Supersymmetric Grand Research Articles

Probing stochastic gravitational wave background from SU(5) × U(1)χ strings in light of NANOGrav 15-year data

A realistic model of SU(5) × U(1)χ, embedded in SO(10) supersymmetric grand unified theory, is investigated for the emergence of a metastable cosmic string network. This network eventually decays via the Schwinger production of monopole-antimonopole pairs, subsequently generating a stochastic gravitational wave background that is compatible with the NANOGrav 15-year data. In order to avoid the monopole problem in the breaking of both SO(10) and SU(5), a non-minimal Higgs inflation scenario is incorporated. The radiative breaking of the U(1)χ symmetry at a slightly lower scale plays a pivotal role in aligning the string tension parameter with the observable range. The resultant gravitational wave spectrum not only accounts for the signal observed in the most recent pulsar timing array (PTA) experiments but is also accessible to both current and future ground-based and space-based experiments.

Primordial black holes from D-parity breaking in SO(10) grand unified theory

The growing evidence of gravitational waves from binary black hole mergers has renewed the interest in study of primordial black holes (PBH). Here we study a mechanism for the formation of PBH from collapse of pseudo-topological domain walls which form out of equilibrium during inflation and then collapse post inflation. We apply the study to domain wall formation due to D-parity embedded in a supersymmetric grand unified theory (GUT) based on SO(10) and compare the abundance of resulting PBH with the existing constraints. Thus the macroscopic relics can then be used to constrain or rule out a GUT, or demand a refinement of the theory of PBH formation in this class of GUTs.

Probing the supersymmetric grand unified theories with gravity mediation at the future proton–proton colliders and hyper-Kamiokande experiment

With the grand desert hypothesis, we have proposed to probe the supersymmetric Grand Unified Theories (GUTs) at the future proton–proton (pp) colliders and Hyper-Kamiokande experiment previously. In this paper, we study the supersymmetric GUTs with gravity mediated supersymmetry breaking in details. First, considering the dimension-six proton decay via heavy gauge boson exchange, we point out that we can probe the supersymmetric GUTs with GUT scale M_{GUT} up to 1.778times 10^{16} GeV at the Hyper-Kamiokande experiment. Second, for the supersymmetric GUTs with M_{GUT} ge 1.0times 10^{16} GeV and M_{GUT} ge 1.2times 10^{16} GeV, we show that the upper bounds on the universal gaugino mass are 7.2 TeV and 3.5 TeV, respectively, and thus the corresponding upper bounds on gluino mass are 15 TeV and 8 TeV, respectively. Also, we shall study the masses for charginos, neutralinos, squarks, sleptons, and Higgs particles in details. In particular, the supersymmetric GUTs with M_{GUT} le 1.2times 10^{16} GeV can be probed at the Hyper-Kamiokande experiment, and the supersymmetric GUTs with M_{GUT}ge 1.2times 10^{16} GeV can be probed at the future 100 TeV pp collider experiments such as the textrm{FCC}_textrm{hh} and SppC via gluino searches. Thus, the supersymmetric GUTs with gravity mediation can be probed by the textrm{FCC}_textrm{hh}, SppC, and Hyper-Kamiokande experiments. In our previous study, we have shown that the supersymmetric GUTs with anomaly and gauge mediated supersymmetry breakings are well within the reaches of these experiments. Therefore, our proposal provides the concrete scientific goal for the textrm{FCC}_textrm{hh}, SppC, and Hyper-Kamiokande experiments: probing the supersymmetric GUTs.

Data-driven analysis of a SUSY GUT of flavour

We present a data-driven analysis of a concrete Supersymmetric (SUSY) Grand Unified Theory (GUT) of flavour, based on SU(5) × S4, which predicts charged fermion and neutrino mass and mixing, and where the mass matrices of both the Standard Model and the Supersymmetric particles are controlled by a common symmetry at the GUT scale. This framework also predicts non-vanishing non-minimal flavour violating effects, motivating a sophisticated data-driven parameter analysis to uncover the signatures and viability of the model. This computer-intensive Markov-Chain-Monte-Carlo (MCMC) based analysis includes a large range of flavour as well as dark matter and SUSY observables, predicts distributions for a range of physical quantities which may be used to test the model. The predictions include maximally mixed sfermions, μ → eγ close to its experimental limit and successful bino-like dark matter with nearby winos (making direct detection unlikely), implying good prospects for discovering winos and gluinos at forthcoming collider runs. The results also demonstrate that the Georgi-Jarlskog mechanism does not provide a good description of the splitting of down type quark masses and charged leptons, while neutrinoless double beta decay is predicted at observable rates.

New results in models with reduced couplings

The reduction of couplings concept consists in searching for renormalization group invariant relations among parameters that hold to all orders in perturbation theory. This technique has been applied to [Formula: see text] supersymmetric Grand Unified Theories, some of which can become finite to all loops. We review the basic idea and tools, as well as two theories in which reduction of couplings has been applied: (i) an all-loop finite [Formula: see text] [Formula: see text] model and (ii) a reduced version of the Minimal Supersymmetric Standard Model. The finite model exhibits high relic abundance of cold dark matter, while, on the contrary, the second model has underproduction in the early universe. For each model we select three representative benchmark scenarios. The heavy Higgs and supersymmetric spectrum of the finite [Formula: see text] model lies beyond the reach of the 14 TeV HL-LHC, while large parts of the predicted spectrum can be tested in the 100 TeV FCC-hh, although the higher mass regions are beyond its reach. On the other hand, the Reduced Minimal Supersymmetric Standard Model (Reduced MSSM) is found to be ruled out by LHC searches for heavy neutral MSSM Higgs bosons.

Spinning no-scale {mathcal {F}}-SU(5) in the right direction

The Fermi National Accelerator Laboratory (FNAL) recently announced confirmation of the Brookhaven National Lab (BNL) measurements of the g-2 of the muon that uncovered a discrepancy with the theoretically calculated Standard Model value. We suggest an explanation for the combined BNL+FNAL 4.2sigma deviation within the supersymmetric grand unification theory (GUT) model No-Scale {mathcal {F}}-SU(5) supplemented with a string derived TeV-scale extra 10+overline{10} vector-like multiplet and charged vector-like singlet (XE,XE^c), dubbed flippons. We introduced these vector-like particles into No-Scale Flipped SU(5) many years ago, and as a result, the renormalization group equation (RGE) running was immediately shaped to produce a distinctive and rather beneficial two-stage gauge coupling unification process to avoid the Landau pole and lift unification to the string scale, in addition to contributing through 1-loop to the light Higgs boson mass. The flippons have long stood ready to tackle another challenge, and now do so yet again, where the charged vector-like “lepton”/singlet couples with the muon, the supersymmetric down-type Higgs H_d, and a singlet S, using a chirality flip to easily accommodate the muonic g-2 discrepancy in No-Scale {mathcal {F}}-SU(5). Considering the phenomenological success of this string derived model over the prior 11 years that remains accommodative of all presently available LHC limits plus all other experimental constraints, including no fine-tuning, and the fact that for the first time a Starobinsky-like inflationary model consistent with all cosmological data was derived from superstring theory in No-Scale Flipped SU(5), we believe it is imperative to reconcile the BNL+FNAL developments within the model space.

Leptonic CP and flavor violations in SUSY GUT with right-handed neutrinos

We study leptonic $CP$ and flavor violations in supersymmetric grand unified theory with right-handed neutrinos, paying attention to the renormalization group effects on the slepton mass matrices due to the neutrino and grand unified theory Yukawa interactions. In particular, we study in detail the impacts of the so-called Casas-Ibarra parameters on $CP$ and flavor violating observables. The renormalization group effects induce $CP$ and flavor violating elements of the supersymmetric breaking scalar mass squared matrices, which may result in sizable leptonic $CP$ and flavor violating signals. Assuming a seesaw formula for the active neutrino masses, the renormalization group effects have been often thought to be negligible as the right-handed neutrino masses become small. With the most general form of the neutrino Yukawa matrix, i.e., taking into account the Casas-Ibarra parameters; however, this is not the case. We found that the maximal possible sizes of signals of leptonic $CP$ and flavor violating processes are found to be insensitive to the mass scale of the right-handed neutrinos and that they are as large as (or larger than) the present experimental bounds irrespective of the right-handed neutrino masses.

Implications of gravitational waves for supersymmetric grand unification

Supersymmetric grand unification based on $SO(10)$ is one of the most attractive paradigms in physics beyond the Standard Model. Inspired by the recent NANOGrav signal, we discuss the implications of detecting a stochastic gravitational wave background emitted by a network of cosmic strings for the $SO(10)$ grand unification. Starting from a minimal model with multiple steps of symmetry breaking, we show that it generally prefers a high intermediate scale above ${10}^{14}\text{ }\text{ }\mathrm{GeV}$ that is favored by observable primordial gravitational waves. The observed spectrum can potentially narrow the possible range of the cosmic string scale and restricts the unified couplings and the unification scale by requiring gauge coupling unification. As an indirect consequence of the high cosmic string scale, the monopole abundance places nontrivial constraints on the theory. These are complementary to the proton decay constraints and probe different facets of supersymmetric $SO(10)$ unification theories.

Probing the supersymmetric grand unified theories at the future proton-proton colliders and Hyper-Kamiokande experiment

Gauge coupling unification in the Supersymmetric Standard Models strongly implies the Grand Unified Theories (GUTs). With the grand desert hypothesis, we show that the supersymmetric GUTs can be probed at the future proton-proton (pp) colliders and Hyper-Kamiokande experiment. For the GUTs with the GUT scale MGUT≤1.0×1016 GeV, we can probe the dimension-six proton decay via heavy gauge boson exchange at the Hyper-Kamiokande experiment. Moreover, for the GUTs with MGUT≥1.0×1016 GeV, we study the upper bounds on the gaugino and sfermion masses. We show that the GUTs with anomaly and gauge mediated supersymmetry breakings are well within the reaches of the future 100 TeV pp colliders such as the FCChh and SppC, and the supersymmetric GUTs with gravity mediated supersymmetry breaking can be probed at the future 160 TeV pp collider.

Probing unified theories with reduced couplings at future hadron colliders

The search for renormalization group invariant relations among parameters to all orders in perturbation theory constitutes the basis of the reduction of couplings concept. Reduction of couplings can be achieved in certain N=1 supersymmetric grand unified theories and few of them can become even finite at all loops. We review the basic idea, the tools that have been developed as well as the resulting theories in which successful reduction of couplings has been achieved so far. These include: (i) a reduced version of the minimal N = 1 SU(5) model, (ii) an all-loop finite N = 1 SU(5) model, (iii) a two-loop finite N = 1 SU(3)^3 model and finally (vi) a reduced version of the Minimal Supersymmetric Standard Model. In this paper we present a number of benchmark scenarios for each model and investigate their observability at existing and future hadron colliders. The heavy supersymmetric spectra featured by each of the above models are found to be beyond the reach of the 14 TeV HL-LHC. It is also found that the reduced version of the MSSM is already ruled out by the LHC searches for heavy neutral MSSM Higgs bosons. In turn the discovery potential of the 100 TeV FCC-hh is investigated and found that large parts of the predicted spectrum of these models can be tested, but the higher mass regions are beyond the reach even of the FCC-hh.

Unification predictions with or without supersymmetry

Supersymmetric (SUSY) grand unified theories (GUTs) appear to be best motivated for understanding strong, weak and electromagnetic interactions of nature. We briefly review emergence of new formulas for running fermion masses valid in direct breaking of GUTs. High scale mixing unification of quark and neutrino mixings and existence of theorems on vanishing theoretical uncertainties in GUT predictions are discussed. D-Parity properties of SO(10) representations leading to large number of intermediate breaking models are pointed out. Unification predictions of SUSY SO(10) in the light of neutrino mass, lepton flavor violation, baryogenesis via leptogenesis within gravitino constraint, and proton decay are noted. We further discuss realisation of flavour unification and possibility of fitting all fermion masses through R-Parity and D-Parity conserving left-right symmetric intermediate breaking in SUSY SO(10)$\times S_4$. In the absence of SUSY two interesting possibilities of minimal grand desert modifications with only one intermediate mass scalar in each case and their applications to dark matter decay through type-I seesaw are briefly noted. Heavy scalar triplet decay leptogenesis through new ansatz for type-II seesaw dominance in non-SUSY SO(10), emergence of new CP asymmetry formulas and model capabilities to explain WIMP dark matter, vacuum stability of the scalar potential and experimentally observed limit on proton lifetime are briefly summarized.

Precision unification and Higgsino dark matter in GUT scale supersymmetry

Even if the concerns related to the naturalness of the electroweak scale are repressed, the Higgs mass and stability of the electroweak vacuum do not allow arbitrarily large supersymmetry breaking scale, $M_S$, in the minimal models with split or high-scale supersymmetry. We show that $M_S$ can be raised to the GUT scale if the theory below $M_S$ contains a Higgs doublet, a pair of TeV scale Higgsino and widely separated gauginos in addition to the Standard Model particles. The presence of wino and gluino below ${\cal O}(100)$ TeV leads to precision unification of the gauge couplings consistent with the current limits on the proton lifetime. Wino, at this scale, renders the Higgsino as pseudo-Dirac dark matter which in turn evades the existing constraints from the direct detection experiments. Bino mass scale is required to be $\gtrsim 10^{10}$ GeV to get the observed Higgs mass respecting the current limit on the charged Higgs mass. The framework predicts, $1 \lesssim \tan\beta \lesssim 2.2$ and $\tau[p\to e^+\, \pi^0] < 7 \times 10^{35}$ years, almost independent of values of the other parameters. The electroweak vacuum is found to be stable or metastable. The underlying framework provides an example of a viable sub-GUT scale theory of supersymmetric grand unified theory in which supersymmetry and unified gauge symmetry are broken at a common scale.

New ultraviolet operators in supersymmetric SO(10) GUT and consistent cosmology

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

Updates and New Results in Models with Reduced Couplings

AbstractThe idea of reduction of couplings consists in searching for renormalization group invariant relations between parameters of a renormalizable theory that hold to all orders of perturbation theory. Based on the principle of the reduction of couplings, one can construct Finite Unified Theories which are supersymmetric Grand Unified Theories that can be made all‐order finite. The prediction of the top quark mass well in advance of its discovery and the prediction of the light Higgs boson mass in the range GeV much earlier than its discovery are among the celebrated successes of such models. Here, after a brief review of the reduction of couplings method and the properties of the resulting finiteness in supersymmetric theories, we analyse four phenomenologically favoured models: a minimal version of the , a finite , a finite model and a reduced version of the Minimal Supersymmetric Standard Model. A relevant update in the phenomenological evaluation has been the improved light Higgs‐boson mass prediction as provided by the latest version of FeynHiggs. All four models predict relatively heavy supersymmetric spectra that start just below or above the TeV scale, consistent with the non‐observation LHC results. Depending on the model, the lighter regions of the spectra could be accessible at CLIC, while the FCC‐hh will be able to test large parts of the predicted spectrum of each model. The lightest supersymmetric particle, a neutralino, is considered as a cold dark matter candidate and put to test using the latest MicrOMEGAs code.

Trans-Planckian censorship and inflation in grand unified theories

The recently proposed trans-Planckian censorship conjecture (TCC) amounts to the claim that inflation models with an inflationary energy scale larger than Λinfmax∼109GeV belong to the swampland, i.e., cannot be embedded into a consistent theory of quantum gravity. In this paper, we point out that this constraint can be readily satisfied in D-term hybrid inflation (DHI), which is a well-motivated inflation scenario in the context of supersymmetric grand unification. In DHI, the amplitude of the primordial scalar power spectrum originates from a Fayet–Iliopoulos term of the order of the unification scale, ξ∼1016GeV. At the same time, the TCC results in an upper bound on the corresponding gauge coupling constant of gmax∼10−14. We are able to show that this constraint translates into an upper bound on the gravitino mass of m3/2max∼10MeV, which opens the possibility that dark matter is accounted for by thermally produced gravitinos, if the reheating temperature is close to Treh∼100TeV. Interestingly enough, a somewhat similar gravitino mass range has recently been derived in a model that aims at explaining dark energy in terms of axion quintessence and resolving the Hubble tension by means of decaying gravitino dark matter.

Non-minimal flavour violation in A4 \xd7 SU(5) SUSY GUTs with smuon assisted dark matter

We study CP-conserving non-minimal flavour violation in A4 × SU(5) inspired Supersymmetric Grand Unified Theories (GUTs), focussing on the regions of parameter space where dark matter is successfully accommodated due to a light right-handed smuon a few GeV heavier than the lightest neutralino. In this region of parameter space we find that some of the flavour-violating parameters are constrained by the requirement of the dark matter relic density, due to the delicate interplay between the smuon and neutralino masses. By scanning over GUT scale flavour violating parameters, constrained by low-energy quark and lepton flavour violating observables, we find a striking difference in the results in which individual parameters are varied to those where multiple parameters are varied simultaneously, where the latter relaxes the constraints on flavour violating parameters due to cancellations and/or correlations. Since charged lepton-flavour violation provides the strongest constraints within a GUT framework, due to relations between quark and lepton flavour violation, we examine in detail a prominent correlation between some of the flavour violating parameters at the GUT scale consistent with the stringent lepton flavour violating process μ → eγ. We also examine the relation between GUT scale and low scale flavour violating parameters, for both quarks and leptons, and show how the usual expectations may be violated due to the correlations when multiple parameters are varied simultaneously.

E6 inspired SUSY models with custodial symmetry

The breakdown of [Formula: see text] within the supersymmetric (SUSY) Grand Unified Theories (GUTs) can result in SUSY extensions of the standard model (SM) based on the SM gauge group together with extra [Formula: see text] gauge symmetry under which right-handed neutrinos have zero charge. In these [Formula: see text] extensions of the minimal supersymmetric standard model (MSSM) a single discrete [Formula: see text] symmetry may be used to suppress the most dangerous operators, that give rise to proton decay as well as nondiagonal flavour transitions at low energies. The SUSY models under consideration involves [Formula: see text] and extra exotic matter beyond the MSSM. We discuss leptogenesis within this SUSY model and argue that the extra exotic states may lead to the nonstandard Higgs decays.

Axion isocurvature perturbations in low-scale models of hybrid inflation

The quantum chromodynamics (QCD) axion solves the strong $CP$ problem and represents an attractive particle candidate for cold dark matter (CDM). However, quantum fluctuations of the axion field during inflation easily result in large CDM isocurvature perturbations that are in conflict with observations of the cosmic microwave background. In this paper, we demonstrate how this problem can be solved in low-scale models of hybrid inflation that may emerge from supersymmetric grand unified theories. We consider both F-term hybrid inflation and D-term hybrid inflation in supergravity, explicitly taking into account the effect of hidden-sector supersymmetry breaking. We discuss the production of cosmic strings and show how the soft terms in the scalar potential readily allow us to achieve the correct scalar spectral index. In both cases, we are able to identify large regions in parameter space that are consistent with all constraints. In particular, we find that evading the CDM isocurvature constraint always requires a small Yukawa or gauge coupling of $\mathcal{O}({10}^{\ensuremath{-}3})$ or smaller. This translates into upper bounds on the gravitino mass of $\mathcal{O}({10}^{5})\text{ }\text{ }\mathrm{GeV}$ in F-term hybrid inflation and $\mathcal{O}({10}^{9})\text{ }\text{ }\mathrm{GeV}$ in D-term hybrid inflation. Our results point to interesting scenarios in well-motivated parameter regions that will be tested in future axion and cosmic microwave background experiments.

The LHC Higgs Boson Discovery: Updated Implications for Finite Unified Theories and the SUSY Breaking Scale

Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made finite to all orders in perturbation theory, based on the principle of the reduction of couplings. The latter consists of searching for renormalization group invariant relations among parameters of a renormalizable theory holding to all orders in perturbation theory. FUTs have proven very successful so far. In particular, they predicted the top quark mass one and half years before its experimental discovery, while around five years before the Higgs boson discovery, a particular FUT was predicting the light Higgs boson in the mass range ∼121–126 GeV, in striking agreement with the discovery at LHC. Here, we review the basic properties of the supersymmetric theories and in particular finite theories resulting from the application of the method of reduction of couplings in their dimensionless and dimensionful sectors. Then, we analyze the phenomenologically-favored FUT, based on SU(5). This particular FUT leads to a finiteness constrained version of the Minimal SUSY Standard Model (MSSM), which naturally predicts a relatively heavy spectrum with colored supersymmetric particles above 2.7 TeV, consistent with the non-observation of those particles at the LHC. The electroweak supersymmetric spectrum starts below 1 TeV, and large parts of the allowed spectrum of the lighter might be accessible at CLIC. The FCC-hhwill be able to fully test the predicted spectrum.

Likelihood analysis of the sub-GUT MSSM in light of LHC 13-TeV data

We describe a likelihood analysis using MasterCode of variants of the MSSM in which the soft supersymmetry-breaking parameters are assumed to have universal values at some scale M_mathrm{in} below the supersymmetric grand unification scale M_mathrm{GUT}, as can occur in mirage mediation and other models. In addition to M_mathrm{in}, such ‘sub-GUT’ models have the 4 parameters of the CMSSM, namely a common gaugino mass m_{1/2}, a common soft supersymmetry-breaking scalar mass m_0, a common trilinear mixing parameter A and the ratio of MSSM Higgs vevs tan beta , assuming that the Higgs mixing parameter mu > 0. We take into account constraints on strongly- and electroweakly-interacting sparticles from sim 36/fb of LHC data at 13 TeV and the LUX and 2017 PICO, XENON1T and PandaX-II searches for dark matter scattering, in addition to the previous LHC and dark matter constraints as well as full sets of flavour and electroweak constraints. We find a preference for M_mathrm{in}sim 10^5 to 10^9 ,, mathrm {GeV}, with M_mathrm{in}sim M_mathrm{GUT} disfavoured by Delta chi ^2 sim 3 due to the mathrm{BR}(B_{s, d} rightarrow mu ^+mu ^-) constraint. The lower limits on strongly-interacting sparticles are largely determined by LHC searches, and similar to those in the CMSSM. We find a preference for the LSP to be a Bino or Higgsino with m_{tilde{chi }^0_{1}} sim 1 ,, mathrm {TeV}, with annihilation via heavy Higgs bosons H / A and stop coannihilation, or chargino coannihilation, bringing the cold dark matter density into the cosmological range. We find that spin-independent dark matter scattering is likely to be within reach of the planned LUX-Zeplin and XENONnT experiments. We probe the impact of the (g-2)_mu constraint, finding similar results whether or not it is included.