The $(B-L)$ Supersymmetric Standard Model (BLSSM) motivates several Dark
Matter (DM) candidates beyond the Minimally Supersymmetric Standard Model
(MSSM). We assess the comparative naturalness of the two models and discuss the
potential detection properties of a particular candidate, the Right-Handed (RH)
sneutrino.Comment: Prepared for proceedings for La Thuile 2018, talk by Simon Kin

Khalil, Shaaban

King, Simon J. D.

Kulkarni, Suchita

Marzo, Carlo

Moretti, Stefano

Rose, Luigi Delle

Un, Cem S.

English

arXiv

The (B − L) Supersymmetric Standard Model (BLSSM) motivates

several Dark Matter (DM) candidates beyond the Minimally Supersymmetric Standard Model (MSSM). We assess the comparative naturalness of the two models and discuss the potential detection properties of a particular candidate, the RightHanded (RH) sneutrino

King, Simon J.D.

Delle Rose, Luigi

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2018-18138-0Colloquia: LaThuile 2018IL NUOVO CIMENTO 41 C (2018) 138Prospects for sneutrino Dark Matter in the BLSSMSimon J.D. King(1)(∗), Luigi Delle Rose(1)(2), Shaaban Khalil(3), SuchitaKulkarni(4), Carlo Marzo(5), Stefano Moretti(1)(2) and Cem S. Un(6)(1) School of Physics and Astronomy, University of Southampton - Highfield, SouthamptonSO17 1BJ, UK(2) Particle Physics Department, Rutherford Appleton Laboratory - Chilton, Didcot, Oxon OX110QX, UK(3) Center for Fundamental Physics, Zewail City of Science and Technology - Sheikh Zayed,12588 Giza, Egypt(4) Institut für Hochenergiephysik, Österreichische Akademie der Wissenschaften - NikolsdorferGasse 18, 1050 Wien, Austria(5) National Institute of Chemical Physics and Biophysics - Rävala 10, 10143 Tallinn, Estonia(6) Department of Physics, Uludag̃ University - TR16059 Bursa, Turkeyreceived 6 September 2018Summary. — The (B − L) Supersymmetric Standard Model (BLSSM) motivatesseveral Dark Matter (DM) candidates beyond the Minimally Supersymmetric Stan-dard Model (MSSM). We assess the comparative naturalness of the two modelsand discuss the potential detection properties of a particular candidate, the Right-Handed (RH) sneutrino.1. – IntroductionIn the SM there is a global (B − L) symmetry which is conserved. By extending theMSSM by gauging this symmetry, based on the group SU(3)c × SU(2)L × U(1)Y ×U(1)B−L, one finds a significantly enriched particle content. Firstly, when gauging(B − L), one must add three SM singlet fields to cancel the triangle anomaly diagrams,which may be identified as the RH neutrinos. We combine this with a low (TeV) scaleType-I see-saw mechanism to explain the light, non-vanishing Left-Handed (LH) neu-trino masses; something the MSSM does not do. In addition to these RH neutrinos, onemay spontaneously break the (B−L) symmetry with new Higgses, called bileptons whichcarry a (B−L) charge of ±2. This will give rise to a new, massive, gauge boson associated(∗) SpeakerCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 SIMON J.D. KING et al.with this group, a Z ′. Finally, one finds the superpartners of these new particles, theRH sneutrinos, bileptinos and partner of the new B′ boson, the BLino.In this work, we consider the implications of this extension to the MSSM. One finds allthe benefits of the MSSM (gauge coupling unification, hierarchy problem solution, etc.)in addition to several new DM candidates and an explanation of light, non-vanishingneutrino masses. We compare the naturalness of the two models, the MSSM and BLSSM,in the presence of universal scalar and gaugino masses (often called the ConstrainedMSSM (CMSSM) scenario).We proceed as follows. In sect. 2 we introduce the concept of naturalness and comparethe non-minimal scenario to the MSSM. Then, we consider the various DM candidatesof the model, and compare the relic abundances of the candidates for each model insect. 3. For the remainder of this work, we discuss the ability to detect sneutrino DMvia direct/indirect and collider detections, respectively, in sects. 4 and 5. Finally, weconclude.2. – NaturalnessWhilst there is no fundamental measure of naturalness in nature, to compare twomodels quantitatively one must use some metric. The weak scale (MZ) depends onthe soft Supersymmetry (SUSY) breaking terms through the Renormalisation GroupEquations (RGEs) and the Electro-Weak (EW) minimisation conditions, which can beexpressed as(1)12M2Z =m2Hd − m2Hutan2 βtan2 β − 1 − μ2.Because of this, we choose here to adopt the criterion of Fine Tuning (FT) related to achange in the Z-boson mass. We denote this as Δ, defined by the largest change whenaltering parameters in the theory [1, 2](2) Δ = Max∣∣∣∣∂ ln v2∂ ln ai∣∣∣∣ = Max∣∣∣∣aiv2∂v2∂ai∣∣∣∣ = Max∣∣∣∣aiM2Z∂M2Z∂ai∣∣∣∣ .A point in parameter space has a low FT if the SM Z mass does not largely deviate whendeviating from its position. A natural model will consequently posses large regions ofviable parameter space with such points. The absolute scale of FT is largely irrelevant asΔ has no physical meaning, we thus are only concerned with the relative value betweentwo models. In this work we consider the fundamental parameters of the theory to bethe Grand Unification Theory (GUT) ones, though other works consider the FT at EWlevel as well [3-6]. The input GUT parameters are: the unification masses for scalars(m0) and gauginos (m1/2), the universal trilinear coupling (A0), the μ parameter andthe quadratic soft SUSY term (Bμ),(3) ai ={m0, m1/2, A0, μ, Bμ}.For the BLSSM, one also has two further parameters, (μ′, Bμ′). We find that thedominating term for both the MSSM and BLSSM comes from μ, which is fixed by EWSymmetry Breaking (EWSB). It is important to check the level of FT in the BLSSM, asone may have expected that a heavy Z ′ would lead to a large μ′ which could, in principle,PROSPECTS FOR SNEUTRINO DARK MATTER IN THE BLSSM 3Fig. 1. – Fine-tuning in the plane of unification of scalar, gaugino masses for BLSSM and MSSMfor GUT-parameters (Δ). The FT is indicated by the colour of the dots: blue for FT < 500;orange for 500 < FT < 1000; green for 1000 < FT < 5000; and red for FT > 5000.have surpassed all other contributions, however we do not see such behaviour. We willnow compare the FT for the two models.The scan performed to obtain these data has been done by SPheno [7] with all pointsbeing passed through HiggsBounds [8-11] and HiggsSignals [12]. We have scannedover the range [0, 5] TeV in both m0 and m1/2, tan β in [0, 60], A0 in [−15, 15] TeV,which are common universal parameters for both the MSSM and the BLSSM, while forthe BLSSM we also required tanβ′ in the interval [0, 2] with neutrino Yukawa couplingsY (1,1), Y (2,2), Y (3,3) in [0, 1]. The MZ′ value has been fixed to 4 TeV to comply withcollider searches [13].In fig. 1, we compare the FT for the MSSM and BLSSM in the plane of (m0, m1/2).We colour the parameter points according to their FT, Δ: red for Δ > 5000, orangefor 500 < Δ < 1000 and blue (the least finely-tuned points) for Δ < 500. Overall thepicture between the two models is very similar. Firstly, we see that there are few viableBLSSM parameter points for low m0. Both models follow the general trend that theFT is strongly related to universal gaugino mass m1/2, due to the μ dependence on this.Finally, we summarise that the MSSM and the BLSSM have very similar levels of FT.3. – Relic abundanceBy our previous measure, Δ, both the universal MSSM and BLSSM scenarios hada similar level of FT. Another measure of FT could be to compare the relative sizeof parameter space in both models, over the same ranges in GUT parameters. Beforeenforcing a DM candidate, in both cases the number of viable points (satisfying LHCsearches and a SM-like Higgs) is a similar fraction of the total number with a uniformrandom scan. However, once we enforce that the LSP be the DM candidate and complywith the correct relic density, one finds that the BLSSM has significantly larger viableregions of parameter space.In SUSY the Lightest Super Partner (LSP) is stable due to R-parity conservation. Inthe MSSM, this is imposed ad hoc, but for the BLSSM this is automatically satisfied asthe R-symmetry is defined as R = (−1)3(B−L)+2S , and B − L is conserved (or broken4 SIMON J.D. KING et al.Fig. 2. – Left: relic density vs. LSP mass for the BLSSM. Right: relic density vs. LSP mass forthe MSSM. In both plots the horizontal lines identify the 2σ region around the current centralvalue of Ωh2.by two units, which leaves a residual Z2). In addition to the bino-like neutralino in theMSSM, there are three extra DM candidates in the BLSSM. Firstly, there are bileptino-like and BLino-like neutralinos, and also the superpartner of the RH neutrino, the RHsneutrino.Figure 2 plots the relic density (with 2σ bounds) [14] against the mass of the LSP(MDM). For the bino-like neutralino in the MSSM (the only allowed candidate due toother constraints in the universal scenario), very few of the parameter points survive.The vast majority here have a very large relic abundance. For the BLSSM, there areseveral bino-like neutralino LSP parameter points which satisfy the relic density, andfurthermore one is guaranteed regions of parameter space where this is satisfied whenMDM ∼ 12MZ′ , in our case around the 2 TeV mass. This effect also occurs for BLinoand bileptino-like neutralinos. However, the RH sneutrinos offer the largest number ofparameter points of our scan which satisfy the relic density requirements and we discussthe potential detection of this DM candidate in subsequent sects.4. – Direct and indirect searchesThe mass eigenstate of the RH sneutrino LSP is CP -even (Re) or CP -odd (Im), dueto lepton number violating operators. Consequently, two DM particles interacting mustproduce a CP -even state, in addition to conservation of angular momentum and spinstatistics. One finds the largest cross section of annihilation into a pair of the lightest(B − L)-like CP -even Higgses, either through the four point (ν̃(R,I)1 ν̃(R,I)1 → hihj) ormediated by a single CP -even Higgs (ν̃(R,I)1 ν̃(R,I)1 → hi → hihj) interaction. If this isnot kinemetically available (i.e. Mh2 > Mν̃), then the next largest cross section is adecay to a charged W+W− pair. It is this decay which will provide a signal for indirectdetection, which we discuss shortly. One also finds RH sneutrino interactions under thegauge boson associated with the U(1)B−L group, the Z ′, but this requires one CP -evenand one CP -odd sneutrino (ν̃(R,I)1 ν̃(I,R)1 → Z ′). All of these processes require a heavymediator and so are suppressed when it comes to Direct Detection (DD).Figure 3 shows the spin-independent WIMP-nucleus scattering cross section vs. the2016 LUX experimental limits [15,16]. One can see that the vast majority of parameterspace is not yet touched by DD, and nearly all of the red sneutrino points are far fromthe near-future experimental reach.PROSPECTS FOR SNEUTRINO DARK MATTER IN THE BLSSM 5Fig. 3. – Spin-independent WIMP-nucleus scattering cross section generated in our scan againstthe upper bounds from 2016 run of the LUX experiment.Another method of detecting sneutrino DM comes from indirect detection. Here anni-hilations to charged W+W− pairs can then radiate photons in the galactic centre, whichmay be observed by the Fermi -LAT experiment. In fig. 4 we plot the self-annihilationcross section in the charged W+W− channel vs. the DM mass for both CP -even andCP -odd sneutrinos. We overlay the current Fermi -LAT limit, which uses 15 dwarfSpheroidal galaxies (dSphs) [17]. The projected sensitivity over the next 15 years isalso drawn, which extends the search via observation of 60 dSphs samples. A singleGUT-constrained parameter point exists which is detectable according to the projectedlimits. This signals that there are regions of parameter space which are beginning toFig. 4. – Thermal cross section for DM DM → W+W− annihilation as predicted by theory asa function of the DM mass, for CP -even (blue) and CP -odd (orange) sneutrinos. Also shownare the FermiLAT limit from dSphs at present (solid black) and as projection for 15 years fromnow (dashed black). All points obey the relic density upper limit, for which rescaling, wherenecessary, has been applied.6 SIMON J.D. KING et al.Fig. 5. – Differential flux of γ-ray secondary radiation induced by DM DM → W+W− anni-hilation as a function of the photon energy, with fixed DM mass, for our benchmark CP -oddsneutrino (orange). The corresponding distribution for the background is also given (red). TheFermiLAT present data (with error) are in black. The sneutrino point considered is compliantwith the relic density constraint taken as an upper limit.be excluded over the next few years of observation. In addition to the total integratedflux measurement, one may also study the differential γ-ray flux due to sneutrino an-nihilations in the centre of the Milky Way. This is done in fig. 5, where we show thedifferential γ-ray flux vs. the energy of photons for a particular CP -odd sneutrino LSPDM candidate. We also plot the background and Fermi -LAT data, with errors. Thesignal from the sneutrino is well below the background, so one may not see a large signalat particular photon energy. We notice here, though, that the limiting photon energyis by an experimental upper limit of ∼ 300 GeV, and the sneutrino is capable of emit-ting γ-rays of energies up to its mass, 661 GeV. In the future, when one is able to detecthigher photon energies, there may be a characteristic signal emerge. Should such a signalbe observed, one may wonder whether this could disentangle the CP -odd and CP -evencase with other DM candidates. We draw the spectrum shape for these three candidatesFig. 6. – Differential flux of γ-ray secondary radiation induced by DM DM → W+W− scatteringsas a function of the photon energy, with fixed DM mass, for our benchmark CP -even (blue) andCP -odd (orange) sneutrinos. The corresponding distribution for a neutralino is also given forcomparison (green). Normalisation is the same for all curves.PROSPECTS FOR SNEUTRINO DARK MATTER IN THE BLSSM 7in fig. 6. One can see that the CP -odd and CP -even shapes look identical, so one maynot disentangle these two scenarios. However, this does look characteristically differentfrom the neutralino shape. We speculate that this could be to do with the spin of thecandidate, where the sneutrino is a scalar and the neutralino is a fermion.5. – LHC searchesIn addition to direct and indirect detection, one can also search for sneutrino DM viaLHC searches. There is little mixing between the left and RH sneutrinos, as the Yukawacoupling is set to be very small (Yν ∼ O(10−6)) to obtain the correct LH neutrino masseswith an O(1) TeV RH neutrino scale. So there is no hope to produce the DM via W±or Z with any appreciable cross section. Given this, we have performed a general searchusing the MadGraph program [18] using several benchmark sneutrino points, both ofCP -even and CP -odd varieties. The most well-established DM search is via mono-jet,whereby pair production of DM is detected by initial radiation of a single gluon, whichwill show the signature of a mono-jet plus missing energy. However, this does not uniquelyidentify the BLSSM whatsoever. A more unique direct DM production signature couldbe through Z ′ decay, in the process pp → Z ′ → ν̃LSP ν̃NLSP , where the NLSP is forcedto decay to the LSP via a SM Z decay, despite the small coupling. However, as themass of our Z ′ is fixed to be 4 TeV, so as to comply with dilepton searches, the crosssection for this process is too small to observe, σ  0.025 for both CP -even and CP -oddLSP benchmark points. Another possibility to search for sneutrino DM at the LHC canbe through slepton pair production, with cross sections ∼ 0.1 fbs. For a light sleptonmass, the only possible decay path can be through l̃ → W±ν̃LSP , despite the suppressedYukawa coupling, yielding a dilepton signature. For a different mass configuration, onemay find the more complicated decay chain l̃ → χ̃0l with χ̃0 → νhν̃LSP , where νh isthe heavy neutrino. The latter will mainly undergo νh → W±l∓ or νh → Zνl decay,thus providing fully or semi-leptonic signatures which would be very distinctive. Finally,one may also consider signatures from squark pair production, which can offer some ofthe largest cross sections (O(fbs)). The typical decay chain is now through t̃ → χ̃0 t,with large branching fractions. The neutralino may decay as before, χ̃0 → νhν̃LSP . Thissignature would involve several jet plus multi-lepton final states.6. – ConclusionWe have compared naturalness and DM properties of the BLSSM and MSSM. Wehave seen that both models possess similar levels of FT but, when one includes therequirement of an LSP which satisfies the DM bounds, the BLSSM has a far largerregion of available parameter space, due to the unique RH sneutrino. We then went onto assess the ability to detect this DM candidate, and saw that whilst direct detection inthe near future seems unlikely, both CP -even and CP -odd candidates may be observedvia indirect detection in the next few years. Finally, we identified several interesting LHCsignatures which, if seen, would provide strong evidence for sneutrino DM.∗ ∗ ∗SM is supported in part through the NExT Institute. The work of LDR has beensupported by the STFC/COFUND Rutherford International Fellowship scheme. Thework of CM is supported by the “Angelo Della Riccia” foundation and by the Centre ofExcellence project No TK133 “Dark Side of the Universe”. The work of SK is partially8 SIMON J.D. KING et al.supported by the STDF project 13858. SK, SJDK and SM acknowledge support from thegrant H2020-MSCA-RISE-2014 n. 645722 (NonMinimalHiggs). SJDK and SM acknowl-edge support from the STFC Consolidated grant ST/L000296/1. SuK is supported bythe “New Frontiers” program of the Austrian Academy of Sciences and by FWF projectnumber V592-N27.REFERENCES[1] Ellis J. R., Enqvist K., Nanopoulos D. V. and Zwirner F., Mod. Phys. Lett. A, 1(1986) 57.[2] Barbieri R. and Giudice G. F., Nucl. Phys. B, 306 (1988) 63.[3] Ross G. G., Schmidt-Hoberg K. and Staub F., JHEP, 03 (2017) 021, arXiv:1701.03480[hep-ph].[4] Delle Rose L., Khalil S., King S. J. D., Marzo C., Moretti S. and Un C. S., Phys.Rev. D, 96 (2017) 055004, arXiv:1702.01808 [hep-ph].[5] Delle Rose L., Khalil S., King S. J. D., Marzo C., Moretti S. and Un C. S., PoS,DIS 2017 (2018) 301, arXiv:1706.01301 [hep-ph].[6] Delle Rose L., Khalil S., King S. J. D., Marzo C., Moretti S. and Un C. S., PoSEPS-HEP2017 (2017) 067, arXiv:1710.01116 [hep-ph].[7] Porod W., Comput. Phys. Commun., 153 (2003) 275, arXiv:hep-ph/0301101.[8] Bechtle P., Brein O., Heinemeyer S., Weiglein G. and Williams K. E., Comput.Phys. Commun., 181 (2010) 138, arXiv:0811.4169 [hep-ph].[9] Bechtle P., Brein O., Heinemeyer S., Weiglein G. and Williams K. E., Comput.Phys. Commun., 182 (2011) 2605, arXiv:1102.1898 [hep-ph].[10] Bechtle P., Brein O., Heinemeyer S., Stl O., Stefaniak T., Weiglein G. andWilliams K. E., Eur. Phys. J. C, 74 (2014) 2693, arXiv:1311.0055 [hep-ph].[11] Bechtle P., Heinemeyer S., Stal O., Stefaniak T. and Weiglein G., Eur. Phys. J.C, 75 (2015) 421, arXiv:1507.06706 [hep-ph].[12] Bechtle P., Heinemeyer S., Stl O., Stefaniak T. and Weiglein G., Eur. Phys. J.C, 74 (2014) 2711, arXiv:1305.1933 [hep-ph].[13] CMS Collaboration (Khachatryan V. et al.), Phys. Lett. B, 768 (2017) 57,arXiv:1609.05391 [hep-ex].[14] Planck Collaboration (Ade P. A. R. et al.), Astron. Astrophys., 594 (2016) A13,arXiv:1502.01589 [astro-ph.CO].[15] LUX Collaboration (Akerib D. S. et al.), Phys. Rev. Lett., 116 (2016) 161302,arXiv:1602.03489 [hep-ex].[16] LUX Collaboration (Akerib D. S. et al.), Phys. Rev. Lett., 118 (2017) 021303,arXiv:1608.07648 [astro-ph.CO].[17] Fermi-LAT Collaboration (Ackermann M. et al.), Phys. Rev. Lett., 115 (2015)231301, arXiv:1503.02641 [astro-ph.HE].[18] Alwall J. et al., JHEP, 07 (2014) 079, arXiv:1405.0301 [hep-ph].

Prospects for sneutrino Dark Matter in the BLSSM

Prospects for Sneutrino Dark Matter in the BLSSM

Prospects for Sneutrino Dark Matter in the BLSSM

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