Grand Unification Scale Research Articles

General bounds in Hybrid Natural Inflation

Recently we have studied in great detail a model of Hybrid Natural Inflation (HNI) by constructing two simple effective field theories. These two versions of the model allow inflationary energy scales as small as the electroweak scale in one of them or as large as the Grand Unification scale in the other, therefore covering the whole range of possible energy scales. In any case the inflationary sector of the model is of the form V(ϕ)=V0 (1+a cos(ϕ/f)) where 0⩽ a<1 and the end of inflation is triggered by an independent waterfall field. One interesting characteristic of this model is that the slow-roll parameter ϵ(ϕ) is a non-monotonic function of ϕ presenting a maximum close to the inflection point of the potential. Because the scalar spectrum \U0001d4abs(k) of density fluctuations when written in terms of the potential is inversely proportional to ϵ(ϕ) we find that \U0001d4abs(k) presents a minimum at ϕmin. The origin of the HNI potential can be traced to a symmetry breaking phenomenon occurring at some energy scale f which gives rise to a (massless) Goldstone boson. Non-perturbative physics at some temperature T<f might occur which provides a potential (and a small mass) to the originally massless boson to become the inflaton (a pseudo-Nambu-Goldstone boson). Thus the inflaton energy scale Δ is bounded by the symmetry breaking scale, Δ≡ VH1/4 <f. To have such a well defined origin and hierarchy of scales in inflationary models is not common. We use this property of HNI to determine bounds for the inflationary energy scale Δ and for the tensor-to-scalar ratio r.

A stronger case for superunification post Higgs boson discovery

Supersymmetry and more specifically supergravity grand unification allow one to extrapolate physics from the electroweak scale up to the grand unification scale consistent with electroweak data. Here we give a brief overview of their current status and show that the case for supersymmetry is stronger as a result of the Higgs boson discovery with a mass measurement at ∼125 GeV consistent with the supergravity grand unification prediction that the Higgs boson mass lies below 130 GeV. Thus the discovery of the Higgs boson and the measurement of its mass provide a further impetus for the search for sparticles to continue at the current and future colliders.

Dark Energy, QCD Axion, and Trans-Planckian-Inflaton Decay Constant

Pseudoscalars appear frequently in particle spectra. They can be light if they appear as pseudo-Goldstone bosons from some spontaneously broken global symmetries with the decay constant f. Since any global symmetry is broken at least by quantum gravitational effects, all pseudoscalars are massive. The mass scale of a pseudoscalar is determined by the spontaneous symmetry breaking scale f of the corresponding global symmetry and the explicit breaking terms in the effective potential. The explicit breaking terms can arise from anomaly terms with some non-Abelian gauge groups among which the best-known example is the potential of the QCD axion. Even if there is no breaking terms from gauge anomalies, there can be explicit breaking terms in the potential in which case the leading term suppressed by f determines the pseudoscalar mass scale. If the breaking term is extremely small and the decay constant is trans-Planckian, the corresponding pseudoscalar can be a candidate for a quintessential axion. In the other extreme that the breaking scales are large, still the pseudo-Goldstone boson mass scales are in general smaller than the decay constants. In such a case, still the potential of the pseudo-Goldstone boson at the grand unification scale is sufficiently flat near the top of the potential that it can be a good candidate for an inflationary model. We review these ideas in the bosonic collective motion framework.

Lepton Flavor Violating Higgs Boson Decays in Supersymmetric High Scale Seesaw Models

Within the MSSM, we have evaluated the decay rates for the lepton flavour violating Higgs boson decays (LFVHD) $h \rightarrow l_i l_j$ where $l_{i,j}$ are charged leptons and $i\neq j$. This has been done in a model independent (MI) way as well as in supersymmetric high scale seesaw models, in particular Type I see-saw model. Lepton flavour violation (LFV) is generated by non-diagonal entries in the mass matrix of the sleptons. In a first step we use the model independent approach where LFV (off-diagonal entries in the mass matrix) is introduced by hand while respecting the direct search constraints from the charged lepton flavor violating (cLFV) processes. In the second step we use high scale see-saw models where LFV is generated via renormalization group equations (RGE) from the grand unification scale (GUT) down to electroweak scale. cLFV decays are the most restrictive ones and exclude a large part of the parameter space for the MI as well as the high scale see-saw scenarios. Due to very strict constraints from cLFV, it is difficult to find large corrections to LFVHD. This applies in particular to $h \rightarrow \tau \mu$ where hints of an excess have been observed. If this signal is confirmed, it could not be explained with the models under investigation.

Constraints of chromoelectric dipole moments to natural SUSY type sfermion spectrum

We investigate the lower bounds of sfermion masses from the constraints of chromoelectric dipole moments (CEDMs) in the natural SUSY-type sfermion mass spectrum, in which stop mass $m_{\tilde t}$ is much smaller than the other sfermion masses $m_0$. The natural SUSY-type sfermion mass spectrum has been studied since the supersymmetric (SUSY) flavor-changing neutral currents (FCNC) are suppressed because of large sfermion masses of the first two generations, and the weak scale is stabilized because of the light stop. However, this type of sfermion mass spectrum is severely constrained by CEDM, because the light stop contributions to the up quark CEDM are not decoupled in the limit $m_0\rightarrow\infty$, while the down quark CEDM is decoupled in the limit. It is important that the constraints are severe even if SUSY-breaking parameters (and Higgsino mass) are taken to be real because complex diagonalizing matrices of Yukawa matrices, which are from complex Yukawa couplings, generate nonvanishing CP phases in off-diagonal elements of sfermion mass matrices. We calculate the CEDM of up and down quarks numerically in the minimal SUSY standard model, and give the lower bounds for stop mass and the other sfermion masses. We show that the lower bound of stop mass becomes 7 TeV to satisfy the CEDM constraints from Hg EDM. The result is not acceptable if the weak scale stability is considered seriously. We show that if the up-type Yukawa couplings are taken to be real at the grand unification scale, the CEDM constraints are satisfied even if $m_{\tilde t}\sim 1$ TeV.

Future CMB tests of dark matter: Ultralight axions and massive neutrinos

Measurements of cosmic microwave background (CMB) anisotropies provide strong evidence for the existence of dark matter and dark energy. They can also test its composition, probing the energy density and particle mass of different dark-matter and dark-energy components. CMB data have already shown that ultra-light axions (ULAs) with mass in the range $10^{-32}~{\rm eV} \to 10^{-26}~{\rm eV}$ compose a fraction $< 0.01$ of the cosmological critical density. Here, the sensitivity of a proposed CMB-Stage IV (CMB-S4) experiment (assuming a 1 arcmin beam and $< 1~\mu K{\rm-arcmin}$ noise levels over a sky fraction of 0.4) to the density of ULAs and other dark-sector components is assessed. CMB-S4 data should be $\sim 10$ times more sensitive to the ULA energy-density than Planck data alone, across a wide range of ULA masses $10^{-32}< m_{a}< 10^{-23}~{\rm eV}$, and will probe axion decay constants of $f_{a}\approx 10^{16}~{\rm GeV}$, at the grand unified scale. CMB-S4 could improve the CMB lower bound on the ULA mass from $\sim 10^{-25}~{\rm eV}$ to $10^{-23}~{\rm eV}$, nearing the mass range probed by dwarf galaxy abundances and dark-matter halo density profiles. These improvements will allow for a multi-$\sigma$ detection of percent-level departures from CDM over a wide range of masses. Much of this improvement is driven by the effects of weak gravitational lensing on the CMB, which breaks degeneracies between ULAs and neutrinos. We also find that the addition of ULA parameters does not significantly degrade the sensitivity of the CMB to neutrino masses. These results were obtained using the axionCAMB code (a modification to the CAMB Boltzmann code), presented here for public use.

Low-mass neutralino dark matter in supergravity scenarios: phenomenology and naturalness

The latest experimental results from the LHC and dark matter (DM) searches suggest that the parameter space allowed in supersymmetric theories is subject to strong reductions. These bounds are especially constraining for scenarios entailing light DM particles. Previous studies have shown that light neutralino DM in the Minimal Supersymmetric Standard Model (MSSM), with parameters defined at the electroweak scale, is still viable when the low energy spectrum of the model features light sleptons, in which case, the relic density constraint can be fulfilled. In view of this, we have investigated the viability of light neutralinos as DM candidates in the MSSM, with parameters defined at the grand unification scale. We have analysed the optimal choices of non-universalities in the soft supersymmetry-breaking parameters for both, gauginos and scalars, in order to avoid the stringent experimental constraints. We show that light neutralinos, with a mass as low as 25 GeV, are viable in supergravity scenarios if the gaugino mass parameters at high energy are very non universal, while the scalar masses can remain of the same order. These scenarios typically predict a very small cross section of neutralinos off protons and neutrons, thereby being very challenging for direct detection experiments. However, a potential detection of smuons and selectrons at the LHC, together with a hypothetical discovery of a gamma-ray signal from neutralino annihilations in dwarf spheroidal galaxies could shed light on this kind of solutions. Finally, we have investigated the naturalness of these scenarios, taking into account all the potential sources of tuning. Besides the electroweak fine-tuning, we have found that the tuning to reproduce the correct DM relic abundance and that to match the measured Higgs mass can also be important when estimating the total degree of naturalness.

Large BR(h→τμ) in supersymmetric models

We analyze the Lepton Flavor Violating (LFV) Higgs decay h -> tau mu in three supersymmetric models: Minimal Supersymmetric Standard Model (MSSM), Supersymmetric Seesaw Model (SSM), and Supersymmetric B-L model with Inverse Seesaw (BLSSM-IS). We show that in generic MSSM, with non-universal slepton masses and/or trilinear couplings, it is not possible to enhance BR(h -> tau mu) without violating the experimental bound on the BR(tau -> mu gamma). In SSM, where flavor mixing is radiatively generated, the LFV process mu -> e gamma strictly constrains the parameter space and the maximum value of BR(h -> tau mu) is of order 10^-10, which is extremely smaller than the recent results reported by the CMS and ATLAS experiments. In BLSSM-IS, with universal soft SUSY breaking terms at the grand unified scale, we emphasize that the measured values of BR(h -> tau mu) can be accommodated in a wide region of parameter space without violating LFV constraints. Thus, confirming the LFV Higgs decay results will be a clear signal of BLSSM-IS type of models. Finally, the signal of h -> tau mu in the BLSSM-IS at the LHC, which has a tiny background, is analyzed.

Constraints on small-field axion inflation

We study general class of small-field axion inflations which are the mixture of polynomial and sinusoidal functions suggested by the natural and axion monodromy inflations. The axion decay constants leading to the successful axion inflations are severely constrained in order not to spoil the Big-Bang nucleosynthesis and overproduce the isocurvature perturbation originating from the QCD axion. We in turn find that the cosmologically favorable axion decay constants are typically of order the grand unification scale or the string scale which is consistent with the prediction of closed string axions.

High-scale validity of a two-Higgs-doublet scenario: metastability included

We identify regions in a Type-II two-Higgs-doublet model which correspond to a metastable electroweak vacuum with lifetime larger than the age of the universe. We analyse scenarios which retain perturbative unitarity up to grand unification and Planck scales. Each point in the parameter space is restricted using data from the Large Hadron Collider (LHC) as well as flavour and precision electroweak constraints. We find that substantial regions of the parameter space are thus identified as corresponding to metastability, which complement the allowed regions for absolute stability, for top quark mass at the high as well as low end of its currently allowed range. Thus, a two-Higgs-doublet scenario with the electroweak vacuum, either stable or metastable, can sail through all the way up to the Planck scale without facing any contradiction.

Sparticle spectroscopy of the minimal SO(10) model

The supersymmetric (SUSY) minimal SO(10) model is a well-motivated grand unified theory, where the Standard Model (SM) fermions have Yukawa couplings with only one 10-plet and one 126‾-plet Higgs fields and it is highly non-trivial if the realistic quark and lepton mass matrices can be reproduced in this context. It has been known that the best fit for all the SM fermion mass matrices is achieved by a vacuum expectation value of the 126‾-plet Higgs field being at the intermediate scale of around O(1013) GeV. Under the presence of the SO(10) symmetry breaking at the intermediate scale, the successful SM gauge coupling unification is at risk and likely to be spoiled. Recently, it has been shown that the low-energy fermion mass matrices, except for the down-quark mass predicted to be too low, are very well-fitted without the intermediate scale. In order to resolve the too-low down quark mass while keeping the other fittings intact, we consider SUSY threshold corrections to reproduce the right down quark mass. It turns out that this requires flavor-dependent soft parameters. Motivated by this fact, we calculate particle mass spectra at low energies with flavor-dependent sfermion masses at the grand unification scale. We present a benchmark particle mass spectrum which satisfies a variety of phenomenological constraints, in particular, the observed SM-like Higgs boson mass of around 125 GeV and the relic abundance of the neutralino dark matter as well as the experimental result of the muon anomalous magnetic moment. In the resultant mass spectrum, sleptons in the first and second generations, bino and winos are all light, and this scenario can be tested at the LHC Run-2 in the near future.

MSSM without free parameters

It is often argued that the minimal supersymmetric standard model has O(100) free parameters and the generic parameter region is already excluded by the null observation of the flavor and CP violating processes as well as the constraints from the LHC experiments. This situation naturally leads us to consider the case where all the dangerous soft supersymmetry breaking terms such as the scalar masses and scalar couplings are absent, while only the unified gaugino mass term and the mu term are non-vanishing at the grand unification scale. We revisit this simple situation taking into account the observed Higgs boson mass, 125 GeV. Since the gaugino mass and the mu term are fixed in order to explain the Higgs boson and the Z boson masses, there is no free parameter left in this scenario. We find that there are three independent parameter sets exist including ones which have not been discussed in the literature. We also find that the abundance of the dark matter can be explained by relic gravitinos which are non-thermally produced as decay products of the SUSY particles while satisfying constraints from Big Bang Nucleosynthesis. We discuss the effects of the gravity mediation which generically give contribution to the soft terms of the order of the gravitino mass. It turns out that newly found parameter set is preferable to explain the Higgs boson mass as well as the gravitino dark matter while satisfying the constraints from the electric dipole moments of the electron and the nucleon.

Metastable dark energy

We build a model of metastable dark energy, in which the observed vacuum energy is the value of the scalar potential at the false vacuum. The scalar potential is given by a sum of even self-interactions up to order six. The deviation from the Minkowski vacuum is due to a term suppressed by the Planck scale. The decay time of the metastable vacuum can easily accommodate a mean life time compatible with the age of the universe. The metastable dark energy is also embedded into a model with $SU(2)_R$ symmetry. The dark energy doublet and the dark matter doublet naturally interact with each other. A three-body decay of the dark energy particle into (cold and warm) dark matter can be as long as large fraction of the age of the universe, if the mediator is massive enough, the lower bound being at intermediate energy level some orders below the grand unification scale. Such a decay shows a different form of interaction between dark matter and dark energy, and the model opens a new window to investigate the dark sector from the point-of-view of particle physics.

Quasi-Yukawa unification and fine-tuning in U(1) extended SSM

We consider the low scale implications in the U(1)' extended MSSM (UMSSM). We restrict the parameter space such that the lightest supersymmetric particle (LSP) is always the lightest neutralino. In addition, we impose quasi Yukawa unification (QYU) at the grand unification scale (M_GUT). QYU strictly requires the ratios among the yukawa couplings as y_t/y_b ~ 1.2, y_tau/y_b ~ 1.4, and y_t/y_tau ~ 0.8. We find that the need of fine-tuning over the fundamental parameter space of QYU is in the acceptable range (Delta_EW <= 10^3), even if the universal boundary conditions are imposed at M_ GUT, in contrast to CMSSM and NUHM. UMSSM with the universal boundary conditions yields heavy stops (m_{stop} >~ 2.5 TeV), gluinos (m_gluino >~ 2 TeV), and squarks from the first two families (m_squarks >~ 4 TeV). Similarly the stau mass is bounded from below at about 1.5 TeV. Despite this heavy spectrum, we find Delta_EW >~ 300, which is much lower than that needed for the minimal supersymmetric models. In addition, UMSSM yield relatively small mu-term, and the LSP neutralio is mostly form by the Higgsinos of mass >~ 700 GeV. We obtain also bino-like dark matter (DM) of mass about 400 GeV. Wino is usually found to be heavier than Higgsinos and binos, but there is a small region where mu ~ M_1 ~ M_2 ~ 1 TeV. We also identify chargino-neutralino coannihilation channel and A-resonance solutions which reduce the relic abundance of LSP neutralino down to the ranges compatible with the current WMAP measurements.

Neutrino anarchy and renormalization group evolution

The observed pattern of neutrino mixing angles is in good agreement with the hypothesis of neutrino anarchy, which posits that Nature has chosen the entries of the leptonic mixing matrix at random. In this paper we investigate how stable this conclusion is under renormalization group effects. Working in the simplest type-I seesaw model and two variants of the inverse seesaw model we study how the statistical distributions of the neutrino mixing parameters evolve between the Grand Unification scale and the electroweak scale. Especially in the inverse seesaw case we find significant distortions: mixing angles tend to be smaller after RG running, and the Dirac CP phase tends to be closer to zero. The p-value describing the compatibility between the observed mixing angles and the anarchy hypothesis increases by 10-20%. This illustrates that RG effects are highly relevant for quantitative studies of the anarchy scenario.

Vacuum stability and supersymmetry at high scales with two Higgs doublets

We investigate the stability of the electroweak vacuum for two-Higgs doublet models with a supersymmetric UV completion. The supersymmetry breaking scale is taken to be of the order of the grand unification scale. We first study the case where all superpartners decouple at this scale. We show that contrary to the Standard Model with one Higgs doublet, matching to the supersymmetric UV completion is possible if the low-scale model contains two Higgs doublets. In this case vacuum stability and experimental constraints point towards low values of tan(beta) < 2 and pseudoscalar masses of at least about a TeV. If the higgsino superpartners of the Higgs fields are also kept light, the conclusions are similar and essentially independent of the higgsino mass. Finally, if all gauginos are also given electroweak-scale masses (split supersymmetry with two Higgs doublets), the model cannot be matched to supersymmetry at very high scales when requiring a 125 GeV Higgs. Light neutral and charged higgsinos therefore emerge as a promising signature of a supersymmetric UV completion of the Standard Model at the grand unification scale.

Implications of the CMS search for W R on grand unification

The CMS experiment at the Large Hadron Collider has reported a 2.8$\sigma$ excess in the $(2e)(2jets)$ channel around 2.1 TeV. Interpretation of this data is reconsidered in terms of the production of a right-handed weak gauge boson, $W_R$, of the left-right symmetric model and in an $SO(10)$ grand unified theory abiding by the Extended Survival Hypothesis. The left-right symmetric model can be consistent with this excess if (a) the heavy right-handed neutrino has a mass near $W_R$, or (b) if $g_L \neq g_R$, or (c) the right-handed CKM matrix is nontrivial. Combinations of the above possibilities are also viable. A $W_R$ with a mass in the TeV region if embedded in $SO(10)$ is not compatible with $g_L = g_R$. Rather, it implies $0.64 \leq g_R/g_L \leq 0.78$. Further, a unique symmetry-breaking route -- the order being left-right discrete symmetry breaking first, followed by $SU(4)_C$ and finally $SU(2)_R$ -- to the standard model is picked out. The $L \leftrightarrow R$ discrete symmetry has to be broken at around $10^{16}$ GeV. The grand unification scale is pushed to $10^{18}$ GeV making the detection of proton decay in ongoing searches rather unlikely. The $SU(4)_C$ breaking scale can be at its allowed lower limit of $10^6$ GeV so that $n - \bar{n}$ oscillation or flavour changing processes such as $K_L \rightarrow \mu e$ and $B_{d,s} \rightarrow \mu e$ may be detectable. The Higgs scalar multiplets responsible for $SO(10)$ symmetry breaking at various stages are uniquely identified so long as one adheres to a minimalist principle. We also remark, {\em en passant}, about a partially unified Pati-Salam model.

Beyond the CMSSM without an accelerator: proton decay and direct dark matter detection.

We consider two potential non-accelerator signatures of generalizations of the well-studied constrained minimal supersymmetric standard model (CMSSM). In one generalization, the universality constraints on soft supersymmetry-breaking parameters are applied at some input scale M_{mathrm{in}}below the grand unification (GUT) scale M_{mathrm{GUT}}, a scenario referred to as ‘sub-GUT’. The other generalization we consider is to retain GUT-scale universality for the squark and slepton masses, but to relax universality for the soft supersymmetry-breaking contributions to the masses of the Higgs doublets. As with other CMSSM-like models, the measured Higgs mass requires supersymmetric particle masses near or beyond the TeV scale. Because of these rather heavy sparticle masses, the embedding of these CMSSM-like models in a minimal SU(5) model of grand unification can yield a proton lifetime consistent with current experimental limits, and may be accessible in existing and future proton decay experiments. Another possible signature of these CMSSM-like models is direct detection of supersymmetric dark matter. The direct dark matter scattering rate is typically below the reach of the LUX-ZEPLIN (LZ) experiment if M_{mathrm{in}} is close to M_{mathrm{GUT}}, but it may lie within its reach if M_{mathrm{in}} lesssim 10^{11} GeV. Likewise, generalizing the CMSSM to allow non-universal supersymmetry-breaking contributions to the Higgs offers extensive possibilities for models within reach of the LZ experiment that have long proton lifetimes.

Shift symmetry and Higgs inflation in supergravity with observable gravitational waves

We demonstrate how to realize within supergravity a novel chaotic-type inflationary scenario driven by the radial parts of a conjugate pair of Higgs superfields causing the spontaneous breaking of a grand unified gauge symmetry at a scale assuming the value of the supersymmetric grand unification scale. The superpotential is uniquely determined at the renormalizable level by the gauge symmetry and a continuous R symmetry. We select two types of Kahler potentials, which respect these symmetries as well as an approximate shift symmetry. In particular, they include in a logarithm a dominant shift-symmetric term proportional to a parameter c- together with a small term violating this symmetry and characterized by a parameter c+. In both cases, imposing a lower bound on c-, inflation can be attained with subplanckian values of the original inflaton, while the corresponding effective theory respects perturbative unitarity for r+-=c+/c-<1. These inflationary models do not lead to overproduction of cosmic defects, are largely independent of the one-loop radiative corrections and accommodate, for natural values of r+-, observable gravitational waves consistently with all the current observational data. The inflaton mass is mostly confined in the range (3.7-8.1)x10^10 GeV.

Multi-lepton signatures at the LHC from sneutrino dark matter

We investigate multi-lepton LHC signals arising from an extension at the grand unification scale of the standard minimal supersymmetric model (MSSM) involving right-handed neutrino superfields. In this framework neutrinos have Dirac masses and the mixed sneutrinos are the lightest supersymmetric particles and hence the dark matter candidates. We analyze the model parameter space in which the sneutrino is a good dark matter particle and has a direct detection cross-section compatible with the LUX bound. Studying the supersymmetric mass spectrum of this region, we find several multilepton signatures relevant for the LHC, which are distinct from the predictions of the MSSM with neutralino dark matter. We point out that if one of these signatures is detected, it might be an indication of sneutrino dark matter.