NNuclear and Particle Physics Proceedings 00 (2018) 1–6
Nuclear andParticle PhysicsProceedings
Supersymmetry, direct and indirect constraints
Farvah Mahmoudi
Univ. Lyon, Univ. Lyon 1, CNRS / IN2P3, Institut de Physique Nucl´eaire de Lyon,UMR5822, F-69622 Villeurbanne, FranceTheoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland
Abstract
We present an overview of direct and indirect constraints in the MSSM, in CP-conserving and CP-violating MSSMscenarios, with some emphasis on the importance of combining the constraints from di ff erent sectors, namely SUSYand Higgs direct searches at the LHC, flavour physics, dark matter and electric dipole moments. Keywords:
Supersymmetry, LHC, Higgs, CP-violation, Electric dipole moments
1. Introduction
The Minimal Supersymmetric extension of the Stan-dard Model (MSSM) is a well motivated and extensivelystudied scenario beyond the Standard Model (SM). Itis a prototypical UV-complete model, for which manydedicated tools have been developed. With more thanone hundred parameters, the MSSM is however di ffi cultto explore in a systematic way. For this reason, mostof the studies have been performed in constrained sce-narios assuming specific SUSY breaking mechanismswith only a handful number of parameters. In absenceof New Physics (NP) signals at the LHC, more system-atic studies in general MSSM scenarios have emerged[1–5]. In the following we present highlights on the cur-rent direct and indirect constraints in the phenomeno-logical MSSM (pMSSM), which is the most generalCP and R-parity conserving scenario assuming minimalflavour violation, described by 19 parameters. The CP-violating version of the pMSSM which di ff ers from theCP-conserving case by the addition of six independentCP-violating phases will also be considered.
2. CP-conserving MSSM
To study the CP-conserving pMSSM, we performrandom scans in the parameter space using SOFT- SUSY [6], varying the SUSY masses between 0 and 3TeV, the trilinear couplings between -10 and +
10 TeV,and tan β between 2 and 60, and assuming the neutralino1 to be the lightest supersymmetric particle, so that itconstitutes a dark matter candidate. Direct searches at the LHC are persued in many dif-ferent channels, and in particular squark and gluinodirect searches (jets + E T / ), stop and sbottom directsearches ( t , b -jets ( + leptons) + E T / ) and chargino andneutralino direct searches (leptons ( + b -jets) + E T / ) at AT-LAS and CMS which are considered in this study forboth Run 1 and Run 2. To this end, events are generatedwith MadGraph [7] and / or Pythia [8], and the detectorresponse is simulated with Delphes [9] (see Refs. [4, 10]for a description of the employed tools and methodol-ogy). The events are then compared with the publishedbackgrounds to determine whether a parameter point isexcluded. In addition to the SUSY searches, we con-sider mono-X searches. Monojets searches provide thestrongest constraints, and correspond to the search for1 hard jet + E T / , which is often considered as the darkmatter search at the LHC. However, in the MSSM oneneeds to recast the results as monojets can be constitutedof one hard jet plus soft jets and E T / [10, 11]. There-fore, monojet searches are particularly constraining in a r X i v : . [ h e p - ph ] D ec Nuclear and Particle Physics Proceedings 00 (2018) 1–6 ) (GeV)q~M(
200 400 600 800 1000 1200 1400 1600 1800 2000 f r a c t i on o f e xc l uded po i n t s ) (GeV)g~M(
200 400 600 800 1000 1200 1400 1600 1800 2000 f r a c t i on o f e xc l uded po i n t s Figure 1: Fraction of excluded points as a function of the lightestsquark mass (upper panel) and gluino mass (lower panel). The dottedlines correspond to 8 TeV results, and the solid lines to 8 +
13 TeV. the MSSM in the cases where the strongly interactingsparticles (squarks, gluino) have a small mass splittingwith the lightest neutralino, whose decays generate softjets.In Figure 1, we show the fraction of pMSSM pointsexcluded by the LHC direct searches at 8 and 13 TeV, asa function of the lightest of the first and second genera-tion squarks and of the gluino mass. First, we observethat squarks above 500 GeV can easily escape detection.In addition, there are still a few parameter points wherelight squarks below 500 GeV can escape. Concerningthe gluinos, most of them are excluded with masses be-low 1 TeV. This result sharply contrasts with the resultsobtained for simplified and constrained SUSY scenar-ios, where squarks and gluinos below 2-3 TeV are notviable. This can be understood as it is possible in thepMSSM to have long decay chains in compressed orcomplicated scenarios.
Indirect constraints can also set strong limits on theMSSM. In particular, the mass of the Higgs boson aswell as the measurements of its couplings at the LHC,set strong constraints on the Higgs and stop sectors of the MSSM [12–14]. Similarly, flavour physics observ-ables can lead to strong limits on the MSSM parameterspace. In particular, the branching ratio of B s → µ + µ − ,which has been measured by the LHCb and CMS Col-laborations [15], is very sensitive to the mass of thepseudo-scalar Higgs boson at large tan β [16], and theinclusive branching fraction of B → X s γ is sensitiveto the charged Higgs boson as well as the stops andcharginos [17]. These observables are complementaryto the direct searches for heavy Higgs bosons [18].Further constraints can be set on the MSSM assumingthat the lightest neutralino constitutes dark matter. First,the relic density can be computed assuming that it is athermal relic [19] and compared to the Planck limit [20].Second, dark matter direct detection experiments suchas XENON1T [21] can constrain the scattering crosssection of neutralino 1 with nucleons. Third, indirectdetection can set constraints on the annihilation crosssections of neutralinos into SM particles. Even if thedark matter sector constraints su ff ers from uncertain-ties [22–25], they can strongly constrain the pMSSMparameter space, and are very sensitive to the nature ofthe neutralino 1, as can be seen in Figure 2.The complementarity of the constraints from di ff er-ent sectors is of utmost importance, as it will consti-tute the only way to identify the underlying theory incase of discovery of new phenomena or particles at col-liders or in space [23, 26]. Figures 3 and 4 illustratethe complementary between di ff erent searches, show-ing that Higgs, flavour, dark matter and supersymmetricparticle searches probe di ff erent regions of the pMSSMparameter space, and that in case of detection of newparticles, only the combination of all these constraintswill allow us to disentangle the parameters of the un-derlying theory.
3. CP-violating MSSM
So far, we investigated the observables which are onlyweakly sensitive to CP-violation, so that the pMSSMwas well suited. However, the MSSM can contain manypossible sources of CP violation beyond the SM. Wetherefore extend our analysis by adding to the standardpMSSM 6 CP-violating phases, corresponding to thephases of the M , , masses and A t , b ,τ trilinear couplings,which is the minimal extension of the pMSSM to in-clude CP-violation, for a total of 25 parameters. TheCP phases can take values between −
180 and 180 de-grees, and modify the mixing matrices and couplings[27]. The main phenomenological di ff erence with theCP-conserving pMSSM is that the three neutral Higgs Nuclear and Particle Physics Proceedings 00 (2018) 1–6 bosons are now mixed, giving three states h , h , h withscalar and pseudoscalar components. Electric dipole moments (EDM) are the most sen-sitive observables to CP-violation. In absence of CP-violation, the EDMs are extremely small, hence any de-viation would constitute a proof for the existence of NP.Let us consider the following Lagrangian density: L EDM = − i d f F µν ¯ f σ µν γ f , (1)where f corresponds to the SM fermions and d f theircorresponding EDM. The quark EDMs are however notobserved and only the nucleon EDM can be seen whichis related to the quark EDMs by: d N = η E ( ∆ Nd d d + ∆ Nu d u + ∆ Ns d s ) , (2)where ∆ Nq and η E are of order 1.The current experimental limits at 95% C.L. are givenin Table 1. The proton EDM is expected to be studied by Figure 3: Fraction of points excluded by flavour physics and darkmatter direct detection in the ( M A , tan β ) parameter plane. The linedelimits the region excluded by the heavy Higgs H / A → ττ searchesat the LHC.Figure 4: In the ( µ, M ) parameter plane, points excluded by the LHCHiggs and SUSY searches (in gray), as well as dark matter direct de-tection (in red), indirect detection (in yellow), and both types of de-tections (in orange). EDM Upper limit (e.cm) Equivalent limit (e.cm)Thallium [28] 1 . × − | d e | : 2 . × − Thorium monoxide [29] - | d e | : 1 . × − Muon [30] 1 . × − | d µ | : 1 . × − Mercury [31] 7 . × − | d n | : 1 . × − | d p | : 2 . × − Neutron [32] 4 . × − | d n | : 4 . × − Table 1: The most relevant EDM experimental limits at 95% C.L. . the CPEDM Collaboration using a proton ring at CERNin the future (2021 + ), strongly improving upon the pro-ton EDM limit: | d p | < × − e . cm . (3) In the MSSM, the EDMs are a ff ected by di ff erent sec-tors of the theory, such that [33]: d f = d ˜ χ ± f + d ˜ χ f + d ˜ gf ( + higher order d Hf ) . (4) Nuclear and Particle Physics Proceedings 00 (2018) 1–6 where f = e , µ, u , d , s . The chargino-mediated one-loopEDMs are given by: d ˜ χ ± l = − e π (cid:88) i m ˜ χ ± i m ν l Im (cid:16) g ˜ χ ± l ˜ ν ∗ Ri g ˜ χ ± l ˜ ν Li (cid:17) f ( m χ ± i / m ν l ) , d ˜ χ ± u = e π (cid:88) i , j m ˜ χ ± i m d j Im (cid:18) g ˜ χ ± u ˜ d ∗ Ri j g ˜ χ ± u ˜ dLi j (cid:19) , × (cid:20) f ( m χ ± i / m d j ) − g ( m χ ± i / m d j ) (cid:21) , d ˜ χ ± d = e π (cid:88) i , j m ˜ χ ± i m u j Im (cid:16) g ˜ χ ± d ˜ u ∗ Ri j g ˜ χ ± d ˜ uLi j (cid:17) × (cid:20) − f ( m χ ± i / m u j ) + g ( m χ ± i / m u j ) (cid:21) . The neutralino-mediated one-loop EDMs are: d ˜ χ f = e π (cid:88) i , j m ˜ χ i m f j Im (cid:18) g ˜ χ f ˜ f ∗ Ri j g ˜ χ f ˜ fLi j (cid:19) Q ˜ f g ( m χ i / m f j ) . (5)The gluino-mediated one-loop EDMs read: d ˜ gq = e π (cid:88) i m ˜ g m q i Im (cid:16) g ˜ gq ˜ q ∗ Ri g ˜ gq ˜ qLi (cid:17) Q ˜ f g ( m g / m q i ) . (6)The g ˜ G f f (cid:48) contains the gaugino / neutralino / squark mix-ing matrices, and Q ˜ f is the charge of ˜ f . The remainingterm d Hf is a ff ected by the Higgs bosons and correspondsto higher order terms. The EDMs are therefore sensitiveto the CP-violating phases as well as the masses of thesfermions and gauginos. A di ffi culty appears when applying the EDM con-straints to the CP-violating pMSSM parameter space:the thorium monoxyde imposes a limit so strong thatonly zero phases would pass the constraints in a ran-dom scan, due to the limited statistics in a 25 dimen-sional parameter space. To access the regions where Figure 6: Distributions of the Φ M , Φ M , Φ A t and Φ A b phases afterimposing the current EDM constraints. large phases are still compatible with the experimentalresults, which generally correspond to degeneracies be-tween the di ff erent components of the EDMs, we usethe geometric approach described in Refs. [34–36]. Theidea is to determine the direction in the phase parameterspace minimising the EDMs, E i , and maximising an-other CP-violating observable, O . We showed that theoptimal direction, computed for each choice of the 19CP-conserving pMSSM parameters, is given by: φ ∗ α = (cid:15) αβγδµη (cid:15) ηνλρστ E a β E b γ E c δ E d µ O ν E a λ E b ρ E c σ E d τ , (7)with φ α = φ , , , t , b ,τ , E i α ≡ ∂ E i /∂φ α and O α ≡ ∂ O /∂φ α .The obtained direction remains correct in the limit ofsmall phases, and we use an iterative approach to reachlarger phases: we start with phases at 0, determine theoptimal direction, move by at most 20 degrees, and it-erate to determine the optimal direction at the new po-sition. After imposing in addition flavour constraints,cosmological upper bound on the dark matter density,direct detection limit and requiring squarks and gluinosto have masses above 500 GeV, the obtained distribu-tion of phases is given in Figure 5, and is similar for allphases. After imposing the current EDM constraints,the distribution is modified di ff erently for each of theCP phases. The four most a ff ected ones are shown inFigure 6.First, after imposing the EDM constraints the statis-tics is strongly reduced, by a factor 30. Whereas Φ M , Φ A t have shapes still similar to the original distribution,the distribution of Φ A b is deformed preferring interme-diate values of Φ A b , and Φ M is strongly a ff ected show-ing that the weakly-interacting sector is severely con-strained. This is mainly led by the thorium monoxide Nuclear and Particle Physics Proceedings 00 (2018) 1–6 Φ M and Φ M phases after imposing thecurrent EDM constraints and the prospective proton EDM limit. EDM limit, which sets a very strong constraint on theelectron EDM.On the contrary, phases from the strongly interact-ing sector are less a ff ected, because of the much weakernucleon EDM limits. The CPEDM prospect to mea-sure precisely the proton EDM will therefore be ex-tremely useful. Figure 7 shows the distribtuions of thephases after imposing a limit on the proton EDM of2 × − e.cm. As can be seen, the statitics is againstrongly reduced, and Φ M is restricted to nearly zerophases. In addition, Φ M becomes strongly a ff ected,and only phases up to 30 ◦ could survive. This showsthat the strongly interacting sector can be tested, pro-viding a complementary way to probe the gluino andsquark masses and couplings along with the SUSY di-rect searches at the LHC, in the case additional sourcesof CP-violation exist. The SUSY direct searches are not a ff ected by CP-violation, even if the sparticle spectrum can be. TheHiggs sector can on the contrary be sensitive to CP-violation. However, the 125 GeV Higgs has been mea-sured to be CP-conserving, severely limiting the possi-bility to have a pseudoscalar component. Consequently,only heavier Higgs states could reveal CP-violation.The observations of the decay of heavy Higgs states intotops or taus of specific polarisations would help prob-ing the CP-violating content of the Higgs bosons [37].Concerning the dark matter sector, we showed that it israther insensitive to CP-violation [35].Flavour physics on the other hand is very sensitive toCP-violation. Two observables are particularly relevantfor our study: the CP asymmetry in b → s γ and the B s meson mixing ∆ M NPB s . In the MSSM, b → s γ is sensi-tive to the charged Higgs, gaugino and squark sectors.Charged Higgs is mostly insensitive to CP-violation, butbecause of chargino / stop loops CP-violation can be vis-ible in b → s γ . CP asymmetry in b → s γ has been mea-sured at B factories, but the current limits are not strong Figure 8: Distribution of the CP asymmetry of b → s γ . The graycurve corresponds to the number of points in absence of EDMs, theblack curve using the current EDM limits and the blue one also con-sidering the prospective proton EDM. The red lines correspond to thecurrent b → s γ CP asymmetry limits and the green one to the prospec-tive limits of Belle-II. enough to provide insightful constraints on CP-violationin the pMSSM. Belle-II will however provide in the nearfuture stronger limits [38]. Figure 8 shows the distribu-tion of CP asymmetry in b → s γ depending on the EDMconstraints, as well as the current and future experimen-tal limits. We note that the current EDM limits super-sede the measurements of CP asymmetry. The futureBelle-II results will strongly improve on the limits, andprobe CP-violation in the MSSM. It is remarkable to seethat the future proton EDM measurement will providecomparable constraints on CP-violation.Similarly the B s meson mixing is strongly sensitive tothe gaugino and squark sectors [39]. However, the cur-rent experimental measurements are extremely precise,and the main limitation comes from the theoretical un-certainties from the determination of form factors. Wecan nevertheless expect in the future an improvement bya factor ten on the uncertainties. In Figure 9, the distri-butions of ∆ M NPB s depending on the EDM constraints isshown, as well as the current and future limits includingthe theoretical uncertainties. The current limits are notcompetitive with the EDM constraints for CP-violation,but a strong reduction of the theoretical uncertaintieswould allow for a significant improvement in probingCP-violation.
4. Conclusions
We have discussed the interplay between the con-traints from di ff erent sectors to probe the MSSM param-eter space. We have shown that it is important to com-bine the constraints from direct searches for Higgs and Nuclear and Particle Physics Proceedings 00 (2018) 1–6 ∆ M NPB s . The gray curve corresponds tothe number of points in absence of EDMs, the black curve using thecurrent EDM limits and the blue one also considering the prospec-tive proton EDM. The red line corresponds to the current theoreticaluncertainties and the yellow one to the prospective uncertainties. supersymmetric particles at the LHC, flavour physicsand dark matter observables to study the 19-parameterspace of the phenomenological MSSM. In presence ofadditional sources of CP-violation, we have also quan-tified the importance of electric dipole moments andflavour observables sensitive to CP-violation. We haveshown that a measurement of the proton EDM as pro-jected by the CPEDM collaboration is of utmost impor-tance, and will be complementary to the theoretical andexperimental improvements in flavour physics in orderto deeply probe CP-violation. Acknowledgements
The author is grateful to the organisers of the Capriworkshop for their invitation and the great workshop,and to A. Arbey, M. Battaglia, J. Ellis and G. Robbinsfor their collaboration on the material presented here.
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