Probing the MSSM explanation of the muon g-2 anomaly in dark matter experiments and at a 100 TeV pp collider
FFeb. 2017
Probing the MSSM explanation of the muon g-2 anomaly indark matter experiments and at a 100 TeV pp collider Archil Kobakhidze , Matthew Talia and Lei Wu , ARC Centre of Excellence for Particle Physics at the Terascale,School of Physics, The University of Sydney, NSW 2006, Australia Department of Physics and Institute of Theoretical Physics, Nanjing Normal University,Nanjing, Jiangsu 210023, ChinaE-mails: archil.kobakhidze, matthew.talia, [email protected]
Abstract
We explore the ability of current and future dark matter and collider experimentsin probing anomalous magnetic moment of the muon, ( g − µ , within the MinimalSupersymmetric Standard Model (MSSM). We find that the latest PandaX-II/LUX-2016 data gives a strong constraint on parameter space that accommodates the ( g − µ within 2 σ range, which will be further excluded by the upcoming XENON-1T (2017)experiment. We also find that a 100 TeV pp collider can cover most of our survivingsamples that satisfy DM relic density within 3 σ range through Z or h resonant effect bysearching for trilepton events from ˜ χ ˜ χ +1 associated production. While the samples thatare beyond future sensitivity of trilepton search at a 100 TeV pp collider and the DMdirect detections are either higgsino/wino-like LSPs or bino-like LSPs co-annihilatingwith sleptons. Such compressed regions may be covered by the monojet(-like) searchesat a 100 TeV pp collider. a r X i v : . [ h e p - ph ] M a r Introduction
The discovery of Higgs boson [1,2] and subsequent measurements of its properties com-pleted the Standard Model (SM) and provided it with very convincing evidence for thesimplest perturbative realisation of the electroweak symmetry breaking (EWSB). De-spite this overwhelming empirical success, our understanding of EWSB is incomplete.Namely, the quantum corrections are known to drive the Higgs mass (and hence theelectroweak scale) towards high-energy scales and thus the SM requires unnaturallyprecise fine-tuning of parameters to satisfy the observations. In addition, observationsof neutrino oscillations and dark matter (DM) certainly require beyond the standardmodel (BSM) physics.Another deviation from the SM prediction are long seen in the measurements ofthe anomalous magnetic moment of the muon, a µ = ( g − µ / a Exp − SM µ = (cid:40) (28 . ± . × − [8] , (26 . ± . × − [9] , (1)are more than 3 σ away from the SM prediction, which includes improved QED [10] andelectroweak [11] contributions. The upcoming experiments at NBL will measure the( g − µ with a precision of 0.14 ppm [12], which would potentially allow a 5 σ discoveryof new physics through such measurements. Needless to say, there are several candidateexplanations for ( g − µ anomaly proposed within various new physics frameworks.The weak-scale supersymmetry (SUSY) has long been the dominant paradigm fornew particle physics. The minimal supersymmetric standard model (MSSM) not onlyprovides an elegant solution to the hierarchy problem but also may successfully explain( g − µ anomaly [13–33]. In the MSSM, the most significant contribution to a µ is dueto the one-loop diagrams involving the smuon (cid:101) µ , muon sneutrino (cid:101) ν µ , neutralinos (cid:101) χ and charginos (cid:101) χ ± . The one-loop contribution to a µ arises if there is a chirality flipbetween incoming and outgoing external muon lines, which may be induced throughthe L − R mixing in the smuon sector or the SUSY Yukawa couplings of Higgsinos tomuon and (cid:101) µ or (cid:101) ν µ . Therefore, these contributions to a µ are typically proportional to m µ /M SUSY . Thus, to generate the sizable contributions to a µ , the SUSY scale M SUSY encapsulating slepton and electroweakino masses has to be around O (100) GeV. So,the detection of light sleptons and electroweakinos will provide a test for the MSSMsolution to the ( g − µ problem.The negative results of direct searches for sparticles during the LHC Run-1 havepushed up the mass limits of the first two generation squarks and gluino into the TeVregion [34, 35]. The third generation squarks have been tightly constrained in the sim-plified models [36, 37], such as in Stealth SUSY [38] and Natural SUSY [39–44]. Unlikethe colored sparticles, the bounds on the sleptons [45, 46] and electroweakinos [47, 48]are relatively weak, especially for the region of compressed spectrum. The lightestneutralino still remains as a successful dark matter (DM) candidate and significant1igure 1: One-loop diagram contributions of the MSSM to the muon anomalous mag-netic moment, ( g − µ . The first involves a smuon-neutralino (left) and the second achargino-muon sneutrino loop (right).effort has been made to obtain a lower mass limit on the neutralino LSP in MSSM, seee.g. [49–52].In this paper, we explore the potential of the current and future dark matter andcollider experiments to probe the anomalous magnetic moment of the muon withinthe MSSM. Using LEP and Higgs data and demanding that the theory accommodates( g − µ measurements within 2 σ range, we derive bounds on the electroweakino masses.Following this, we impose dark matter constraints from Planck, PandaX-II/LUX 2016data and constraints from LHC searches for dilepton and trilepton events. Then, weevaluate the prospect of a future 100 TeV hadron collider in probing electroweakinosin trilepton events within this scenario. Finally, our conclusions are presented. ( g − µ in MSSM The low-energy effective operator for magnetic dipole moment (MDM) is given by: L MDM = e m µ a µ ¯ µσ ρλ µF ρλ . (2)where e is the electric charge and m µ is the muon mass. F ρλ is the field strength ofthe photon field and σ ρλ = i [ γ ρ , γ λ ].In the MSSM, there are essentially two types of diagrams which contribute to a µ atone-loop, i.e. one is the (cid:101) χ − (cid:101) µ loop diagram (left panel of Fig. 1) and the other is thechargino (cid:101) χ ± − (cid:101) ν µ loop diagram (right panel of Fig. 1). The expressions for one-loopSUSY corrections to a µ (including the complex phases effects) are given by [14] a (cid:101) χ µ = m µ π (cid:88) i,α (cid:110) − m µ m (cid:101) µ m ( | n Liα | + | n Riα | ) F N ( x iα ) + m (cid:101) χ i m (cid:101) µ m Re( n Liα n Riα ) F N ( x iα ) (cid:111) , (3) a (cid:101) χ + µ = m µ π (cid:88) j (cid:110) m µ m (cid:101) ν µ ( | c Lj | + | c Rj | ) F C ( x j ) + 2 m (cid:101) χ ± j m (cid:101) ν µ Re( c Lj c Rj ) F C ( x j ) (cid:111) (4)2here i = 1 , , , j = 1 , α = 1 , n Riα = √ g N i X α + y µ N i X α ,n Liα = 1 √ g N i + g N i ) X ∗ α − y µ N i X ∗ α ,c Rj = y µ U j ,c Lj = − g V j , (5)where the muon Yukawa coupling y µ = g m µ / √ m W cos β . N are the neutralino and U, V are the chargino mixing matrices, respectively. X denotes the slepton mixingmatrix. In terms of the kinematic variables x iα = m (cid:101) χ i /m (cid:101) µ α and x j = m (cid:101) χ ± j /m (cid:101) ν µ , theloop functions F are defined as follows F N ( x ) = 2(1 − x ) (cid:104) − x + 3 x + 2 x − x ln x (cid:105) ,F N ( x ) = 3(1 − x ) (cid:104) − x + 2 x ln x (cid:105) ,F C ( x ) = 2(1 − x ) (cid:104) x − x + x + 6 x ln x (cid:105) ,F C ( x ) = − − x ) (cid:104) − x + x + 2 ln x (cid:105) . (6)These one-loop corrections mainly rely on the bino/wino masses M , , the Higgsinomass µ , the left- and right-smuon mass parameters, M (cid:101) µ L , (cid:101) µ R , and the ratio of the twoHiggs vacuum expectation values, tan β . They have a weak dependence on the secondgeneration trilinear coupling A µ . In the limit of large tan β , when all the mass scalesare roughly of the same order of M SUSY , the contributions Eq. (3) and Eq. (4) can beapproximately written as a (cid:101) χ ± µ (cid:39) m µ g π M SUSY tan β ; (7) a (cid:101) χ µ (cid:39) m µ π M SUSY (cid:16) g − g (cid:17) tan β. (8)The detailed dependence of a µ on the five relevant mass parameters tan β is compli-cated. For two-loop corrections, it should be noted that if the squark masses (or massesof the first or third generation slepton) become large, the SUSY contributions to a µ do not decouple but are logarithmically enhanced. Depending on the mass pattern, apositive or negative correction of O(10%) for squark masses in the few TeV region canbe obtained, see Ref. [53]. 3 Constraints on MSSM Explanation of ( g − µ In the following, we numerically calculate ∆ a µ by using the FeynHiggs-2.12.0 [54]package and scan the relevant MSSM parameter space:10 < tan β < , − < M , M < , − < µ < , . < m (cid:101) l L , m (cid:101) l R < . (9)where we have the subscript (cid:96) = e, µ . Due to the small effects on a µ , the slepton trilinearparameters of the first two generation are assumed as A (cid:96) = 0. We also decouple thestau sector by setting the soft stau mass parameters m ˜ τ L = m ˜ τ R = 5 TeV and trilinearparameter A τ = 0. So the stau will not contribute to the trilepton signals in oursimulations. To satisfy the 125 GeV Higgs mass within a 2 GeV deviation, we varythe stop trilinear parameter in the range | A t | < | X t /M S | < FeynHiggs-2.12.0 [54].
In our scan, we also consider the following experimental bounds: • LEP: the direct searches for the slepton and chargino at LEP produce the lowermass limits on the first two generation sleptons and lightest chargino [56]: m (cid:101) l L , m (cid:101) l R >
100 GeV ( l = e, µ ) (10) m (cid:101) χ ± >
105 GeV (11) • Higgs data: the exclusion limits at 95% CL from the experimental cross sec-tions from higgs searches at LEP, Tevatron and LHC are examined by using
HiggsBounds-4.2.1 [57]. • We require the lightest neutralino (cid:101) χ as the LSP and m (cid:101) χ >
30 GeV to be con-sistent with the bound on light MSSM neutralino dark matter [58].In Fig. 2, we present the dependence of ∆ a µ on the masses of neutralinos ( (cid:101) χ , ),charginos ( (cid:101) χ ± , ) and smuons ( (cid:101) µ , ). Within the scan ranges of Eq. 9, We find that the (cid:101) χ ± - (cid:101) ν µ loop dominates over the (cid:101) χ - (cid:101) µ loop. A sizable SUSY contribution to a µ can beobtained, if M , M and µ have the same sign and (cid:101) χ , and (cid:101) χ ± have a sizable higgsino,wino or both components with large tan β . The explanation of ∆ a µ within a 2 σ rangerequires m (cid:101) χ < . m (cid:101) µ < .
03 TeV . However, a higgsino or wino-likeLSP typically cannot satisfy the constraints of the dark matter relic density and areconstrained using data from direct detection experiments. It should be noted that if the higgsino mass parameter µ is large enough, the g − µ scenario is disfavored by the vacuum stability [59], the naturalness [60] and arehighly constrained by the dark matter relic density [61]. a µ and sparticle masses. Green circles satisfythe constraints from LEP and LHC Higgs data. The dashed lines represent the 2 σ band on ∆ a µ given by Eq.(1). Next, we confront the MSSM explanation of ( g − µ with the various dark matterexperiments. We use MicrOmegas-4.2.3 [62] to calculate the dark matter relic densityΩ h and the spin-independent neutralino scattering cross sections with nuclei, denotedas σ SI . It should be noted that the thermal relic abundance of the light higgsino orwino-like neutralino dark matter is typically low due to the large annihilation ratein the early universe. This leads to the standard thermally produced WIMP darkmatter being under-abundant. In order to have the correct relic density, several al-ternatives have been proposed, such as choosing the axion-higgsino admixture as adark matter candidate [63]. So we rescale the scattering cross section σ SI by a factorof (Ω h / Ω P lanck h ), where Ω P lanck h = 0 . ± .
006 is the relic density measured byPlanck satellite [64].In Fig. 3, we show the neutralino dark matter relic density Ω h (left) and the spin-5igure 3: The neutralino dark matter relic density Ω h (left) and the spin-independentneutralino-nucleon scattering cross section σ SI (right). The dashed line is the PLANCKcentral value and the dashed-dotted lines are corresponding 3 σ bands. The exclusionlimits on the σ SI from LUX (2013) [65] (black line), LUX (2016) (magenta line) [67],PandaX-II (red line) [66], and XENON1T (2017) projected [70] (blue line). Greencircles satisfy the LEP, Higgs data and 2 σ bound of ( g − µ (left) and 3 σ upper boundof Ω h , while the black squares further require Ω h within 3 σ range.independent neutralino-nucleon scattering cross section σ SI (right). All samples satisfythe LEP, Higgs data and ( g − µ within 2 σ . In the left panel of Fig. 3, it can be seenthat there are an amount of samples above the 3 σ upper bound of the Planck relicdensity measurement. Those samples are bino-like and annihilate to the SM particlesvery slowly, which leads to an overabundance of dark matter in the universe. Onthe other hand, there are two dips around M Z and M h , respectively, where (cid:101) χ (cid:101) χ canefficiently annihilate through the resonance effect. When the LSP higgsino or winocomponent dominates, the annihilation cross section of (cid:101) χ (cid:101) χ is small so that the relicdensity is less than the 3 σ lower bound of the Planck value. A mixed LSP with a certainhiggsino or wino fraction [61] can be reconciled with the measured relic abundance Ω h within the 3 σ range. In the right panel of Fig. 3, we project the samples that satisfy3 σ upper bound Ω P lanck h on the plane of σ SI versus m (cid:101) χ .A significant portion of the parameter space where the LSP has a sizable higgsinoor wino component is excluded by the recent PandaX-II [66] and LUX data [67]. Thesamples with nearly pure higgsino or wino LSPs escape experimental constraints due tothe large reduction in the DM abundance. We also find some samples with the correctDM relic density (within 3 σ ) and satisfying the LUX constraints. These samples canbe placed in two categories. The smaller portion of samples belong to the so calledMSSM blind-spot region of parameters [68, 69] where the LSP coupling to the Higgs/Zboson is so small that the DM-nucleon scattering cross section is highly suppressed. Thesfermions and other heavy higgs bosons are decoupled for these particular samples. The6igure 4: Exclusion limits from LHC Run-1 dilepton and trilepton events. All samplessatisfy the LEP, Higgs data, 3 σ upper bound of the dark matter relic density, LUX2016 and ( g − µ within the 2 σ . Red squares (Ω h < +3 σ ) and blue diamonds( − σ < Ω h < +3 σ ) are excluded by 2 (cid:96) + (cid:0)(cid:0) E T and 3 (cid:96) + (cid:0)(cid:0) E T events.second case is that the bino-like LSPs coannihilate with the sleptons. The scatteringcross section of the bino-like LSP with the nucleon can be small to avoid the LUXbound. The future XENON1T (2017) experiment [70] will further cover the theseparameter space. Given the great progress of LHC experiments, we recast the results of searching for2 (cid:96) + (cid:0)(cid:0) E T and 3 (cid:96) + (cid:0)(cid:0) E T signatures at LHC-8 TeV. We focus on 8 TeV data. In fact,most of dedicated analyses at 13 TeV are either preliminary [77–79] or do not providestronger constraints in general due to the still small luminosity [80]. The main processescontributing to 2 (cid:96) + (cid:0)(cid:0) E T events can arise from the production of sleptons pair andcharginos: pp → (cid:101) (cid:96) + (cid:101) (cid:96) − , (cid:101) χ +1 (cid:101) χ − (12)with the subsequent decays to leptons: • slepton decay: (cid:101) (cid:96) ± → (cid:96) ± (cid:101) χ ; • chargino decays: (a) through sleptons: (cid:101) χ ± → (cid:101) (cid:96) ± ( → (cid:96) ± (cid:101) χ ) ν (cid:96) , (b) through sneu-trinos: (cid:101) χ ± → (cid:101) ν (cid:96) ( → ν (cid:96) (cid:101) χ ) (cid:96) ± , (c) through W boson: (cid:101) χ ± → W ± ( → (cid:96) ± ν (cid:96) ) (cid:101) χ .7hile 3 (cid:96) + (cid:0)(cid:0) E T events mainly come from the associated production of chargino andneutralino: pp → (cid:101) χ i (cid:101) χ ± j (13)where i = 2 , , j = 1 ,
2. They then decay in two different ways: • through sleptons/sneutrinos: (a) (cid:101) χ i → (cid:96) ∓ (cid:101) (cid:96) ± ( → (cid:96) ± (cid:101) χ ), (cid:101) χ ± j → (cid:101) (cid:96) ± ( → (cid:96) ± (cid:101) χ ) ν (cid:96) , (b) (cid:101) χ i → (cid:96) ∓ (cid:101) (cid:96) ± ( → (cid:96) ± (cid:101) χ ), (cid:101) χ ± j → (cid:101) ν (cid:96) ( → ν (cid:96) (cid:101) χ ) (cid:96) ± ; • through the SM gauge bosons: (cid:101) χ i → Z ( ∗ ) ( → (cid:96) ± (cid:96) ∓ ) (cid:101) χ , (cid:101) χ ± j → W ± ( ∗ ) ( → (cid:96) ± ν (cid:96) ) (cid:101) χ .We use SPheno-3.3.8 [71] to produce the SLHA file to employ in
MadGraph5 aMC@NLO [72] and generate the parton level signal events. Then the events are showered andhadronized by
PYTHIA [73]. The detector effects are included by using the tuned
Delphes [74].
FastJet [75] is used to cluster jets with the anti- k t algorithm [76]. Werecast the ATLAS dilepton [45] and trilepton [47] analyses by using CheckMATE-1.2.2 [81]. We include the NLO correction effects in the production of (cid:101) (cid:96) ± (cid:101) (cid:96) ∓ , (cid:101) χ ± i (cid:101) χ ∓ i and (cid:101) χ i (cid:101) χ ± j productions by multiplying a K -factor 1 . W Z , ZZ and ttV ( V = W, Z ). To estimate the exclusion limit, we define the ratio r = max ( N S,i /S obs,i ), where N S,i and S obs,i are the event numbers of the signal for i -thsignal region and the corresponding observed 95% C.L. upper limit, respectively. Themax is over all signal regions defined in the analysis. We conclude that a sample isexcluded at 95% C.L., if r > m (cid:101) χ ± and m (cid:101) χ . All samples satisfy the LEP, Higgs data, 3 σ upper bound ofrelic density, LUX 2016 and ( g − µ within 2 σ range. Red squares (Ω h < +3 σ ) andblue diamonds ( − σ < Ω h < +3 σ ) are excluded by 2 (cid:96) + (cid:0)(cid:0) E T and 3 (cid:96) + (cid:0)(cid:0) E T events.In Fig. 4, we can see that a portion of samples in (cid:101) χ ± <
710 GeV and (cid:101) χ <
300 GeVcan be excluded. A bulk of samples in the parameter space with (cid:101) χ being higgsinoor wino-like can not be covered because of the small mass difference between (cid:101) χ ± and (cid:101) χ . Such a region may be accessed by the monojet(-like) or the VBF productionat HL-LHC [83–89]. In addition, when (cid:101) χ has a sizable bino component, the limitfrom trilepton events will become weak because of the reduction of cross section of (cid:101) χ ± (cid:101) χ . We also find that the dilepton channel can be complimentary to the trileptonchannel when the latter is suppressed by small neutralino leptonic branching ratios. Animportant factor in the dilepton and trilepton yields is the leptonic branching fractionwhich can vary widely throughout the parameter space. If the slepton is on shell,the chargino two-body decays then dominate and its leptonic branching fraction ismaximized, Br ( (cid:101) χ ± → (cid:101) χ (cid:101) (cid:96) ± ( → (cid:96) ± ν (cid:96) )) max = 2 /
3. When the sneutrino is on-shell and islighter than the corresponding slepton, the channel (cid:101) χ → ν (cid:96) (cid:101) ν (cid:96) will dominate the decaywidth, and the neutralino leptonic branching ratio is suppressed. On the other hand,if the slepton and sneutrino are heavy enough, the decay amplitudes of (cid:101) χ ± and (cid:101) χ are dominated by W and Z boson exchange, respectively, which give (cid:101) χ ± → (cid:101) χ W ± ( → (cid:96) ± ν (cid:96) ) (cid:39) / (cid:101) χ → (cid:101) χ Z ( → (cid:96) ± (cid:96) ∓ ) (cid:39) (cid:101) χ can decay to h (cid:101) χ To hunt for new fundamental particles, a 100 TeV pp collider has been under discussionin recent years, which will allow us to probe the new physics scale roughly an order ofmagnitude higher than we can possibly reach with the LHC [90]. In this section, weestimate the prospects of probing the MSSM explanation of the ( g − µ anomaly byextrapolating the above 8 TeV trilepton analysis to a 100 TeV pp collider. For eachallowed sample above, we use the most sensitive signal region in 8 TeV analysis andsimply assume the same detection efficiency in the 100 TeV analysis. We rescale thesignal ( S ) and background ( B ) events by the following ratio: N
100 TeV = ( σ
100 TeV /σ )(3000 fb − / . − ) N (14)Such a treatment can be considered as a preliminary theoretical estimation. Theoptimized analysis strategy may be achieved once the details of the collider environmentis known. To obtain the expected exclusion limits, we use the following equation, S (cid:112) B + ( β sys B ) ≥ β sys parameterizes the systematic uncertainty. In Fig. 4, we can seethat when β sys = 0 .
1, a majority of samples allowed by ( g − µ in the parameter spacewith (cid:101) χ <
530 GeV and (cid:101) χ ± <
940 GeV can be excluded. Such a range will be extendedto (cid:101) χ <
710 GeV and (cid:101) χ ± <
940 GeV, if β sys = 0.It should be noted that the region that satisfies the DM relic density within the3 σ range through the Z or h resonant annihilation in the blind spots can be coveredby searching for trilepton events from ˜ χ ˜ χ +1 associated production at a 100 TeV pp collider. The samples that are beyond future sensitivity of this trilepton search andthe DM direct detections are either higgsino/wino-like LSPs with the compressed massspectrum or bino-like LSPs co-annihilating with sleptons. Such compressed regionsmay be probed by the monojet(-like) searches at a 100 TeV pp collider [91]. In this work we have studied the prospect of current and future dark matter and colliderexperiments in probing the anomalous magnetic moment of the muon in the MSSM.Under the constraints of Higgs data, dark matter relic density, PandaX-II/LUX-2016experiments and LHC-8 TeV searches for dilepton/trilepton events, we find the Planckdata and the recent PandaX-II/LUX data can significantly exclude the MSSM pa-rameter space satisfying ( g − µ , which will be further excluded by the upcoming9igure 5: Same as Fig. 4, but for expected exclusion limit at a 100 TeV pp colliderwith the luminosity of 3000 fb − . Red squares (Ω h < +3 σ ) and blue diamonds − σ < Ω h < +3 σ are excluded by searching for 3 (cid:96) + MET events. The systematicuncertainty β sys is taken as 0.1 and 0, respectively.XENON-1T (2017) experiment. We also find that most of our surviving samples thatsatisfy DM relic density within 3 σ range through Z or h resonant effect can be cov-ered by searching for trilepton events from ˜ χ ˜ χ +1 associated production a 100 TeV pp collider. While the samples that are beyond the future sensitivity of this trilep-ton search and DM direct detections are either higgsino/wino-like LSPs or bino-likeLSPs co-annihilating with sleptons. Such compressed regions may be probed by themonojet(-like) searches at a future 100 TeV pp collider. Acknowledgement.
This work was partially supported by the Australian ResearchCouncil. LW was also supported in part by the National Natural Science Foundationof China (NNSFC) under grants Nos. 11305049, 11275057.
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