Supersymmetric models in view of recent LHC data

TL;DR

This paper reviews the current status of supersymmetric models considering recent LHC data, especially focusing on how the measured Higgs mass constrains these models, including both minimal and non-minimal extensions.

Contribution

It provides an updated analysis of supersymmetric models in light of recent experimental constraints from the LHC, highlighting the impact of the Higgs mass measurement.

Findings

Higgs mass measurement constrains supersymmetric parameter space

Minimal and non-minimal models are evaluated against LHC data

Certain supersymmetric models remain viable under current constraints

Abstract

We summarize the status of various supersymmetric models in view of the existing LHC data. A particular focus is on the implications of the measured Higgs mass on these models which gives important constraints. We consider here minimal and non-mininal supersymmetric extension of the Standard Model.

Equations

$$\Delta m_h^2=+\frac{3m_t^4}{4{\pi }^2{v}^2}\left[\ln \left(\frac{M_S^2}{m_t^2}\right)+\frac{X_t^2}{M_S^2}\left(1-\frac{X_t^2}{12M_S^2}\right)\right].$$

$$SO(10)$$

Full text

1 Introduction

The discovery of the Higgs boson at the LHC [1, 2] marks one of the most important milestones in particle physics. Its mass is known rather precisely: $m_{h}=125.09\pm 0.21$ (stat.) $\pm 0.11$ (syst.) GeV [3]. Moreover, the signal strength of LHC searches in various channels has been found consistent with predictions of the Standard Model (SM). While this completes the SM particle-wise, several questions still remain open, e.g. (i) Is it possible to include the SM in a grand unified theory where all gauge forces unify? (ii) What stabilizes the Higgs mass at the electroweak scale? (iii) Is there a particle physics explanation of the observed dark matter relic density?

Supersymmetry (SUSY) is still one of the best motivated extensions of SM addressing several of these questions. Consequently, the search for SUSY is among the main priorities of the LHC collaborations. Up to now no sign for supersymmetry or any significant deviation from the Standard Model (SM) prediction has been found, e.g. in simplified models bounds on the gluino mass of up to about 2 TeV have been set [4, 5] exploiting about 36 fb*-1* of data in each experiment. These bounds depend on the spectrum and get reduced significantly if the spectrum is rather compressed as has been noted early on [6].

In the minimal supersymmetric standard model (MSSM) the mass of the lighter Higgs boson is bounded to be below the mass of the $Z$-boson at tree level implying the need of very large radiative corrections of about 90% and larger as $m_{h}^{2}\simeq m^{2}_{Z}+86^{2}$ GeV. It has been known for a long time that large radiative corrections due to the top-quark and stops, the scalar partners of the top-quark, indeed exist as the top-Yukawa coupling is order 1. This requires that either the geometric average of the stop masses $M^{2}_{S}=m_{\tilde{t}_{1}}m_{\tilde{t}_{2}}$ is large and/or the existence of a large trilinear coupling $A_{t}$ [7] as can be seen by inspecting the most dominant contributions which are given by

[TABLE]

$X_{t}=A_{t}-\mu\cot\beta$ is a measure of the left-right mixing with $\mu$ being the higgsino mass parameter, $\tan\beta=v_{u}/v_{d}$ the ratio of the two vacuum expectation values and $v^{2}=v^{2}_{u}+v^{2}_{d}=4m^{2}_{W}/g^{2}$.

2 Implication for models with MSSM particle content

The question, to which extent the observed Higgs mass can be explained within a given supersymmetric high-scale model and what are the resulting implications on the spectrum has been investigated by several authors. The main results can be summarized as follows: in minimal gauge mediated SUSY breaking (GMSB) models one finds m_{\tilde{t}_{1}}\raise 1.29167pt\hbox{;>\kern-7.5pt\raise-4.73611pt\hbox{\sim;}}6 TeV with $\tilde{t}_{1}$ being the lightest among the coloured SUSY particles [8]. The main reason is that at the so-called messenger on finds $A_{t}=0$ requiring the stops to be heavy. If this were realized in nature, the LHC at 14 TeV would not be able to discover SUSY. However, in case of extended GMSB models one finds corners in parameter space[9] with m_{\tilde{t}_{1}}\simeq m_{\tilde{b}_{1}}\raise 1.29167pt\hbox{;>\kern-7.5pt\raise-4.73611pt\hbox{\sim;}}1 TeV which is the mass range explored by the current LHC run [5]. In the constrained MSSM (CMSSM) or slightly extended versions with non-universal Higgs mass parameters (NUHM-models) the explanation of the observed Higgs mass implies [10, 11, 12] $|A_{0}|\simeq 2m_{0}$. Here $A_{0}$ and $m_{0}$ are the trilinear coupling and the common scalar mass parameter, respectively, at the scale $M_{GUT}$ of grand unification. Fitting the CMSSM to the Higgs mass taking into account low energy and LHC constraints one finds that the best fit point [13] has the typical mass scales m_{\tilde{g}},m_{\tilde{q}}\raise 1.29167pt\hbox{;>\kern-7.5pt\raise-4.73611pt\hbox{\sim;}}2 TeV, $m_{\tilde{l}_{R}}\simeq 600$ GeV and $m_{\tilde{\chi}^{0}_{1}}\simeq 450$ GeV. Thus, the up-to now negative search results is consistent with this part of the parameter which, however, will be probed by the current and next LHC runs [4, 5]. Even in more general high scale models with non-universal parameter at $M_{GUT}$ one typically finds large trilinear couplings[14], e.g. $|A_{0}|\simeq(1-3)\max(M_{1/2},m_{Q_{3}},m_{U_{3}})$. There is however a problem with large trilinear couplings such as $A_{t}$ or $A_{0}$ as they potentially imply the existence of a global minimum of the scalar potential which is colour and/or charge breaking. It has been shown that large regions of the CMSSM parameter space with $m_{h}\simeq 125$ GeV are indeed ruled out by color/charge breaking minima [15].

High scale models like GMSB or CMSSM imply a rather hierarchical mass spectrum of the supersymmetric particles giving rise to hard jets and leptons at the LHC in combination with large missing transverse momentum with only small/tiny SM background. However, in the general MSSM where one can take some parts of the spectrum relatively compressed leading to substantial reduction of mass the bounds of various supersymmetric particles [6, 16, 17, 18]. A particular subclass of the general MSSM are so-called ‘natural SUSY’ scenarios [19, 20, 21]. Here the basic idea is to take only those SUSY particles close the electroweak scale which do give a sizeable contribution to $m_{h}$ in order to avoid a too large fine-tuning of parameters of unrelated sectors and to assign to all other particles masses at the multi-TeV scale. In particular, the higgsinos, the partners of the Higgs bosons, and the light stop should have masses of the order of a few hundred GeV. In addition the masses of the gluino and the heavier stop should be close to the TeV scale. This implies a rather compressed spectrum of the lightest neutralinos and the lightest chargino with mass differences of $O(1$ GeV$)$ which are rather difficult to detect in direct searches [22] at the LHC. While these models are interesting from the point of view of fine-tuning they cannot explain the observed relic dark matter density as the annihilation cross sections of higginos are rather large. Moreover, also this class of models requires large $A_{t}$ and, thus, gets constrained if one wants to avoid charge and colour breaking minima [23]. As already mentioned above, data from the current LHC run imply mass bounds of up to $m_{\tilde{t}_{1}}\simeq 1$ TeV assuming a large mass hierarchy between the stop and the higgsinos [24]. However, we note for completeness that even in Natural SUSY the higgsinos might have larger masses due to possible existence of the soft SUSY breaking term [25] $\mu^{\prime}\tilde{H}_{u}\tilde{H}_{d}$ resulting in higgsino mass of order $\mu+\mu^{\prime}$.

3 Extended supersymmetric models

The requirement of having very large radiative corrections to explain $m_{h}$ is a hint to go beyond the MSSM. In non-minimal extensions, the tree-level bound can be pushed to larger values due to the extra $F$-contributions as in the next to minimal MSSM (NMSSM) [26] or due to extra $D$-term contributions in models with an enlarged gauge group [27] close to the electroweak scale. As examples we consider $SO(10)$ inspired left-right symmetric models, which have several virtues: (i) They gives an explanation of the observed neutrino masses and mixing pattern, (ii) They can explain the conservation of R-parity as $U(1)_{B-L}$ is a subgroup of $SO(10)$, (iii) The R-sneutrino, the partner of the right-handed neutrino, is a potential dark matter candidate [28, 29]. In view of the Higgs mass, taking for example the breaking chain

[TABLE]

on obtains larger tree-level bounds such as [30] $m_{h}\leq m_{Z}^{2}+\frac{1}{4}g_{\chi}^{2}v^{2}$ where $g_{\chi}\simeq g_{Y}$ reducing the need for radiative corrections to about 50% which still is large but reduces the need for rather large $A_{t}$ and thus the danger of charge/color breaking minima. The additional particle content has several phenomenological implications: (i) In particular in scenarios where a R-sneutrino is the lightest supersymmetric particle (LSP) one finds an enhanced lepton multiplicity in the cascade decays of supersymmetric particles [31]. (ii) The existence of a light additional, SM gauge singlet Higgs boson [27, 30, 32]. (iii) Gauge kinetic mixing and additional $Z^{\prime}$ decay modes can significantly alter the LHC bounds on the $Z^{\prime}$ mass [30, 32].

One might ask if the additional particle content can potentially solve the dark matter problem of Natural SUSY. In principle, a light right-handed neutrino $\nu_{R}$ with a mass in the keV range can do this as in the $\nu$SM [33]. We note for completeness that this is rather difficult to achieve such a scenario in a simple $SO(10)$ scenario. If this were the only change, then the LHC phenomenology of Natural SUSY would not change. However, it might well be that the mechanism causing the lightness of the $\nu_{R}$ implies also that the sleptons and sneutrinos are rather light. Assuming that a $R$-sneutrino is the LSP one gets immediately constraints $\mu$ from higgsino pair production as now the decay $\tilde{\chi}^{+}_{1}\simeq\tilde{h}^{+}_{1}\to l^{+}\tilde{\nu}_{R}$ is allowed [34]. Using 8-TeV and 13 TeV (with an integrated luminosity ${\cal L}=13.9$ fb*-1*) LHC data one obtains a bound of about 380 GeV on $\mu$ provided there is sufficient phase space. In case that also the usual sleptons have masses in the range of a few hundred GeV, then they are mainly produced via $pp\to\tilde{l}_{L}\tilde{\nu}_{L}$. In such a scenario one gets constraints from LHC data on the soft SUSY breaking parameter $M_{\tilde{L}}$, which sets the mass scale of the sleptons, of up to 580 GeV. We refer to ref. [34] for further details. Note, that these bounds apply to any other model containing the corresponding particles.

4 Conclusions

Within the MSSM the explanation of the observed Higgs mass $m_{h}\simeq 125.1$ GeV requires large radiative correction. This can be either achieved via heavy stops and/or large left-right mixing. The latter can lead to charge/color breaking minima putting severe constraints on the corresponding parameter space. Within high scale models such as CMSSM, NUHM or general GMSB, squarks and gluinos have masses in the 1-2 TeV range in the corresponding parameter regions which are currently probed at the LHC. If minimal GMSB were realised in nature then the Higgs mass requires a spectrum of coloured SUSY particles beyond the reach of LHC at 14 TeV. In generic models with MSSM particle content the LHC bounds can be substantially reduced if the spectrum is compressed. However, if this realized in Nature, this will require a quite unusual pattern for supersymmetry breaking as the renormalisation group evaluation of the underlying parameters yields a quite hierarchical mass spectrum in unified models.

The relatively large value of $m_{h}$ might be a hint to go beyond the MSSM as in non-minimal models additional tree-level contributions to $m_{h}$ due to F-terms, like in the NMSSM, or due to D-terms, like in models with extended gauge symmetries, reduce somewhat the need for large radiative corrections. We have briefly sketched some important features of $SO(10)$ inspired models. Moreover, we have shown that in scenarios with an $R$-sneutrino LSP the LHC gives bounds on electroweakly produced particles of up to 580 GeV.