {ital c}}{times}SU(2){sub {ital L}}{times}U(1){sub {ital Y}} near the grand unification scale. In terms of 12 parameters expressed as the Yukawa couplings times vacuum expectation values for the Higgs representations employed, a realistic set of 15 quark and lepton massesmore » (including those for the three heavy right-handed Majorana neutrinos) and eight mixing parameters emerges for the neutrino scenario involving the nonadiabatic conversion of solar neutrinos and the depletion of atmospheric muon neutrinos through oscillations into {tau} neutrinos. {copyright} {ital 1996 The American Physical Society.}« less

We investigate the spectrum of supersymmetric grand unification models based on the gauge groups SU(5), SO(10) and E6, paying particular attention to the first and second generation. We demonstrate how the measurement of the first or second generation sfermion spectrum may be used to constrain the underlying grand unification structure. The smallness of first and second generation Yukawa interactions allows us to perform an analytic analysis, deriving expressions for the high scale parameters in terms of the low scale sfermion masses. We also describe a sum rule that provides an SO(10) mass prediction, distinct from SU(5), and discuss E6 models, both with and without extra exotic matter at low energies. The derived relations are compared with numerical results including two-loop running and the full Yukawa dependence., 21 pages, 2 figures (with 3 subfigures each). Version published in Phys. Rev. D

Considerations of massive neutrinos, baryogenesis as well as fermion mass textures in the grand unified theory framework provide strong motivations for supersymmetric(SUSY) SO(10) as the theory beyond the standard model. If one wants to simultaneously solve the strong CP problem via the Peccei-Quinn mechanism, the most natural way to implement it within the framework of the SUSY SO(10) model is to have an intermediate scale ($v_{BL}$) (corresponding to B-L symmetry breaking) around the invisible axion scale of about 10$^{11}$ - 10$^{12}$ GeV. Such a scale is also desirable if $\nu_{\tau}$ is to constitute the hot dark matter (HDM) of the universe. In this paper, we discuss examples of superstring inspired SUSY SO(10) models with intermediate scales that are consistent with the low energy precision measurements of the standard model gauge couplings. The hypothesis of $b-\tau$ unification which is a successful prediction of many grand unified theories is then required of these models and the resulting prediction of $b$-quark mass is used as a measure of viability of these schemes. Detailed analysis of a model with a $v_{BL}\simeq 10^{11}$ GeV, which satisfies both the requirements of invisible axion and $\nu_{\tau}$ as HDM is presented and shown to lead to $m_b\simeq 4.9$ GeV in the one-loop approximation., Comment: Latex file; 20 pages; Four figures available on request

In the context of supersymmetric $SO(10)$ grand unified models, it is shown that the gauge symmetry breaking as well as a natural doublet--triplet splitting can be achieved with a minimal Higgs system consisting of a single adjoint and a pair of vector and spinor multiplets. Such a Higgs spectrum has been shown to arise in the free fermionic formulation of superstrings. Since the symmetry breaking mechanism relies on non--renormalizable operators, some of the Higgs particles of the model turn out to have masses somewhat below the GUT scale. As a consequence, the unification scale is raised to about $2 \times 10^{17}~GeV$ and sin$^2\theta_W$ is predicted to be slightly larger than the minimal SUSY--$SU(5)$ value. Including threshold uncertainties, which turn out to be surprisingly small in the model, we show that sin$^2\theta_W$ prediction is consistent with experiments., Comment: 23 pages, BA-94-45

Recently realization of TeV scale inverse seesaw mechanism in supersymmetric SO(10) framework has led to a number of experimentally verifiable predictions including low-mass W_R and Z' gauge bosons and nonunitarity effects. Using nonsupersymmetric SO(10) grand unified theory, we show how a TeV scale inverse seesaw mechanism for neutrino masses is implemented with a low-mass Z' boson accessible to Large Hadron Collider. We derive renormalization group equations for fermion masses and mixings in the presence of the intermediate symmetries of the model and extract the Dirac neutrino mass matrix at the TeV scale from successful GUT-scale parameterization of fermion masses. We estimate leptonic nonunitarity effects measurable at neutrino factories and lepton flavor violating decays expected to be probed in near future. While our prediction on the nonunitarity matrix element $\eta_{\mu\tau}$ for degenerate right-handed neutrinos is similar to the supersymmetric SO(10) case, we find new predictions with significantly enhanced value of its phase $\delta_{\mu\tau}\simeq 10^{-4}-10^{-2}$ when partial degeneracy among these neutrino masses is adequately taken into account by a constraint relation that emerges naturally in this approach. Other predictions on branching ratios and CP-Violating parameters are discussed. An important distinguishing characteristic as another test of the minimal model is that the threshold corrected two-loop prediction of the proton lifetime with maximum value ({\tau}_p)_{max}\simeq 10^{35} yrs. is accessible to ongoing search experiments for the decay $p\to e^+\pi^0$ in the near future. Simple model extensions with longer proton lifetime predictions are also discussed.

We show that grand unified theories based on $SO(10)$ generate quite naturally baryon number violating dimension seven operators that violate $B\mathrm{\text{\ensuremath{-}}}L$, and lead to novel nucleon decay modes such as $n\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{K}^{+}$, ${e}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ and $p\ensuremath{\rightarrow}\ensuremath{\nu}{\ensuremath{\pi}}^{+}$. We find that in two-step breaking schemes of nonsupersymmetric $SO(10)$, the partial lifetimes for these modes can be within reach of experiments. The interactions responsible for these decay modes also provide a new way to understand the origin of matter in the Universe via the decays of grand unified theory (GUT) scale scalar bosons of $SO(10)$. Their ($B\mathrm{\text{\ensuremath{-}}}L$)--violating nature guarantees that the GUT scale induced baryon asymmetry is not washed out by the electroweak sphaleron interactions. In minimal $SO(10)$ models this asymmetry is closely tied to the masses of quarks, leptons and the neutrinos.

We show that grand unified theories based on $SO(10)$ generate naturally the next-to-leading baryon number violating operators of dimension seven. These operators, which violate $(B\ensuremath{-}L)$, lead to unconventional decays of the nucleon such as $n\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{K}^{+}$, ${e}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ and $p\ensuremath{\rightarrow}\ensuremath{\nu}{\ensuremath{\pi}}^{+}$. In two-step breaking schemes of nonsupersymmetric $SO(10)$, nucleon lifetime for decays into these modes is found to be within reach of experiments. We also identify supersymmetric scenarios where these decays may be accessible, consistent with gauge coupling unification. Further, we show that the $(B\ensuremath{-}L)$ asymmetry generated in the decays of GUT scale scalar bosons and/or gauge bosons can explain consistently the observed baryon asymmetry of the universe. The induced $(B\ensuremath{-}L)$ asymmetry is sphaleron-proof, and survives down to the weak scale without being erased by the electroweak interactions. This mechanism works efficiently in a large class of nonsupersymmetric and supersymmetric $SO(10)$ models, with either a ${126}_{H}$ or a ${16}_{H}$ Higgs field employed for rank reduction. In minimal models the induced baryon asymmetry is tightly connected to the masses of quarks, leptons and neutrinos and is found to be compatible with observations.

In a recent paper, a minimal supersymmetric (SUSY) $SO(10)\ifmmode\times\else\texttimes\fi{}{S}_{4}$ based unified model of flavor for quarks and leptons was proposed with two $\mathbf{10}$ and one $\mathbf{126}$ contributing to fermion masses. An important aspect of this model is that Yukawa couplings emerge dynamically from minimization of the flavon potential, thereby reducing the number of parameters considerably. We make a detailed numerical analysis of this model for fermion mixings including SUSY threshold effects at the TeV scale and type-I corrections to a type-II dominant seesaw for neutrino masses. This is a single-step breaking model with SUSY $SO(10)$ broken at the grand unified theory scale of $2\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\text{ }\mathrm{GeV}$ to the minimal supersymmetric standard model. The minimal model has only 11 parameters, and therefore, the charged fermion fits predict the masses (up to an overall scale) and mixings in the neutrino sector. We present correlations for the different predictions in the neutrino mixing parameters. The recent experimental ``large'' ${\ensuremath{\theta}}_{13}$ value of $\ensuremath{\sim}9\ifmmode^\circ\else\textdegree\fi{}$ can be obtained by a simple extension of the minimal model. We also find that proton decay mode $p\ensuremath{\rightarrow}{K}^{+}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ has a partial lifetime of $\ensuremath{\sim}{10}^{34}\text{ }\text{ }\mathrm{yrs}$, which is within reach of the next round of planned proton decay searches. The successful fit for fermion masses requires the Higgs mass to be below 129 GeV in this model. If the Higgs mass lies between 120 and 128 GeV, as suggested by the recent LHC data, we find a lower limit on the light stop mass of 755 (211) GeV for $\ensuremath{\mu}g0(l0)$.

We present a new class of unified SO(10) models where the GUT symmetry breaking down to the standard model gauge group involves just one scale, in contrast to the conventional SO(10) models which require two scales. Further, the models we discuss possess a natural doublet-triplet splitting via the missing partner mechanism without fine tuning. Such models involve $560+\ov{560}$ pair of heavy Higgs fields along with a set of light fields. The $560+\ov{560}$ are the simplest representations of SO(10) besides the $126+\ov{126}$ which contain an excess of color triplets over $SU(2)_L$ doublets. We discuss several possibilities for realizing the missing partner mechanism within these schemes. With the $126+\ov{126}$ multiplets, three viable models are found with additional fields belonging to ${210 + 2 \times 10 + 120}$, ${45 + 10 + 120}$, or ${210 + 16 + \ov{16} + 10 + 120}$. With the $560+\ov{560}$, a unique possibility arises for the missing partner mechanism, with additional ${2\times 10+ 320}$ fields. These models are developed in some detail. It is shown that fully realistic fermion masses can arise in some cases, while others can be made realistic by addition of vector--like representations. Naturally large neutrino mixing angles, including sizable $\theta_{13}$, can emerge in these models. The couplings of the $H_u(H_d)$ Higgs doublets of the MSSM which give masses to the up quarks (down quarks and leptons) are not necessarily equal at the grand unification scale and would lead to a new phenomenology at the low energy scales.

We investigate the status of predictive fermion mass ansatzes which make use of the grand unification scale conditions $m_e=m_d/3$, $m_\mu =3m_s$, and $\mid V_{cb}\mid =\sqrt{m_{c}/m_{t}}$ in non-supersymmetric SO(10) grand unification. The gauge symmetry below an intermediate symmetry breaking scale $M_I$ is assumed to be that of the standard model with either one Higgs doublet or two Higgs doublets . We find in both cases that a maximum of 5 standard model parameters may be predicted within $1\sigma$ experimental ranges. We find that the standard model scenario predicts the low energy $\mid V_{cb}\mid$ to be in a range which includes its experimental mid-value 0.044 and which for a large top mass can extend to lower values than the range resulting in the supersymmetric case. In the two Higgs standard model case, we identify the regions of parameter space for which unification of the bottom quark and tau lepton Yukawa couplings is possible at grand unification scale. In fact, we find that unification of the top, bottom and tau Yukawa couplings is possible with the running b-quark mass within the $1\sigma$ preferred range $m_b=4.25\pm 0.1\, GeV$ provided $\alpha_{3c}(M_Z)$ is near the low end of its allowed range. In this case, one may make 6 predictions which include $\mid V_{cb}\mid$ within its $90\%$ confidence limits. However unless the running mass $m_b>4.4\, GeV$, third generation Yukawa coupling unification requires the top mass to be greater than, Comment: 30 pages, 8 figures available on request from evan@oregon.uoregon.edu, Latex

We construct an $SO(10)$ grand unified theory in the formulation of non-com-\break mutative geometry. The geometry of space-time is that of a product of a continuos four dimensional manifold times a discrete set of points. The properties of the fermionic sector fix almost uniquely the Higgs structure. The simplest model corresponds to the case where the discrete set consists of three points and the Higgs fields are ${\u {16}_s}\times \overline{\u {16}}_s$ and ${\u {16}_s}\times {\u {16}_s} $. The requirement that the scalar potential for all the Higgs fields not vanish imposes strong restrictions on the vacuum expectation values of the Higgs fields and thus the fermion masses. We show that it is possible to remove these constraints by extending the number of discrete points and adding a singlet fermion and a ${\u {16}_s}$ Higgs field. Both models are studied in detail., Comment: 24 pages, ZU-TH-10/1993 and ETH/TH/93/12

A new procedure is developed which enables one to start from the quark and lepton mass and mixing data at the low scale and construct mass matrices which exhibit simple SO(10) structure at the supersymmetric-grand-unification scale. This approach is applied to the present data involving quark and charged lepton masses, the quark mixing matrix and the nonadiabatic solar neutrino and atmospheric neutrino depletion effects. In terms of just 12 model parameters suggested by the procedure for the 5 mass matrices, we can reproduce remarkably well all the masses and mixing parameters for the scenario considered.

We calculate the two loop contributions to the predictions of the mass scales in an SO(10) grand unified theory. We consider the modified unification scale boundary conditions due to the nonrenormalizable higher dimensional terms arising from quantum gravity or spontaneous compactification of extra dimensions in a Kaluza-Klein-type theory. We find the range of these couplings which allows left-right symmetry to survive till very low energy (as low as [similar to] TeV) and still be compatible with the latest values of sin[sup 2][theta][sub [ital W]] and [alpha][sub [ital s]] derived from CERN LEP. We consider both the situation when the left-right parity is broken and conserved. We consider both supersymmetric and nonsupersymmetric versions of the SO(10) theory. Taking the [ital D]-conserved non-SUSY case as an example we calculate the effects of moderate threshold uncertainties at the heavy scale, due to the unknown Higgs boson masses, on the gravity-induced couplings.

Certain cosmic strings that occur in GUT models such as SO(10) can carry a magnetic flux which acts nontrivially on objects carrying ${\mathrm{SU}(3)}_{\mathrm{color}}$ quantum numbers. We show that such strings are non-Abelian Alice strings carrying nonlocalizable colored "Cheshire" charge. We examine claims made in the literature that SO(10) strings can have a long-range, topological Aharonov-Bohm interaction that turns quarks into leptons, and observe that such a process is impossible. We also discuss flux-flux scattering using a multisheeted formalism.

The vacuum conditions for preserving supersymmetry in the minimal supersymmetric SO(10) grand unified theory are constructed and studied. The mass spectrum for each symmetry-breaking chain which preserves supersymmetry is considered. It is found that in the minimal supersymmetric SO(10) grand unified theory only one-step symmetry breaking is allowed, whether or not supersymmetry remains unbroken in an intermediate symmetry breaking.

Recently type-II seesaw in a supersymmetric$SO(10)$ framework has been found useful in explaining large solar and atmospheric mixing angles as well as a larger value of ${\ensuremath{\theta}}_{13}$ while unifying quark and lepton masses. An important question in these models is whether there exists consistency between coupling unification and type-II seesaw dominance. Scenarios where this consistency can be demonstrated have been given in a SUSY framework. In this paper we give examples where type-II dominance occurs in $SO(10)$ models without supersymmetry but with additional TeV-scale particles and also in models with split-supersymmetry. Grand unification is realized in a two step process via breaking of $SO(10)$ to $SU(5)$ and then to a TeV-scale standard model supplemented by extra fields and an $SU(5)$ Higgs multiplet ${15}_{H}$ at a scale of about ${10}^{12}\text{ }\text{ }\mathrm{GeV}$ to give a type-II seesaw. The predictions for proton lifetime in these models are in the range ${\ensuremath{\tau}}_{p}^{0}=2\ifmmode\times\else\texttimes\fi{}{10}^{35}\text{ }\text{ }\mathrm{yrs}$. to $6\ifmmode\times\else\texttimes\fi{}{10}^{35}\text{ }\text{ }\mathrm{yrs}$. A number of recent numerical fits to GUT-scale fermion masses can be accommodated within this model.

We consider an $SU(3{)}_{c}\ensuremath{\bigotimes}SU(2{)}_{L}\ensuremath{\bigotimes}SU(2{)}_{R}\ensuremath{\bigotimes}U(1{)}_{B\ensuremath{-}L}$ left-right symmetric model with three Higgs scalars including an $SU(2{)}_{L}$ doublet, an $SU(2{)}_{R}$ doublet and an $SU(2{)}_{L}\ensuremath{\bigotimes}SU(2{)}_{R}$ bidoublet. In addition to usual $SU(2)$-doublet fermions, our model contains $SU(2)$-triplet fermions with Majorana masses. The neutral components of the left-handed triplets can contribute a canonical seesaw while the neutral components of the right-handed triplets associated with the right-handed neutrinos can contribute a double/inverse-type seesaw. Our model can be embedded into an $SO(10)$ grand unification theory where the triplets belong to the $\mathbf{45}=(\mathbf{1},\mathbf{3},\mathbf{1},0)\ensuremath{\bigoplus}(\mathbf{1},\mathbf{1},\mathbf{3},0)\ensuremath{\bigoplus}\dots{}$ representations.

The specific shape of the squark, slepton and gaugino mass spectra, if measured with sufficient accuracy, can provide invaluable information not only about the dynamics underpinning their origin at some very high scale such as the unification scale ${M}_{G}$, but also about the intermediate scale physics encountered throughout their renormalization group equations evolution down to the energy scale accessible for the LHC. In this work, we study general features of the TeV scale soft supersymmetry breaking parameters stemming from a generic mSugra configuration within certain classes of supersymmetry $SO(10)$ GUTs with different intermediate symmetries below ${M}_{G}$. We show that particular combinations of soft masses show characteristic deviations from the mSugra limit in different models and thus, potentially, allow to distinguish between these, even if the new intermediate scales are outside the energy range probed at accelerators. We also compare our results to those obtained for the three minimal seesaw models with mSugra boundary conditions and discuss the main differences between those and our $SO(10)$ based models.

We show how gauge coupling unification is successfully implemented through non-supersymmetric grand unified theory, $SO(10)\times G_f (~G_f=S_4, SO(3)_f, SU(3)_f)$, using low-scale flavor symmetric model of the type $SU(2)_L\times U(1)_Y$ $ \times SU(3)_C \times S_4$ recently proposed by Hagedorn, Lindner, and Mohapatra, while assigning matter-parity discrete symmetry for the dark matter stability. For gauge coupling unification in the single-step breaking case, we show that a color-octet fermion and a hyperchargeless weak-triplet fermionic dark matter are the missing particles needed to complete its MSSM-equivalent degrees of freedom. When these are included the model automatically predicts the nonsupersymmetric grand unification with a scale identical to the minimal supersymmetric standard model/grand unified theory scale. We also find a two-step breaking model with Pati-Salam intermediate symmetry where the dark matter and a low-mass color-octet scalar or the fermion are signaled by grand unification. The proton-lifetime predictions are found to be accessible to ongoing or planned searches in a number of models. We discuss grand unified origin of the light fermionic triplet dark matter, the color-octet fermion, and their phenomenology., Comment: 26 pages LaTeX, 3 figures, typos added, references removed