MIMAC potential discovery and exclusion of neutralinos in the MSSM and NMSSM
TTitle : will be set by the publisher
Editors : will be set by the publisherEAS Publications Series, Vol. ?, 2018
MIMAC POTENTIAL DISCOVERY AND EXCLUSION OFNEUTRALINOS IN THE MSSM AND NMSSM
Daniel Albornoz V´asquez Abstract.
The MIMAC project aims to provide a nominal fluorine de-tector for directional detection of galactic dark matter recoil events.Its expected behavior reaches an important part of the predicted spindependent elastic scattering interactions of the supersymmetric neu-tralino with protons. Hence, the parameter space in the MSSM andthe NMSSM models with neutralino dark matter could be probed bysuch experimental efforts. In particular, a good sensitivity to spindependent interactions tackles parameter space regions to which thepredictions on spin independent interactions and indirect signaturesare far below current and projected experiments.
Recent and rapid experimental developments have been constraining particle darkmatter (DM) candidates. In particular, the direct detection community has showedits capacity to scan DM-nucleon interactions for candidates of masses at the elec-troweak scale with spin independent interactions down to ∼ − cm and spindependent cross sections down to ∼ − cm (see (Censier, 2011) for a reviewon the subject).The directional technique relies on the fact that the solar system is in motion withrespect to the galactic reference frame with a velocity pointing toward the Cygnusconstellation. The interaction between the DM of the galaxy and a detector onEarth would happen in a preferred direction: recoil events could record this asym-metry. In (Billard et al., 2010a; Billard et al., 2010b) the projected sensitivityto spin dependent proton-DM interactions of a forthcoming fluorine detector isestimated. The characteristics of the simulated detector are set to be those of theMIMAC project, but are also representative of the whole generation of detectorscurrently in development. Data was simulated and analyzed for a detector madeof 10 kg of CF , operated at 50 mbar, assuming that recoil tracks can be solved, LAPTH, U. de Savoie, CNRS, BP 110, 74941 Annecy-Le-Vieux, Francec (cid:13)
EDP Sciences 2018DOI: (will be inserted later) a r X i v : . [ h e p - ph ] N ov Title : will be set by the publisherincluding the head-tail determination of the event, with a threshold at 5 keV, andan exposure of 30 kg yr.Supersymmetric models provide neutralinos as a DM candidate. The Minimal Su-persymmetric Standard Model (MSSM) and Next-to-MSSM (NMSSM) (Ellwangeret al., 2010) are well established realizations of Supersymmetry in which the light-est supersymmetric particle (LSP) is stable. In the MSSM and NMSSM withnon-universal gaugino masses one could find neutralinos as light as ∼
13 GeV(see (Albornoz Vasquez et al., 2011b) and references therein) and ∼ Supersymmetry offers a large number of possibilities in a multidimensional pa-rameter space with new interactions and particles. The phenomenology relatedto a neutralino DM candidate is mostly determined by its mass and composition,as well as by the Higgs sector. Hence among the relevant free parameters aregaugino masses M , M and M , the ratio of the vacuum expectation values ofthe two Higgs doublets tan β , and the µ mass term. The MSSM and the NMSSMdiffer in the Higgs sector, where the NMSSM has an extra singlet scalar field. Thisgives a natural explanation to the energy scale of the MSSM µ mass term, whichbecomes effective in the NMSSM. To complete the Higgs sector parametrization,in the MSSM we have the pseudoscalar mass M A which is replaced in the NMSSMby the scalar couplings λ and κ , as well as the corresponding trilinear couplingsA λ and A κ . The Higgs particle spectrum is expanded from the MSSM -with h, H,H ± and A- to the NMSSM -with H , H , H , H ± , A and A . In particular, thestringent constraints on the lightest MSSM scalar Higgs h do not necessarily applyto the lightest NMSSM scalar Higgs H , since it could be strongly dominated bya singlet component. This, in turn, is at the origin of a broader set of possibilitiesfor physics below the 100 GeV scale in the NMSSM. The set of free parameters iscompleted by the soft sfermion masses and the trilinear coupling of the top sectorA t -the other trilinear couplings being set to zero.Scanning the multidimensional supersymmetric parameter spaces is not an easytask. To this end a Markov Chain Monte-Carlo code was developed to scanthe multidimensional supersymmetric parameter spaces (Albornoz Vasquez et al.,2010). This code, built on micrOMEGAs 2.4 (Belanger et al., 2005), evaluates eachsupersymmetric parametrization using a likelihood function to fit particle physicslimits, including limits on masses -such as the chargino or the Higgs bosons-, elec-troweak observables -such as (g − µ or the Z invisible width-, and B-physicsIMAC and neutralinos 3-such as the b → s γ , B s → µ + µ − and B → τ ν τ branching ratios. Neutralinosare also required to represent at least 10% of the cosmological DM as measuredby WMAP (Komatsu et al., 2011), hence a likelihood function was established forthe relic density of the neutralinos after thermal freeze-out. An iteration processbased on a Metropolis-Hastings algorithm generates a random walk in the multi-dimensional parameter space.Once the parameter space is explored and configurations allowed by particle physicsexperiments are found, we may compare the direct and indirect detection yield.Therefore, we compute the spin independent cross sections times neutralino-to-DM fraction ξ , to which we apply the exclusion limits by XENON100 (Aprileet al., 2011). We also apply Fermi-LAT constraints on γ -ray fluxes from the Dracodwarf spheroidal galaxy (dSph) (Abdo et al., 2010). The γ -ray flux stemmingfrom neutralino annihilations in the DM dominated Draco galaxy was estimatedby computing the γ -ray production cross section and spectrum from neutralinoannihilations, and multiplied by the line-of-sight integral, provided by Fermi-LATfor a Navarro-Frenk-White halo profile (Navarro et al., 1996). For more details,see (Albornoz Vasquez et al., 2011a). Directional detectors based on fluorine are sensitive mostly to the spin depen-dent interactions of DM with protons. The directional detection prospects for aMIMAC-like detector show that if no background events are recorded, the detec-tor would be able to exclude cross section down to (cid:39) × − cm for a massof 10 GeV. Furthermore, determining the directionality increases the number ofobservables. Using a likelihood analysis, it is possible to determine the WIMPmass and interaction cross section. The needed statistics to solve these charac-teristics can be translated into a sensitivity curve, which is, of course, above theexclusion limit. In light of these sensitivity curves, three regions are defined in the ξσ SDp vs. m χ plane ( ξ being the neutralino to DM fraction at Earth’s position):above the discovery limit, between discovery and exclusion limits, and below theexclusion limits. In the first region, neutralinos are expected to be detected, theirmass and cross section could be measured. Of course, if no event is measured,then the corresponding configuration would be ruled out. In the second region,neutralinos would produce some signal but not enough to be solved. If they donot, then scenarios lying in this region would be excluded. Finally the third regionis populated by neutralinos that would not yield any effect in the forthcoming di-rectional detection experiments.We present the results for the MSSM and NMSSM in Fig. 1. It is importantto notice that many configurations lie above the projected exclusion limit of MI-MAC in both the MSSM and the NMSSM. This already encourages the efforts forbuilding fluorine directional detectors. We show in green points allowed by bothXENON100 and Fermi-LAT, while points failing one or the other are tagged inyellow. Those excluded by both are tagged in red.The predictions for neutralinos in these two models only differ significantly for neu- Title : will be set by the publisher Fig. 1.
Spin dependent proton-neutralino interactions as a function of neutralino massin the MSSM (top panel) and the NMSSM (bottom panel). The projected sensitivityof a typical directional detector are also shown. In green: points safe with respect toXENON100 limits on spin independent interactions and Fermi-LAT limits on γ -rays fromthe Draco dwarf spheroidal galaxy. In yellow: points in conflict with either one or theother. In red: points failing to overcome both exclusion limits. tralino masses below ∼
30 GeV, This is a direct consequence of the very differentconfigurations in the Higgs sector. Indeed, as it was found in (Albornoz Vasquezet al., 2010) and further explored in (Albornoz Vasquez et al., 2011a), NMSSMneutralinos below 30 GeV achieve the relic density by resonantly annihilating vialight scalar or pseudoscalar Higgs bosons, absent in the MSSM. In the latter, theonly possibilities are to push as much as possible the masses of the lightest scalarHiggs in order to allow lighter pseudoscalar masses, and have efficient enough anni-hilations. This scenario is actually heavily constrained and should not be regardedas plausible, as shown in (Albornoz Vasquez et al., 2011b). The other possibility isexchanging very light staus, which provides neutralinos down to 12.6 GeV. SinceIMAC and neutralinos 5the MSSM is contained in the NMSSM, this configuration is also realizable in theNMSSM. Hence, a detection below 30 GeV implies different predictions for bothmodels: in the MSSM we would expect to observe light sleptons ( (cid:46)
100 GeV),while the NMSSM could predict a very light Higgs boson.In both models, there is a prominent concentration of points with m χ ∼
45 GeV,corresponding to neutralinos in resonant annihilations through a Z boson, an ef-ficient mechanism to attain the correct relic density. The points that can bedetected around the Z resonance are those not falling exactly in it, but ratherthose of masses (cid:46)
40 GeV and (cid:38)
50 GeV. This is easily understood in terms ofthe elastic scattering cross section: the spin dependent interactions occur mainlyvia the exchange of a Z boson. While the Z resonance represents a good way toobtain a plausible relic density, a too fine-tuned relation between neutralino and Zmasses leads to too small abundances unless the coupling to the Z is small. Thus,for points with m χ sitting too close to M Z /
2, the Z χ χ coupling is small, hencespin dependent interactions are consequently reduced.For the larger masses, for LSP with larger higgsino components, the Z χ χ cou-pling is usually large, since it is proportional to N − N ( N and N beingthe higgsino-d and higgsino-u fractions of the neutralino). However, above a fewhundred GeV the mass split between the lightest neutralino and squarks narrows.Hence both Z and ˜ q u, d contribute to the interactions. It turns out that these twocontributions are destructive. Therefore, for a generally dominating Z exchangewith rather large couplings, those configurations having a large enough squarkexchange can lower the spin dependent proton-neutralino cross section by a feworders of magnitude. This is why not all the higgsino points have large interac-tions. Thus, only a fraction of them falls in the discovery region. The general trendto have smaller cross sections towards larger neutralino masses is a consequence ofthe kinematic behavior of the cross section: when m χ (cid:29) m p , then the neutralino-proton cross section is proportional to m − χ . When the maximum Z χ χ couplingis achieved -i.e., N − N (cid:39) . ∼
150 GeV. This implies that the detectionof a neutralino fixes the µ mass term to be lighter than 200 GeV. In turn, thispredicts a chargino of mass below 200 GeV, which should be observed at LHC.The other possibility would be small squark masses, which, however, seem to benot an option any more after the first round of results at ATLAS and CMS.It is also important to notice that many points escape both the discovery regionand the exclusion region. This should not be taken as a drawback, but encourageexperimental efforts to develop as good techniques as possible. Consequently, itis also important to keep an eye on other detection techniques, in order to tacklethe most difficult configurations. Title : will be set by the publisher In Figs. 2 we display the points in the γ -ray flux vs. ξσ SI plane, using the ma-genta, cyan and blue tagging for those configurations that could be discovered,excluded or would not yield any effect in a nominal directional detector.The XENON100 exclusion limits rule out part of the parameter space, which is Fig. 2.
Predicted γ -ray fluxes from the Draco dwarf galaxy as a function of ξσ SI in theMSSM (top panel) and the NMSSM (bottom panel). Points excluded by XENON100are not drawn. The Fermi-LAT limits for the flux are shown. In magenta: points fallingin the MIMAC discovery region. In cyan: points falling in the MIMAC exclusion region.In blue: points beyond the MIMAC sensitivity. not shown in these figures. Hence, a fluorine based directional detector would scanconfigurations that are safe with respect to XENON100 limits on spin independentinteractions. Furthermore, in the MSSM, the magenta point with the smallest spindependent interaction reads ξσ SI (cid:39) × − cm , which is unlikely to be withinthe sensitivity of the projected XENON1ton or other spin independent-orientedprojected detectors. In the NMSSM this is even more drastic: there is a point inIMAC and neutralinos 7magenta with ξσ SI (cid:39) − cm !Regarding the indirect γ -ray flux from the Draco dSph, the conclusion is similar:we find discoverable configurations which lie up to four orders of magnitude belowthe Fermi-LAT limits in the MSSM, and even more in the NMSSM.It is important for the prospect of directional experiments that we find large con-centrations of points which are not excluded by any experiment yet, which are faraway from detectability by other techniques such as indirect detection and directdetection, and which could be discovered or excluded by such projected detectors. The projected sensitivity for directional detectors such as MIMAC would allow toprobe a large portion of parameter space of neutralino DM supersymmetric config-urations, especially towards the lightest LSP regions, below 30 GeV. A detectioncould happen below 150 GeV, and would imply a significant higgsino fraction inthe neutralino composition, which in turn predicts a chargino lighter than 200GeV. For discoveries of even lighter neutralinos, the predictions of the MSSM andthe NMSSM are quite different: the former points towards light sleptons while thelatter implies light scalar or pseudoscalar Higgs bosons.The interplay between the projected sensitivity of fluorine directional detectors,the spin independent interactions and the γ -ray fluxes expected for neutralinosin the MSSM and the NMSSM is a crucial feature for the future explorations ofneutralino DM. If the LHC tells us something about Supersymmetry, then we mayhave indications for which technique is the most adapted to discover or excludethe existence of a neutralino in galactic systems. Conversely, signals in direct,directional or indirect detection could help the LHC to confirm or rule out theMSSM and/or the NMSSM. References
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