Minimal model for dark matter and unification

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.

The dark matter issue is among the most perplexing in contemporary physics. The problem is more enigmatic due to the wide range of possible solutions, ranging from the ultra-light to the super-massive. String theory gives rise to plausible dark matter candidates due to the breaking of the non--Abelian Grand Unified Theory (GUT) symmetries by Wilson lines. The physical spectrum then contains states that do not satisfy the quantisation conditions of the unbroken GUT symmetry. Given that the Standard Model states are identified with broken GUT representations, and provided that any ensuing symmetry breaking is induced by components of GUT states, leaves a remnant discrete symmetry that forbid the decay of the Wilsonian states. A class of such states are obtained in a heterotic-string derived $Z^\prime$ model. The model exploits the spinor-vector duality symmetry, observed in the fermionic $Z_2\times Z_2$ heterotic-string orbifolds, to generate a $Z^\prime\in E_6$ symmetry that may remain unbroken down to low energies. The $E_6$ symmetry is broken at the string level with discrete Wilson lines. The Wilsonian dark matter candidates in the string derived model are $SO(10)$, and hence Standard Model, singlets and possess non-$E_6$ $U(1)_{Z^\prime}$ charges. Depending on the $U(1)_{Z^\prime}$ breaking scale and the reheating temperature they give rise to different scenarios for the relic abundance, and in accordance with the cosmological constraints.

In the multiverse the scale of supersymmetry breaking, $$ \widetilde{m} = {F_X}/{M_{ * }} $$ ∗, may scan and environmental constraints on the dark matter density may exclude a large range of m from the reheating temperature after inflation down to values that yield a lightest supersymmetric particle (LSP) mass of order a TeV. After selection effects, for example from the cosmological constant, the distribution for $$ \widetilde{m} $$ in the region that gives a TeV LSP may prefer larger values. A single environmental constraint from dark matter can then lead to multi-component dark matter, including both axions and the LSP, giving a TeV-scale LSP somewhat lighter than the corresponding value for single-component LSP dark matter. If supersymmetry breaking is mediated to the Standard Model sector at order X † X and higher, only squarks, sleptons and one Higgs doublet acquire masses of order $$ \widetilde{m} $$ . The gravitino mass is lighter by a factor of M ∗ /M Pl and the gaugino masses are suppressed by a further loop factor. This Spread Supersymmetry spectrum has two versions, one with Higgsino masses arising from supergravity effects of order the gravitino mass giving a wino LSP, and another with the Higgsino masses generated radiatively from gaugino masses giving a Higgsino LSP. The environmental restriction on dark matter fixes the LSP mass to the TeV domain, so that the squark and slepton masses are order 103 TeV and 106 TeV in these two schemes. We study the spectrum, dark matter and collider signals of these two versions of Spread Supersymmetry. The Higgs boson is Standard Model-like and predicted to lie in the range 110-145 GeV; monochromatic photons in cosmic rays arise from dark matter annihilations in the halo; exotic short charged tracks occur at the LHC, at least for the wino LSP; and there are the eventual possibilities of direct detection of dark matter and detailed exploration of the TeV-scale states at a future linear collider. Gauge coupling unification is at least as precise as in minimal supersymmetric theories. If supersymmetry breaking is also mediated at order X, a much less hierarchical spectrum results. The spectrum in this case is similar to that of the Minimal Supersymmetric Standard Model, but with the superpartner masses 1-2 orders of magnitude larger than those expected in natural theories.

Searches for the monopoles predicted by Grand Unified Theories (GUTs) have required new approaches, since these monopoles should be both slow and highly penetrating. The ability of scintillator to respond to particles of velocity A small monopole detector prototype at the Earth's surface was operated in an effort to understand the problems and possibilities of monopole detection. The design philosophy, techniques, and the lessons learned from the prototype detector could then be applied to much larger monopole detectors. The prototype was not able to set new limits for the GUT monopole flux in cosmic rays, but in a more general analysis it was found that new limits could be set on the flux of lightly ionizing particles of mass ~ 10¹⁰ GeV. When GUT monopole detectors are scaled up to the size needed to challenge astrophysical limits, it becomes more likely that a flux could be found. This motivates a more careful examination of the scintillator counters, since their signal should be clear and unambiguous for a monopole candidate. The performance of the liquid scintillator counters for the MACRO (Monopole And Cosmic Ray Observatory) experiment was given considerable scrutiny, both to try to understand the observed behavior of these counters, and also to improve them for monopole detection. The results of these tests indicate that MACRO should be able either to establish a monopole flux or to limit it to a small fraction of the 'missing mass' of the universe.

Cosmology and GUTs: The matter of the universe

We give here an overview of recent developments in high energy physics and cosmology and their interconnections that relate to unification, and discuss prospects for the future. Thus there are currently three empirical data that point to supersymmetry as an underlying symmetry of particle physics: the unification of gauge couplings within supersymmetry, the fact that nature respects the supersymmetry prediction that the Higgs boson mass lie below 130 GeV, and vacuum stability up to the Planck scale with a Higgs boson mass at [Formula: see text][Formula: see text]125 GeV while the Standard Model does not do that. Coupled with the fact that supersymmetry solves the big hierarchy problem related to the quadratic divergence to the Higgs boson mass square along with the fact that there is no alternative paradigm that allows us to extrapolate physics from the electroweak scale to the grand unification scale consistent with experiment, supersymmetry remains a compelling framework for new physics beyond the Standard Model. The large loop correction to the Higgs boson mass in supersymmetry to lift the tree mass to the experimentally observable value, indicates a larger value of the scale of weak scale supersymmetry, making the observation of sparticles more challenging but still within reach at the LHC for the lightest ones. Recent analyses show that a high energy LHC (HE-LHC) operating at 27 TeV running at its optimal luminosity of [Formula: see text] can reduce the discovery period by several years relative to HL-LHC and significantly extend the reach in parameter space of models. In the coming years several experiments related to neutrino physics, searches for supersymmetry, on dark matter and dark energy will have direct impact on the unification frontier. Thus the discovery of sparticles will establish supersymmetry as a fundamental symmetry of nature and also lend direct support for strings. Further, discovery of sparticles associated with missing energy will constitute discovery of dark matter with LSP being the dark matter. On the cosmology front more accurate measurement of the equation of state, i.e. [Formula: see text], will shed light on the nature of dark energy. Specifically, [Formula: see text] will likely indicate the existence of a dynamical field, possibly quintessence, responsible for dark energy and [Formula: see text] would indicate an entirely new sector of physics. Further, more precise measurements of the ratio [Formula: see text] of tensor to scalar power spectrum, of the scalar and tensor spectral indices [Formula: see text] and [Formula: see text] and of non-Gaussianity will hopefully allow us to realize a Standard Model of inflation. These results will be a guide to further model building that incorporates unification of particle physics and cosmology.

Building up on previous work we propose a Dark Matter (DM) model with gauged matter parity and dynamical gauge coupling unification, driven by the same physics responsible for scotogenic neutrino mass generation. Our construction is based on the extended gauge group SU(3)c ⊗ SU(3)L ⊗ U(1)X ⊗ U(1)N, whose spontaneous breaking leaves a residual conserved matter parity, MP, stabilizing the DM particle candidates of the model. The key role is played by Majorana SU(3)L-octet leptons, allowing the successful gauge coupling unification and a one-loop scotogenic neutrino mass generation. Theoretical consistency allows for a plethora of new particles at the ≲ mathcal{O} (10) TeV scale, hence accessible to future collider and low-energy experiments.

This chapter is based on the work of [439]. We have checked whether the SM gauge couplings unify at the string scale in the class of models similar to Model 1 discussed in the previous chapter. All of the 15 MSSM-like models of [406] have three families of quarks and leptons and one or more pairs of Higgs doublets. They all admit an SU(6) orbifold GUT with gauge-Higgs unification and the third family in the bulk.

The apparent unification of gauge couplings around 1016 GeV is one of the strong arguments in favor of Supersymmetric extensions of the Standard Model (SM). In this contribution a new analysis, using the latest experimental data, is performed. The strong coupling αs emerges as the key factor for evaluating the results of the fits, as the experimental and theoretical uncertainties in its measurements are substantially higher than for the electromagnetic and weak couplings. The present analysis pays special attention to numerical and statistical details. The results, combined with the current limits on the supersymmetric particle masses, favor a value for the SUSY scale ≲ 150 GeV and for αs = 0.118 - 0.119.

The anomaly of a discrete symmetry is defined as the Jacobian of the path-integral measure. Assuming that the anomaly at low energies is cancelled by the Green-Schwarz (GS) mechanism at a fundamental scale, we investigate possible Kac-Moody levels for anomalous discrete family symmetries. As the first example, we consider discrete abelian baryon number and lepton number symmetries in the minimal supersymmetric standard model with the seesaw mechanism, and we find that the ordinary unification of gauge couplings is inconsistent with the GS conditions, indicating the possible existence of further Higgs doublets. We consider various recently proposed supersymmetric models with a non-abelian discrete family symmetry. In a supersymmetric example with Q6 family symmetry, the GS conditions are such that the gauge coupling unification appears close to the Planck scale.

We study SO(10), SU(5) and flipped SU(5) GUT models with non-universal soft supersymmetry-breaking scalar masses, exploring how they are constrained by LHC supersymmetry searches and cold dark matter experiments, and how they can be probed and distinguished in future experiments. We find characteristic differences between the various GUT scenarios, particularly in the coannihilation region, which is very sensitive to changes of parameters. For example, the flipped SU(5) GUT predicts the possibility of ̃t1−χ coannihilation, which is absent in the regions of the SO(10) and SU(5) GUT parameter spaces that we study. We use the relic density predictions in different models to determine upper bounds for the neutralino masses, and we find large differences between different GUT models in the sparticle spectra for the same LSP mass, leading to direct connections of distinctive possible experimental measurements with the structure of the GUT group. We find that future LHC searches for generic missing ET, charginos and stops will be able to constrain the different GUT models in complementary ways, as will the Xenon 1 ton and Darwin dark matter scattering experiments and future FERMI or CTA γ-ray searches.

Inspired by the phenomenological constraints, LHC supersymmetry and Higgs searches, dark matter search as well as string model building, we propose the electroweak supersymmetry around the electroweak scale: the squarks and/or gluinos are around a few TeV while the sleptons, sneutrinos, bino and winos are within one TeV. The Higgsinos can be either heavy or light. We consider bino as the dominant component of dark matter candidate, and the observed dark matter relic density is achieved via the neutralino-stau coannihilations. Considering the Generalized Minimal Supergravity (GmSUGRA), we show explicitly that the electroweak supersymmetry can be realized, and the gauge coupling unification can be preserved. With two Scenarios, we study the viable parameter spaces that satisfy all the current phenomenological constraints, and we present the concrete benchmark points. Furthermore, we comment on the fine-tuning problem and LHC searches.

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.

A selection of searches by the ATLAS experiment at the LHC for the electroweak production of SUSY particles are used to study their impact on the constraints on dark matter candidates. The searches use 20 fb -1 of proton-proton collision data at s = 8 TeV. A likelihood-driven scan of a five-dimensional effective model focusing on the gaugino-higgsino and Higgs sector of the phenomenological minimal supersymmetric Standard Model is performed. This scan uses data from direct dark matter detection experiments, the relic dark matter density and precision flavour physics results. Further constraints from the ATLAS Higgs mass measurement and SUSY searches at LEP are also applied. A subset of models selected from this scan are used to assess the impact of the selected ATLAS searches in this five-dimensional parameter space. These ATLAS searches substantially impact those models for which the mass m( 0 1 ) of the lightest neutralino is less than 65 GeV, excluding 86% of such models. The searches have limited impact on models with larger m( 0 1 ) due to either heavy electroweakinos or compressed mass spectra where the mass splittings between the produced particles and the lightest supersymmetric particle is small.

Prof. David Shih was supported by DOE grant DE-SC0013678 from April 2015 to April 2016. His research during this year focused on the phenomenology of super-symmetry (SUSY) and maximizing its future discovery potential at Run II of the LHC. SUSY is one of the most well-motivated frameworks for physics beyond the Standard Model. It solves the "naturalness" or "hierarchy" problem by stabilizing the Higgs mass against otherwise uncontrolled quantum corrections, predicts "grand unification" of the fundamental forces, and provides many potential candidates for dark matter. However, after decades of null results from direct and indirect searches, the viable parameter space for SUSY is increasingly constrained. Also, the discovery of a Standard Model-like Higgs with a mass at 125 GeV places a stringent constraint on SUSY models. In the work supported on this grant, Shih has worked on four different projects motivated by these issues. He has built natural SUSY models that explain the Higgs mass and provide viable dark matter; he has studied the parameter space of "gauge mediated supersymmetry breaking" (GMSB) that satisfies the Higgs mass constraint; he has developed new tools for the precision calculation of flavor and CP observables in general SUSY models; and he has studied new techniques for discovery of supersymmetric partners of the top quark.