Constrained Minimal Supersymmetric Standard Model Research Articles

Quantifying limits on CP violating phases from EDMs in supersymmetry

We revisit the calculation of the electron, neutron, and proton electric dipole moments (EDMs) in the constrained minimal supersymmetric standard model (CMSSM). The relatively large mass of the Higgs boson, mH ≃ 125 GeV coupled with the (as yet) lack of discovery of any supersymmetric particle at the LHC, has pushed the supersymmetry breaking scale to several TeV or higher. Though one might expect this decoupling to have relaxed completely any bounds on the two CP violating phases in the CMSSM (θμ and θA), the impressive experimental improvements in the limits on the EDMs (particularly the electron EDM) still allow us to set constraints of order (0.01−0.1)π on θA and (0.001−0.1)π on θμ. We also discuss the impact of future improvements in the experimental limits on supersymmetric models.

Investigating non-minimal flavour-violating CMSSM in the light of Higgs-Boson mass using information theory

Flavour-violating interactions of the stop-quarks are expected to provide an additional few GeV contributions to the Higgs-Boson mass, particularly when mix with scharm-quarks, thereby allowing reduced supersymmetry (SUSY) breaking scale compared to flavour-conserving constrained minimal supersymmetric Standard Model (CMSSM). Inspired by this, we analyse the interactions mentioned above in the context of CMSSM using the information entropy of the Higgs-Boson for a wider region of flavour-violating CMSSM parameter space (m0,m1/2,A0, tan⁡β,sgn(μ),δctij), where δctij represents the flavour-violating coupling of the top-quark with the charm-quark and i,j defining left and right chiralities of squarks. Our information-theoretic analysis of the model mentioned above reveals the most favourable values of (m0,m1/2,A0,tan⁡β,δctij) as (4.30TeV,2.32TeV,−4.96TeV, 22.8,0.037) and (4.16TeV, 3.89TeV,−4.10TeV,19.4,0.039) for (i,j)=(L,R) and (R,L), respectively, corresponding to the maximum entropy which suggest the SUSY breaking scale to be about 5 TeV, thereby allowing considerable low values of sparticles masses than the flavour-conserving CMSSM.

Global fits of SUSY at future Higgs factories

In this work, we study the impact of electroweak and Higgs precision measurements at future electron-positron colliders on several typical supersymmetric models, including the constrained minimal supersymmetric Standard Model (CMSSM), nonuniversal Higgs mass generalizations (NUHM1, NUHM2), and the seven-dimensional minimal supersymmetric Standard Model (MSSM7). Using publicly available data from the $\mathsf{GAMBIT}$ community, we postprocess previous SUSY global fits with additional likelihoods to explore the discovery potential of Higgs factories, such as the Circular Electron Positron Collider (CEPC), the Future Circular Collider (FCC), and the International Linear Collider (ILC). We show that the currently allowed parameter space of these models will be further tested by future precision measurements. In particular, dark matter annihilation mechanisms may be distinguished by precise measurements of Higgs observables.

An information theoretic exploration of constrained MSSM

We discuss information theory as a tool to investigate constrained minimal supersymmetric Standard Model (CMSSM) in the light of observation of Higgs boson at the Large Hadron Collider. The entropy of the Higgs boson using its various detection modes has been constructed as a measure of the information and has been utilized to explore a wide range of CMSSM parameter space after including various experimental constraints from the LEP data, B-physics, electroweak precision observables and relic density of dark matter. According to our study while the lightest neutralino is preferred to have a mass around 1.92 TeV, the gluino mass is estimated to be around 7.44 TeV. The values of CMSSM parameters m0, m1/2, A0 and tan⁡β correspond to the most preferred scenario are found to be about 6 TeV, 3.6 TeV, −6.9 TeV and 36.8 respectively.

Charged Higgs boson in MSSM and beyond

We conduct a numerical study over the constrained MSSM (CMSSM), Next-to-MSSM (NMSSM) and $U(1)$ extended MSSM (UMSSM) to probe the allowed mass ranges of the charged Higgs boson and its dominant decay patterns, which might come into prominence in near future collider experiments. {We present results obtained from a limited scan for CMSSM} as a basis and compare its predictions with the extended models. We observe within our data that a wide mass range is allowed as $0.5(1) \lesssim m_{H^{\pm}} \lesssim 17$ TeV in UMSSM (NMSSM). We find that the dominant decay channel is mostly $H^{\pm}\rightarrow tb$ such that ${\rm BR}(H^{\pm}\rightarrow tb) \sim 80\%$. While this mode remains dominant over the whole allowed parameter space of CMSSM, we realize some special domains in the NMSSM and UMSSM, in which ${\rm BR}(H^{\pm}\rightarrow tb) \lesssim 10\%$. In this context, the decay patterns of the charged Higgs can play a significant role to distinguish among the SUSY models. In addition to the $tb$ decay mode, we find that the narrow mass scale in CMSSM allows only the decay modes for the charged Higgs boson to $\tau\nu$ ($\sim 16\%$), and their supersymmetric partners $\tilde{\tau}\tilde{\nu}$ ($\sim 13\%$). On the other hand, it is possible to realize the mode in NMSSM and UMSSM in which the charged Higgs boson decays into a chargino and neutralino pair up to about $25\%$. {This decay mode requires non-universal boundary conditions within the MSSM framework to be available, since CMSSM yields ${\rm BR} (H^{\pm}\rightarrow \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{\pm}) \lesssim 1\%$.} It can also be probed in near future collider experiments through the missing energy and CP-violation measurements...

Big-bang nucleosynthesis and leptogenesis in the CMSSM

We have investigated the constrained minimal supersymmetric standard model with three right-handed Majorana neutrinos whether there still is a parameter region which is consistent with all existing experimental data/limits such as Leptogenesis and the dark matter abundance and we also can solve the Lithium problem. Using Casas-Ibarra parameterization, we have found that a very narrow parameter space of the complex orthogonal matrix elements where the lightest slepton can have a long lifetime, that is necessary for solving the Lithium problem. Further, under this condition, there is a parameter region that can give an explanation for the experimental observations. We have studied three cases of the right-handed neutrino mass ratio \mbox{\em (i)} $M_{2}=2 \times M_{1}$, \mbox{\em (ii)} $M_{2}=4 \times M_{1}$, \mbox{\em (iii)} $M_{2}=10 \times M_{1}$ while $M_{3}=40 \times M_{1}$ is fixed. We have obtained the mass range of the lightest right-handed neutrino mass that lies between $10^9$ GeV and $10^{11}$ GeV. The important result is that its upper limit is derived by solving the Lithium problem and the lower limit comes from Leptogenesis. Calculated low-energy observables of these parameter sets such as BR($\mu \to e \gamma$) is not yet restricted by experiments and will be verified in the near future.

Global fits of GUT-scale SUSY models with GAMBIT

We present the most comprehensive global fits to date of three supersymmetric models motivated by grand unification: the constrained minimal supersymmetric standard model (CMSSM), and its Non-Universal Higgs Mass generalisations NUHM1 and NUHM2. We include likelihoods from a number of direct and indirect dark matter searches, a large collection of electroweak precision and flavour observables, direct searches for supersymmetry at LEP and Runs I and II of the LHC, and constraints from Higgs observables. Our analysis improves on existing results not only in terms of the number of included observables, but also in the level of detail with which we treat them, our sampling techniques for scanning the parameter space, and our treatment of nuisance parameters. We show that stau co-annihilation is now ruled out in the CMSSM at more than 95% confidence. Stop co-annihilation turns out to be one of the most promising mechanisms for achieving an appropriate relic density of dark matter in all three models, whilst avoiding all other constraints. We find high-likelihood regions of parameter space featuring light stops and charginos, making them potentially detectable in the near future at the LHC. We also show that tonne-scale direct detection will play a largely complementary role, probing large parts of the remaining viable parameter space, including essentially all models with multi-TeV neutralinos.

Bayesian analysis and naturalness of (Next-to-)Minimal Supersymmetric Models

The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a ℤ3 conserving semi-constrained Next-to-Minimal Supersymmetric Standard Model (NMSSM) to the constrained MSSM (CMSSM). We contrast popular fine-tuning measures with naturalness priors, which automatically appear in statistical measures of the plausibility that a given model reproduces the weak scale. Our comparison shows that naturalness priors provide valuable insight into the hierarchy problem and rigorously ground naturalness in Bayesian statistics. For the CMSSM and semi-constrained NMSSM we demonstrate qualitative agreement between naturalness priors and popular fine tuning measures. Thus, we give a clear plausibility argument that favours relatively light superpartners.

The super-GUT CMSSM revisited

We revisit minimal supersymmetric SU(5) grand unification (GUT) models in which the soft supersymmetry-breaking parameters of the minimal supersymmetric Standard Model (MSSM) are universal at some input scale, $M_{in}$, above the supersymmetric gauge coupling unification scale, $M_{GUT}$. As in the constrained MSSM (CMSSM), we assume that the scalar masses and gaugino masses have common values, $m_0$ and $m_{1/2}$ respectively, at $M_{in}$, as do the trilinear soft supersymmetry-breaking parameters $A_0$. Going beyond previous studies of such a super-GUT CMSSM scenario, we explore the constraints imposed by the lower limit on the proton lifetime and the LHC measurement of the Higgs mass, $m_h$. We find regions of $m_0$, $m_{1/2}$, $A_0$ and the parameters of the SU(5) superpotential that are compatible with these and other phenomenological constraints such as the density of cold dark matter, which we assume to be provided by the lightest neutralino. Typically, these allowed regions appear for $m_0$ and $m_{1/2}$ in the multi-TeV region, for suitable values of the unknown SU(5) GUT-scale phases and superpotential couplings, and with the ratio of supersymmetric Higgs vacuum expectation values $\tan \beta \lesssim 6$.

Quark flavor violating Higgs boson decayh→b¯s+bs¯in the MSSM

We study the quark flavor violating Higgs-boson decay $h \rightarrow \bar b s + b \bar s$ in the Minimal Supersymmetric Standard Model (MSSM). The decay is analyzed first in a model independent, and in a second step in the minimal flavor violationg (MFV) Constrained MSSM. The experimental constraints from $B$-Physics observables (BPO) and electroweak precision observables (EWPO) are also calculated and imposed on the parameter space. It is shown that in some cases the EWPO restrict the flavor violating parameter space stronger than the BPO. In the model independent analysis values of ${\cal O}(10^{-4})$ can be found for ${\rm BR}(h \rightarrow \bar b s + b \bar s)$. In the MFV CMSSM such results can only be obtained in very restricted parts of the parameter space. The results show that it is not excluded to observe the decay $h \rightarrow \bar b s + b \bar s$ in the MSSM at future $e^+e^-$ colliders.

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.

Dark matter scenarios in a constrained model with Dirac gauginos

We perform the first analysis of Dark Matter scenarios in a constrained model with Dirac Gauginos. The model under investigation is the Constrained Minimal Dirac Gaugino Supersymmetric Standard model (CMDGSSM) where the Majorana mass terms of gauginos vanish. However, $R$-symmetry is broken in the Higgs sector by an explicit and/or effective $B_\mu$-term. This causes a mass splitting between Dirac states in the fermion sector and the neutralinos, which provide the dark matter candidate, become pseudo-Dirac states. We discuss two scenarios: the universal case with all scalar masses unified at the GUT scale, and the case with non-universal Higgs soft-terms. We identify different regions in the parameter space which fullfil all constraints from the dark matter abundance, the limits from SUSY and direct dark matter searches and the Higgs mass. Most of these points can be tested with the next generation of direct dark matter detection experiments.

Effects of sfermion mixing induced by RGE running in the minimal flavor violating CMSSM

Within the Constrained Minimal Supersymmetric Standard Model (CMSSM) with Minimal Flavor Violation (MFV) for scalar quarks we study the effects of intergenerational squark mixing on $B$-physics observables, electroweak precision observables (EWPO) and the Higgs boson mass predictions. Squark mixing is generated through the Renormalization Group Equations (RGE) running from the GUT scale to the electroweak scale due to presence of non diagonal Yukawa matrices in the RGE's, e.g. due to the CKM matrix. We find that the $B$-Physics observables as well as the Higgs mass predictions do not receive sizable corrections. On the other hand, the EWPO such as the $W$ boson mass can receive corrections by far exceeding the current experimental precision. These contributions can place new upper bounds on the CMSSM parameter space. We extend our analysis to the CMSSM extended with a mechanism to explain neutrino masses (CMSSM-seesaw I), which induces flavor violation in the scalar lepton sector. Effects from slepton mixing on the analyzed observables are in general smaller than from squark mixing, but can reach the level of the current experimenal uncertainty for the EWPO.

Light Higgsino dark matter in the MSSM on D-branes

When supersymmetry (SUSY) breaking is dominated by the complex structure moduli and the universal dilaton, a subset of the SUSY parameter space in a realistic minimal supersymmetric standard model constructed from intersecting/magnetized D-branes are universal, similar to the effective minimal supergravity (mSUGRA)/constrained minimal supersymmetric standard model (CMSSM) parameter space with a universal scalar mass m0, a universal gaugino mass and with the universal trilinear term fixed to be minus the gaugino mass, A0 = −m1/2. More generally, the scalar mass-squared terms for sfermions are split about the Higgs mass-squared terms, and , for generic values of the Kähler moduli. The scalar masses are universal only for a specific choice of the Kähler moduli. The hyperbolic branch/focus point (HB/FP) regions of this parameter space are present for both and . Interestingly, it is known that FPs may be realized with any boundary condition of the form with x an arbitrary constant, the same form as those in this model. Thus, we should expect to obtain the same set of FPs in the model regardless of the choice of Kähler moduli. It should be emphasized that the more general choice of Kähler moduli goes beyond (mSUGRA/CMSSM). It is shown that there exists superpartner spectra with a light Higgsino-like LSP with 230–350 GeV and a Higgs mass in the range 124–126 GeV, and which satisfy most standard experimental constraints. Consequently, viable spectra with low electroweak fine-tuning between 3%–7% may be obtained. The spin-independent direct-detection crosssections are in range of future experiments such as XENON−1 T and super CDMS, while the relic density is smaller than the WMAP and Planck bounds by roughly a factor of ten, implying that the LSP is sub-dominant component of dark matter. In addition, most of the spectra are consistent with constraints from indirect-detection experiments.

Exploring CP violation in the MSSM.

We explore the prospects for observing CP violation in the minimal supersymmetric extension of the Standard Model (MSSM) with six CP-violating parameters, three gaugino mass phases and three phases in trilinear soft supersymmetry-breaking parameters, using the CPsuperH code combined with a geometric approach to maximise CP-violating observables subject to the experimental upper bounds on electric dipole moments. We also implement CP-conserving constraints from Higgs physics, flavour physics and the upper limits on the cosmological dark matter density and spin-independent scattering. We study possible values of observables within the constrained MSSM (CMSSM), the non-universal Higgs model (NUHM), the CPX scenario and a variant of the phenomenological MSSM (pMSSM). We find values of the CP-violating asymmetry A_mathrm{CP} in b rightarrow s gamma decay that may be as large as 3 %, so future measurements of A_mathrm{CP} may provide independent information about CP violation in the MSSM. We find that CP-violating MSSM contributions to the B_s meson mass mixing term Delta M_{B_s} are in general below the present upper limit, which is dominated by theoretical uncertainties. If these could be reduced, Delta M_{B_s} could also provide an interesting and complementary constraint on the six CP-violating MSSM phases, enabling them all to be determined experimentally, in principle. We also find that CP violation in the h_{2,3} tau ^+ tau ^- and h_{2,3} {bar{t}} t couplings can be quite large, and so may offer interesting prospects for future pp, e^+ e^-, mu ^+ mu ^- and gamma gamma colliders.

Neutralino and gravitino dark matter with low reheating temperature

Abstract We examine a scenario in which the reheating temperature T R after inflation is so low that it is comparable to, or lower than, the freeze out temperature of ordinary WIMPs. In this case the relic abundance of dark matter is reduced, thus relaxing the impact of the usually strong constraint coming from the requirement that the universe does not overclose. We first re-examine the dynamics of freezeout during reheating. Next we study the parameter space of the MSSM with ten free parameters, the Constrained MSSM and the singlino-dominated regions of the Next-to-MSSM. In each case we often find dramatic departures from the usually considered regime of high T R , with important implications for direct detection dark matter searches. In particular, in the MSSM we examine WIMP mass range up to about 5 TeV, and we find large regions of bino dark matter over the whole mass range, and of higgsino dark matter with mass over a similar range but starting from the ∼ 1 TeV value of the standard high T R scenario. We show that the prospects for bino detection strongly depend on T R , while the higgsino is for the most part detectable by future one-tonne detectors. The wino, which is excluded in the standard scenario, becomes allowed again if its mass is roughly above 3.5 TeV, and can also be partially detectable. In the CMSSM, the bino and higgsino mass ranges become much more constrained although detection prospects remain roughly similar. In the Next-to-MSSM we show that, at low enough T R wide ranges of singlino-dominated parameter space of the model become again cosmologically allowed, although detection prospects remain nearly hopeless. We also study the non-thermal contribution to the DM relic density from direct and cascade decays of the inflaton. Finally, in the framework of the MSSM we consider the case of a gravitino as dark matter. In this case we find strong bounds from overclosure and from Big Bang Nucleosynthesis, and derive lower limits on T R which depend on the gravitino mass and on the nature of the lightest ordinary superpartner.

Particle spectroscopy of supersymmetric SU(5) in light of the 125 GeV Higgs boson and muong−2data

The discovery of the Higgs boson at the Large Hadron Collider (LHC) has a great impact on the minimal supersymmetric extension of the Standard Model (MSSM). In the context of the constrained MSSM (CMSSM) and its extension with non-universal masses for the MSSM Higgs doublets (NUHM2), sparticles with masses $ > 1$ TeV are necessary to reproduce the observed Higgs boson mass of 125-126 GeV. On the other hand, there appears to be a significant amount of discrepancy between the measured muon $g-2$ and the Standard Model prediction. A successful explanation of this discrepancy in the MSSM requires new contributions involving relatively light sparticles with masses $ < 1$ TeV. In this paper, we attempt to accommodate the two conflicting requirements in an SU(5) inspired extension of the CMSSM. We assign non-universal but flavor blind soft supersymmetry breaking masses to the scalar components in $\bar 5$ and 10 matter supermultiplets. The two MSSM Higgs doublets in the 5, $\bar5$ representations of SU(5) are also assigned unequal soft mass$^2$ at $M_{GUT}$. We identify parameter regions which can simultaneously accommodate the observed Higgs boson mass and the muon $g-2$ data, and which are compatible with other phenomenological constraints such as neutralino dark matter relic abundance and rare B-meson decays. Some regions of the allowed parameter space will be explored at the upgraded LHC and by dark matter direct detection experiments.

CMSSM, naturalness and the “fine-tuning price” of the Very Large Hadron Collider

The absence of supersymmetry or other new physics at the Large Hadron Collider (LHC) has lead many to question naturalness arguments. With Bayesian statistics, we argue that natural models are most probable and that naturalness is not merely an aesthetic principle. We calculate a probabilistic measure of naturalness, the Bayesian evidence, for the Standard Model (SM) with and without quadratic divergences, confirming that the SM with quadratic divergences is improbable. We calculate the Bayesian evidence for the Constrained Minimal Supersymmetric Standard Model (CMSSM) with naturalness priors in three cases: with only the $M_Z$ measurement; with the $M_Z$ measurement and LHC measurements; and with the $M_Z$ measurement, $m_h$ measurement and a hypothetical null result from a $\sqrt{s}=100\,\text{TeV}$ Very Large Hadron Collider (VLHC) with $3000/\text{fb}$. The "fine-tuning price" of the VLHC given LHC results would be $\sim400$, which is slightly less than that of the LHC results given the electroweak scale ($\sim500$).

Effects of neutrino inverse seesaw mechanism on the sparticle spectrum in CMSSM and NUHM2

We study the implications of the inverse seesaw mechanism (ISS) on the sparticle spectrum in the Constrained Minimal Supersymmetric Standard Model (CMSSM) and Non-Universal Higgs Model (NUHM2). Employing the maximal value of the Dirac Yukawa coupling involving the up type Higgs doublet provides a 2-3 GeV enhancement of the lightest CP-even Higgs boson mass. This effect permits one to have lighter colored sparticles in the CMSSM and NUHM2 scenarios with LSP neutralino, which can be tested at LHC14. We present a variety of LHC testable benchmark points with the desired LSP neutralino dark matter relic abundance.

First evidence of the constrained minimal supersymmetric standard model is appearing soon

We explore the coannihilation region of the constrained minimal supersymmetric standard model (CMSSM) being consistent with current experimental/observational results. The requirements from the experimental/observational results are the 125 GeV Higgs boson mass and the relic abundances of both the dark matter and light elements, especially lithium-7. We put these requirements on the calculated values, and, thus, we obtain the allowed region. Then we give predictions to the mass spectra of the supersymmetric (SUSY) particles, the anomalous magnetic moment of the muon, the branching fractions of the $B$-meson rare decays, the direct detection of the neutralino dark matter, and the number of SUSY particles produced in a 14 TeV run at the LHC experiment. Comparing these predictions with current bounds, we show the feasibility of the test for this scenario in near future experiments.