PHYSICAL REVIEW D 97, 055035 (2018)
Closing in on the chargino contribution to the muon g − 2 in the MSSM: Current LHC constraints
† ‡ Kaoru Hagiwara,1,2,* Kai Ma,1,3, and Satyanarayan Mukhopadhyay2, 1KEK Theory Center, Tsukuba 305-0801, Japan 2PITT-PACC, Department of Physics and Astronomy, University of Pittsburgh, Pennsylvania 15260, USA 3Department of Physics, Shaanxi Sci-Tech University, Hanzhong 723000, Shaanxi, China
(Received 18 July 2017; published 26 March 2018)
We revisit the current LHC constraints on the electroweak-ino sector parameters in the minimal supersymmetric standard model (MSSM) that are relevant to explaining the ðg − 2Þμ anomaly via the dominant chargino and muon sneutrino loop. Since the LHC bounds on electroweak-inos become weaker if they decay via an intermediate stau or a tau sneutrino instead of the first two generation sleptons, we perform a detailed analysis of the scenario with a bino as the lightest supersymmetric particle (LSP) and a light stau as the next-to-lightest one (NLSP). Even in this scenario, the chargino sector parameters in the MSSM that can account for the ðg − 2Þμ anomaly within 1σ are already found to be significantly constrained by the 8 TeV LHC and the available subset of the 13 TeV LHC limits. We also estimate the current LHC exclusions in the left-smuon (and/or left-selectron) NLSP scenario from multilepton searches, and further combine the constraints from the multitau and multilepton channels for a mass spectrum in which all three generations of sleptons are lighter than the chargino. In the latter two cases, small corners of the 1σ favored region for ðg − 2Þμ are still allowed at present.
DOI: 10.1103/PhysRevD.97.055035
I. INTRODUCTION In the SM, aμ receives relevant QED, electroweak and The anomalous magnetic moment of the muon, hadronic contributions, with the hadronic contribution being the dominant source of the uncertainty in the aμ ¼ðg − 2Þμ=2, is an accurately measured quantity, theoretical prediction. We refer the reader to Ref. [4] for which, at the same time, is precisely predicted within a detailed recent discussion of the different contributions the standard model (SM) [1]. Consequently, it is an and their associated uncertainty estimates, while for the important testing ground for the SM, since new states at current study, we adopt the following SM prediction the electroweak scale with coupling to muons can poten- for aμ [4]: tially contribute to aμ via quantum corrections. Due to the chirality-flip nature of the magnetic moment operator, the SM −10 aμ ¼ð11 659 182.8 4.9Þ × 10 : ð1:2Þ sensitivity of aμ to new particles coupling to leptons is 2 parametrically higher by a factor of ðmμ=meÞ , than that of Thus, the measured value of aμ is larger than the SM the electron anomalous magnetic moment (ae), despite the latter’s higher precision measurements. prediction by The BNL E821 experiment [2,3] provides the current EXP − SM ¼ð26 1 8 0Þ 10−10 ð Þ best measurement for aμ, which reads aμ aμ . . × ; 1:3
which corresponds to a 3.3σ discrepancy. EXP ¼ð11 659 208 9 6 3Þ 10−10 ð Þ aμ . . × : 1:1 The measurement uncertainty on aμ is expected to be reduced further by two upcoming experiments. The * FermiLab FNAL E989 experiment [5], due to start data [email protected] † [email protected] taking in 2017, is projected to achieve a factor of 4 ‡ [email protected] reduction in the current measurement uncertainty. Using a completely different technology with an ultracold muon Published by the American Physical Society under the terms of beam which does not share the same systematic uncertain- the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to ties associated with the BNL and FNAL experiments, the the author(s) and the published article’s title, journal citation, J-PARC E34 experiment also has a competitive potential and DOI. Funded by SCOAP3. [6]. Therefore, if the current 3.3σ deviation is truly a sign of
2470-0010=2018=97(5)=055035(16) 055035-1 Published by the American Physical Society HAGIWARA, MA, and MUKHOPADHYAY PHYS. REV. D 97, 055035 (2018) physics beyond the SM, these follow-up measurements several relevant LHC search channels. The computational would lead to an enhanced statistical significance for the resources required for this analysis is beyond the scope of present discrepancy. Simultaneously, the error in the our present study. However, as we shall argue in the theoretical prediction within the SM also needs better subsequent sections, a relatively small set of computations control, with the recent progress in estimating the hadronic is sufficient to obtain a broad understanding of the current light-by-light contribution from lattice QCD computations constraints. [7] being promising in this regard. The rest of the sections and the general strategy adopted The minimal supersymmetric standard model (MSSM) in this study are as follows. In Sec. II, we provide a brief contains the necessary ingredients to accommodate the overview of the different contributions to the ðg − 2Þμ in the above discrepancy through contributions from scalar MSSM. In Sec. III we determine, to what extent the current muons, the muon sneutrino, charginos and neutralinos LHC bound on the left-smuon mass parameter can be 0 (the latter two will be referred to as electroweakinos in modified in the presence of χ˜1 and χ˜2 states lighter than the the following). A number of studies have been devoted to μ˜ L. Such a lower bound, in turn, leads to an estimate of the computation of the MSSM contribution to the ðg − 2Þμ the maximum possible chargino mass that can explain the [8–18], the constraints on the relevant parameter space ðg − 2Þμ anomaly within 1σ, depending upon the relevant from a subset of the 8 TeV LHC data [19], as well as the mixing matrices in the chargino and neutralino sectors. þ − 0 role of future e e colliders (such as the ILC) in probing As far as the χ˜1 and χ˜2 searches are concerned, we first the light electroweak MSSM sector that can contribute enumerate in Sec. IV the different possible mass hierarchies 0 to the ðg − 2Þμ [20]. The goal of the present study is to between the χ˜1 =χ˜2 and the sleptons that determine the most revisit the current constraints on the dominant contribution relevant search channel(s). We then proceed to obtain the to ðg − 2Þμ in the MSSM, namely that of the chargino and current LHC constraints on the stau NLSP scenario in ≥ 2τ þ muon-sneutrino loop, in the light of recent data from both Sec. IVA, using the ATLAS search results in the h the 8 and 13 TeV runs of the LHC. ET channel. Translating the LHC simplified model-based The ATLAS and CMS Collaborations have carried out search constraints in this case is somewhat involved, due to multiple sets of analyses in their search for the electroweak the required modeling of the tau jet identification and sector of the MSSM and have practically covered all reconstruction efficiencies. Therefore, we perform a possible decay modes of the lighter chargino (χ˜1 ) and detailed Monte Carlo (MC) analysis, including detector the second lightest neutralino (χ˜0). The search for electro- resolution effects, to recast the 8 and 13 TeV LHC search 2 ≥ 2τ þ weakinos at the LHC is complex due to the multitude of limits in the h ET channel to the constraints in the μ − decay modes available, determined by the mass hierarchies M2 plane. Variation in the LHC bounds due to changes and mixing angles in the chargino, neutralino and slepton in the LSP mass and the stau mixing angle are also sectors. Due to the complexity in interpreting the searches illustrated here. in a multidimensional parameter space, so far, most of the In Sec. IV B, we consider the smuon/selectron NLSP ATLAS and CMS results assume one particular decay scenario and utilize the LHC searches in the trilepton and 0 E mode of the χ˜ and χ˜ to have a 100% branching ratio (BR) T channel to estimate the current LHC limits on the 1 2 electroweakino sector parameters for this mass hierarchy. and interpret the results within a simplified model setting. In Sec. IV C, we then combine the limits from the multitau Implications of the LHC search results for the electroweak search channel and the trilpeton channel to obtain the LHC MSSM sector have also been explored in a number of constraints for the scenario in which all three generation phenomenological studies [21]. sleptons are lighter than the chargino. In Sec. V, we revisit In the most general scenario, the MSSM parameters the 1σ favored region for the ðg − 2Þ , in the light of the relevant for the electroweak searches of our interest in this μ above constraints, paying particular attention to the mass study are the mass parameters for the bino (M1), wino (M2) hierarchies. We provide a summary of our results in and Higgsino (μ), the masses of the lighter (Mτ˜ ) and 1 Sec. VI. Our MC simulation setup for the ≥ 2τ þ E heavier stau (Mτ˜ ), the mixing angle in the stau sector (θτ˜), h T 2 search, and its validation against the ATLAS 8 and 13 TeV the soft masses of the left-smuon (Mμ˜ ) and left-selectron L search results are discussed in the Appendix. (Me˜L ), and the ratio of the vacuum expectation values of the two Higgs doublets (tan β). All of these parameters enter II. MUON (g − 2) IN THE MSSM—A the search for electroweakinos and the left-smuon, and all BRIEF OVERVIEW except the stau and selectron sector parameters also determine the MSSM contribution to the ðg − 2Þμ at the In the MSSM, aμ receives contributions at the one loop one-loop level. Therefore, in order to perform a completely level from the chargino ðχ˜ Þ-muon sneutrino ðν˜μÞ loop and 0 general analysis of the current status of ðg − 2Þμ within the the neutralino ðχ˜ Þ-smuon ðμ˜Þ loop [8–18]. In order to MSSM in the light of LHC searches, we need to perform a understand the dependence of the supersymmetric contri- nine parameter global analysis, including, at the same time, bution to the ðg − 2Þμ on different MSSM parameters, we
055035-2 CLOSING IN ON THE CHARGINO CONTRIBUTION TO … PHYS. REV. D 97, 055035 (2018)
1 G4ðxÞ¼ ½ðx − 1Þðx þ 1Þ − 2x ln x : ð2:2dÞ 2ðx − 1Þ3
Faðx; yÞ and Fbðx; yÞ are defined to be positive for all positive x and y, and Faðx; yÞ is always larger than Fbðx; yÞ for the same arguments [17]. These two contributions are enhanced when the wino and Higgsino are maximally mixed, which requires jM2=μj ∼ Oð1Þ. In the approxima- tion of equal masses for the left-smuon and the muon sneutrino, the arguments of Fa;bðx; yÞ in Eqs. (2.1a) and (2.1b) are the same. Taking into account the difference of a factor of 2, and the fact that Faðx; yÞ >Fbðx; yÞ,we can infer that the positive discrepancy between the data and the SM prediction can be explained with M2μ > 0.We note that the right-smuon is not relevant for these two contributions. μ − ðμ˜ → FIG. 1. Parameter space in the M2 plane where BR L The terms proportional to the bino-Higgsino mixing are μ þ Þ ¼ 300 — — X deviates from one, for Mμ˜ L GeV. The green given by the bino neutral Higgsino left-smuon loop and solid (red dashed) area encloses the region where the neutral Higgsino—bino—right-smuon loop as follows: ðμ˜ → μ þ Þ 0 9ð0 5Þ BR L X < . . . In the region above the green solid line (the white space) BRðμ˜ → μ þ XÞ is greater than 0.9. 2 2 μ β L ˜ ˜ gYmμ M1 tan 2 2 2 2 ΔaμðB − H; μ˜ LÞ¼ FbðM1=mμ˜ ; μ =mμ˜ Þ; 16π2 m4 L L μ˜ L follow the discussion in Ref. [17] and classify the con- ð2:3aÞ tributions in the weak eigenstate basis. In this basis, the leading terms in the mEW=mSUSY expansion (here, mEW 2 2 μ β ˜ ˜ gYmμ M1 tan 2 2 2 2 stands for mμ, m or m and m stands for mμ˜, mν˜ , M1, ΔaμðB − H;μ˜ Þ¼− F ðM =m ;μ =m Þ: W Z SUSY R 2 4 b 1 μ˜ R μ˜ R 8π mμ˜ M2 or μ), are given by five one-loop diagrams, see Fig. 1 R and Eq. (2.6) in Ref. [17]. The dominant contributions ð2:3bÞ proportional to the wino-Higgsino mixing are given by the charged wino—charged Higgsino—muon sneutrino loop In a scenario with a light binolike LSP as considered here, and the neutral wino—neutral Higgsino—left smuon loop these terms are generally much smaller than the ones in as follows: Eq. (2.1), due to the smaller hypercharge coupling [with 2 ¼ 2 2 θ ð2Þ gY g tan W, g being the SU L gauge coupling, and 2 2 μ β 2 θ ¼ 0 23 ˜ ˜ g mμ M2 tan 2 2 2 2 sin W . ], as well as due to small bino-Higgsino ΔaμðW − H; ν˜μÞ¼ F ðM =m ; μ =m Þ; 8π2 4 a 2 ν˜μ ν˜μ mixing. Since the focus of our study is the dominant mν˜μ chargino-muon sneutrino loop contribution in Eq. (2.1a), ð2:1aÞ which does not depend upon the right-smuon mass, for our discussion, we shall assume the right-smuon to be 2 2 μ β ˜ ˜ g mμ M2 tan 2 2 2 2 decoupled. This implies that the contribution from ΔaμðW − H;μ˜ Þ¼− F ðM =m ;μ =m Þ; L 2 4 b 2 μ˜ L μ˜ L 16π mμ˜ Eq. (2.3b) will be negligible. The neutralino contribution L in Eq. (2.3a) is determined by the same set of parameters ð Þ 2:1b that enter Eq. (2.1) as well as M1, and it is positive for M1μ > 0. where, the loop functions in the above expressions are Finally, the contribution proportional to the left-smuon given as and right-smuon mixing is given by the bino—left-smuon —right-smuon loop and reads ð Þ − ð Þ ð Þ¼− G3 x G3 y ð Þ Fa x; y − ; 2:2a 2 2 μ β x y ˜ gYmμ tan 2 2 2 2 ΔaμðB; μ˜ − μ˜ Þ¼ F ðm =M ;m =M Þ: L R 2 3 b μ˜ L 1 μ˜ R 1 8π M1 G4ðxÞ − G4ðyÞ F ðx; yÞ¼− ; ð2:2bÞ ð2:4Þ b x − y
1 This contribution can be enhanced for a large value of ð Þ¼ ½ð − 1Þð − 3Þþ2 ð Þ μ β G3 x 3 x x ln x ; 2:2c tan , with a nontrivial dependence on M1. The LHC 2ðx − 1Þ analyses considered by us do not probe this term, which can
055035-3 HAGIWARA, MA, and MUKHOPADHYAY PHYS. REV. D 97, 055035 (2018) be significant when both the left-smuon and the right- compensated by an enhanced cross section for smuon pair smuon are light, while the charginos can be much heavier. production. We can thus translate the 95% C.L. lower Once again, as for Eq. (2.3b), in the limit of a decoupled bound on the left-smuon mass, 300 GeV in Eq. (3.1),as right-smuon, the contribution of Eq. (2.4) also becomes follows: negligible. In our analysis, we include all five contributions given by Eqs. (2.1)–(2.4). Although we have used the above 287 ðμ˜ → μ þ Þ¼0 9 Mμ˜ L > GeV; for BR L X . ; expressions for Δaμ in the weak eigenstate basis in the Mμ˜ > 220 GeV; for BRðμ˜ → μ þ XÞ¼0.5: ð3:2Þ subsequent sections, we have checked that using the mass L L eigenstate basis expressions do not lead to any significant difference for the decoupled right-smuon scenario. With the above lower bound on the left-scalar muon mass, the requirement of explaining the ðg − 2Þμ anomaly III. LEFT-SMUON MASS LIMITS FROM THE LHC by the chargino contribution would imply an upper bound The ATLAS and CMS collaborations have searched for on the chargino mass. The goal of the subsequent sections scalar muon pair production in the dilepton and missing is thus to determine whether the current LHC searches −1 transverse momentum (ET) channel, and with 20.3 fb of allow for a chargino lighter than that upper bound. As data from the 8 TeV LHC, ATLAS obtained the following mentioned in Sec. II, the MSSM contribution to ðg − 2Þμ 95% C.L. lower bounds [22]: from diagrams involving the right-smuon is not discussed in this study, and we therefore take the right-smuon to be Mμ˜ > 300 GeV; with μ˜ decoupled decoupled from the spectrum. L R Mμ˜ > 230 GeV; with μ˜ decoupled R L IV. CHARGINO MASS LIMITS FROM THE LHC 320 μ˜ ð Þ Mμ˜ ;μ˜ > GeV; for a common L;R mass: 3:1 L R As discussed in the Introduction, in a completely general The quoted lower bounds correspond to the case where MSSM scenario, all the electroweak sector mass and 0 mixing parameters are relevant for interpreting the different BRðμ˜ → μ χ˜ Þ¼1, and M ˜0 ¼ 0 GeV. These limits L;R 1 χ1 LHC searches for the electroweakinos. Thus, performing a are not very sensitive to the choice of Mχ˜0 , unless μ˜ and 1 L;R global analysis of the MSSM parameter space, including 0 χ˜1 are nearly degenerate, and we find that the Mμ˜ > L several different LHC search channels, requires very large 300 GeV bound essentially remains unchanged for Mχ˜0 computational resources and is beyond the scope of 1 values of up to 150 GeV [22]. We note that although smuon the present study. However, as we shall demonstrate in masses lower than around 94 GeV are not probed by the the following, to draw certain broad conclusions on the ATLAS search, such lower mass regions are excluded by ðg − 2Þμ-compatible parameter space allowed by current the LEP2 experiment [23]. constraints, performing a smaller subset of analyses is 0 As long as the χ˜1 and χ˜2 are heavier than μ˜ L, the sufficient. 0 χ˜þχ˜− above assumption of BRðμ˜ → μ χ˜1Þ¼1 remains valid. In the interpretation of different searches for 1 1 and L 0 However, in the MSSM parameter space of our interest, χ˜1 χ˜2 production carried out by the LHC collaborations, the 0 0 there are parameter regions where χ˜1 and χ˜2 can be lighter hierarchies between the χ˜1 =χ˜2 and slepton masses play a μ˜ crucial role. Assuming for simplicity Mμ˜ ¼ M˜ , and for than L , and it is important to determine to what extent the L eL θ above lower bound of 300 GeV can be modified. Taking fixed values of Mτ˜2 and τ˜ (which, as we shall see later, are for example a scenario with M1 ¼ 50 GeV and tan β ¼ 50, less relevant parameters), we then have the following 0 we show by the green (red) shaded area in Fig. 1 the possible mass hierarchies for a binolike LSP (χ˜1) scenario: parameter region in the μ − M2 plane in which the (1) Mμ˜ >Mχ˜ ;Mχ˜0 >Mτ˜ BRðμ˜ → μ þ XÞ < 0.9ð0.5Þ, where X stands for anything L 1 2 1 L (2) Mτ˜ >Mχ˜ ;Mχ˜ 0 >Mμ˜ μ μ˜ 1 1 2 L other than the originating from the decay of L . We find 0 (3) Mχ˜ ;Mχ˜ >Mτ˜1 ;Mμ˜ (with either hierarchy between only a very small region of parameter space where the τ˜ 1 μ˜2 L 1 and L) BRðμ˜ → μ þ XÞ is smaller than 50%. The smuon decay 0 L (4) Mμ˜ ;Mτ˜1 >Mχ˜ ;Mχ˜ . BR to muons here includes contributions from the proc- L 1 2 μ˜ → μ þ χ˜ 0 μ˜ → μ þ χ˜0 In the following sections, we take up each of the above esses L 1, as well as from L 2 [and hierarchies in turn and discuss the constraints on the MSSM μ˜ → ν þ χ˜ subdominantly from L μ 1 , where subsequently 0 parameters of interest from the relevant LHC searches. χ˜1 → W ð→ μ νμÞχ˜1 . As we can see from Fig. 1, the branching to χ˜1 is enhanced only when the χ˜1 is winolike and light. In order to obtain the same event yield that can be A. Scenario-1: Stau NLSP excluded by the smuon search under consideration, the We first focus on the mass hierarchy Mμ˜ > L 0 reduction in BR to final states containing muons can be Mχ˜ ;Mχ˜0 >Mτ˜ >Mχ˜0 . In this scenario, the χ˜ and χ˜ 1 2 1 1 1 2
055035-4 CLOSING IN ON THE CHARGINO CONTRIBUTION TO … PHYS. REV. D 97, 055035 (2018) would decay dominantly via the intermediate τ˜1, the tau- take into account their decays via staus, tau-sneutrino as sneutrino, and τ˜2 (when kinematically accessible), and well as via the SM gauge and Higgs bosons, according to subdominantly through W=Z=h, thereby leading to a the relevant BRs. Finally, the impact of variation in the stau multitau final state. Considering hadronic decays of the mixing, the LSP mass, as well as tan β are also studied. ð − 2Þ tau leptons (τh), the final state of interest is then For the dominant chargino contribution to the g μ, β ≥ 2τh þ ET. We follow the corresponding ATLAS search apart from the left-smuon mass and tan , the two other strategies [24,25] in this regard, on which our constraints important parameters are μ and M2, which also determine are based. Utilizing both the 20.3 fb−1 data from the 8 TeV the chargino and heavier neutralino production and decay LHC run [24] and the 14.8 fb−1 of data from 13 TeV [25], rates. Therefore, we demonstrate the LHC constraints in the the ATLAS Collaboration has looked for χ˜ χ˜0 production μ − M2 parameter plane. In Fig. 2, we show the 95% C.L. 1 2 −1 and interpreted the results within a simplified model setup, excluded region in this plane using the 8 TeV, 20.3 fb −1 ¼ð 0 þ 0 Þ 2 data (green) and 13 TeV, 20.3 fb data (red) from the LHC assuming Mτ˜1;ν˜τ Mχ˜ Mχ˜ = . The LHC8 and LHC13 1 2 ≥ 2τ þ searches lead to the following limit from ATLAS: following the ATLAS search in the h ET channel. The results are shown for the left-smuon decoupled scenario (Mμ˜ ¼ 3 TeV), with M1 ¼ 50 GeV, tan β ¼ 50, Mχ˜ ¼ Mχ˜0 > 700 GeV; for Mχ˜0 ¼ 0 GeV; at 95%C:L: L 1 2 1 ¼ 100 ¼ 300 θ ¼ π 4 Mτ˜1 GeV, Mτ˜2 GeV and τ˜ = . While ð4:1Þ the 8 TeV search covers χ˜1 masses of up to around 400 GeV, this reach is significantly extended with the Interpreting the search with at least two hadronically currently analyzed 13 TeV data set, namely χ˜1 masses of decaying tau leptons and E is considerably involved, as T up to around 600 GeV are now excluded across the μ − M2 the crucial tau jet identification and reconstruction effi- 0 plane. Since for the same mass values, the winolike χ˜ χ˜ ciencies are sensitive to the kinematics of the tau jets, and 1 2 production has a higher cross section than the Higgsino- thus in turn to the mass splittings between the sparticles. like one (by a factor of 4), the exclusion is slightly stronger We therefore study in detail how the LHC bounds translate for high μ and smaller M2 values. The cross section to constraints in the corresponding MSSM parameter space, reduction in the Higgsino-like region is, however, partially taking into account both modifications to the relevant compensated by the associated production of additional production rates and BRs, as well as by performing a Higgsino-like heavier neutralino states of similar mass with Monte Carlo study with a simple detector simulation to a χ˜ . We find that apart from the very light χ˜ =χ˜0 mass capture the possible changes in the detection efficiencies. 1 1 2 The details of our MC simulation framework, the kinematic selection criteria employed, as well as the validation of our simulation framework are discussed in the Appendix. We note here that due to our modeling of the tau reconstruction and identification efficiencies based on a simple detector simulation, our event yields are in general larger than that reported by ATLAS. We therefore rescale our event yields to match the ATLAS numbers by a constant fudge factor each for the 8 and 13 TeV searches, as detailed in the Appendix. In our analysis, we have incorporated certain simple but important effects not captured by the above simplified model study by ATLAS. To begin with, we include all possible electroweakino production modes, namely,
→ χ˜ þχ˜− ¼ 1 2 pp i j ; with i; j ; ; → χ˜ χ˜0 ¼ 1 2 ¼ 1 2 3 4 i j ; with i ; ; and j ; ; ; ; þ − → τ˜ τ˜l ; with k; l ¼ 1; 2: ð4:2Þ k FIG. 2. 95% C.L. exclusion in the μ − M2 plane following the ATLAS search in the ≥ 2τh þ ET channel, using the 8 TeV, Clearly, not all of the production processes have appreci- 20.3 fb−1 data (green) and 13 TeV, 14.8 fb−1 data (red) from the able cross sections for a given set of parameters, but there LHC. The results are shown for a scenario where the left-smuon is are regions of parameter space (for example, for Higgsino- ¼ 3 ¼ 50 β ¼ 50 decoupled (Mμ˜ L TeV), with M1 GeV, tan , like χ˜0 and χ˜0), where including the production of heavier ¼ 100 ¼ 300 θ ¼ π 4 ¼ 2 3 Mτ˜1 GeV, Mτ˜2 GeV and τ˜ = . We set Me˜L charginos and neutralinos is important. We do not make any Mμ˜ L for simplicity, and the right selectron and right smuon, which assumptions about the elctroweakino decay branchings and are not relevant for this study, are taken to be decoupled.
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FIG. 3. 95% C.L. exclusion in the μ − M2 plane for different FIG. 4. 95% C.L. LHC13 exclusion contours for different values of the LSP mass, M1 ¼ 10 GeV (blue-dashed line) and values of the mixing angle in the stau sector. The red (solid), M1 ¼ 50 GeV (red solid line). The exclusion contours are based green (dashed) and blue (dot-dashed) lines correspond to the on the 13 TeV, 14.8 fb−1 data from the LHC, following the lighter stau being maximally mixed, right-stau and left-stau ATLAS search in the ≥ 2τh þ ET channel. The results are shown respectively. The other relevant parameters are fixed as in Fig. 2. ¼ 3 for a scenario where the left-smuon is decoupled (Mμ˜ L TeV), β ¼ 50 ¼ 100 ¼ 300 with tan , Mτ˜1 GeV, Mτ˜2 GeV and θ ¼ π 4 ¼ This reduction in the BR to tau-rich final states is also τ˜ = .WesetMe˜L Mμ˜ L for simplicity, and the right selectron and right smuon, which are not relevant for this study, applicable to the maximally mixed scenario, as decays are taken to be decoupled. through the sneutrino state are still accessible, albeit with a slightly smaller branching (due to a somewhat higher mass of the sneutrino compared to the τ˜1). When the lighter stau regions with low μ and high M2 values, the 13 TeV search is a right-stau with the left-stau mass set at 3 TeV, the also covers the region excluded by the 8 TeVanalysis. With sneutrino is not kinematically accessible, thereby enhanc- 0 this in mind, in subsequent figures, we shall only show the ing the BR of χ˜2 to tau’s, and hence increasing the 13 TeV exclusion contours. exclusion reach in the winolike region (M2 < μ). In the In order to demonstrate the impact of change in kin- Higgsino-like region (μ
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Mχ˜ ¼ Mχ˜0 > 1000 GeV; for Mχ˜0 ¼ 0 GeV; at 95% C:L: (blue dashed curve), for Mμ˜ ˜ ¼ 300 GeV, with the 1 2 1 L;eL τ˜ ; τ˜ ; e˜ and μ˜ decoupled (their masses are fixed at ð4:3Þ L R R R 3 TeV). The results are shown for M1 ¼ 50 GeV and 0 tan β ¼ 50. The smuon mass is set at its lower bound from For this ATLAS analysis, the χ˜ and χ˜ are assumed to be 1 2 8 TeV LHC searches, as discussed in Sec. III, which is valid winolike, while the χ˜0 is taken to be binolike. These limits are 1 in almost the entire parameter space except for very small expected to become slightly weaker in the Higgsino-like or M2 values, where it can be slightly lower. χ˜ χ˜0 wino-Higgsino mixed region for 1 = 2. We observe two branches in the blue-dashed exclusion Unlike in the stau-NLSP scenario discussed in the 0 contour in Fig. 5. For the region where the χ˜1 =χ˜2 is lighter previous section, we do not perform a detailed MC analysis than μ˜ L=e˜L, they decay via the SM gauge and Higgs of the kinematic selection efficiencies and detector effects bosons, thereby reducing the BR to the trilepton final state. for this mass hierarchy. This should not lead to significant 0 Therefore, only smaller χ˜1 =χ˜2 mass values are accessible to modifications to the derived constraints, since in the very the trilepton search when only the gauge/Higgs boson clean trilepton and ET channel, the final state recon- decay modes are open. For Mχ˜ ð¼ Mχ˜0 Þ larger than struction and detector resolution effects are expected to 1 2 be small, as long as we do not encounter degeneracies 300 GeV, decays through intermediate sleptons open up, between the electroweakino, slepton and bino mass param- and higher electroweakino masses can be probed as well. However, for the latter case, the bounds are weaker for eters. For example, though the above lower bound is quoted 0 Higgsino-like χ˜1 =χ˜2 region compared to the winolike one, for Mχ˜0 ¼ 0 GeV, it remains essentially unchanged in the 1 0 as only the wino component of the χ˜1 =χ˜2 has significant range 0 GeV ≤ Mχ˜0 ≲ 500 GeV [27]. Similarly, though 1 coupling to the left-smuon or the muon-sneutrino. the smuon/selectron mass for the simplified model based search is assumed to be given by Mμ˜ ˜ ¼ðMχ˜ 0 þMχ˜ 0 Þ=2,it L;eL 1 2 C. Scenario-3: All three generation sleptons has been shown in Ref. [28] that away from the degenerate lighter than chargino mass region, this mass gap does not affect the limits We next study the mass hierarchy: Mχ˜ ;Mχ˜0 > significantly. Therefore, for our discussion in this section, 1 2 Mτ˜ ;Mμ˜ ˜ >Mχ˜0 (with either hierarchy between τ˜1 and we shall only consider the production cross section and 1 L;eL 1 0 μ˜ ), which presents us with a scenario where both the ≥ decay BR modifications of χ˜ and χ˜ in the μ − M2 plane. L 1 2 2τ þ 3l þ In Fig. 5, we show our estimate of the current 13 TeV h ET and the ET searches described in the exclusions in the μ − M2 plane using the trilepton channel previous two sections become important. Let us first consider how the bounds shown in Fig. 2 get modified in the presence of a light left-smuon kinematically acces- 0 sible in χ˜1 =χ˜2 decays. In Fig. 6, we show the LHC13
FIG. 5. Estimated 95% C.L. exclusion region in the μ − M2 plane using the 13 TeV, 13.3 fb−1 data (blue dashed line) from the LHC, following the ATLAS search in the 3l þ ET channel. The results are shown for the scenario with both the staus decoupled FIG. 6. 95% C.L. LHC13 exclusion contours, using the ≥ ¼ ¼ 3 ¼ 50 β ¼ 50 2τ þ μ˜ (Mτ˜L Mτ˜R TeV), with M1 GeV, tan and h ET search only, for different L mass values. The red ¼ 300 ¼ (solid) and blue (dashed) lines correspond to Mμ˜ ¼ 3000 GeV Mμ˜ L GeV. We set Me˜L Mμ˜ L for simplicity, and the L ¼ 300 ¼ right selectron and right smuon, which are not relevant for this and Mμ˜ L GeV respectively. We set Me˜L Mμ˜ L for study, are taken to be decoupled. simplicity.
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0 the 8 TeV LHC run (the 13 TeV analysis for these χ˜1 =χ˜2 decay modes are not yet published by the LHC Collaborations), the ATLAS Collaboration obtains the following limit using a combination of dilepton and trilepton searches [22]:
Mχ˜ ¼ Mχ˜0 > 415 GeV; 1 2
for Mχ˜0 ¼ 0 GeV; at 95% C:L:ðWZ modeÞ: ð4:4Þ 1
In deriving the above limit, it is assumed that BRðχ˜1 → 0 0 0 W χ˜1Þ¼1 and BRðχ˜2 → Zχ˜1Þ¼1. If on the other hand, one adopts a simplified model in which BRðχ˜1 → 0 0 0 W χ˜1Þ¼1 and BRðχ˜2 → hχ˜1Þ¼1, the above bound becomes considerably weaker, and a combination of search results targeting different Higgs decay modes yields the ≥ FIG. 7. 95% C.L. LHC13 exclusion contours, using the following bound from ATLAS (using 20.3 fb−1 of data 2τ þ E search (red solid) and the 3l þ E search (blue h T T from the 8 TeV LHC run) [29]: dashed), in a scenario where both τ˜1 and μ˜ L can be lighter than 0 the χ˜1 =χ˜2. The results are shown for tan β ¼ 50, M1 ¼ 50 GeV, Mμ˜ ¼ 300 GeV, Mτ˜ ¼ 100 GeV, Mτ˜ ¼ 300 GeV and L 1 2 Mχ˜ ¼ Mχ˜0 > 250 GeV; θ ¼ π 4 ¼ 1 2 τ˜ = . We set Me˜L Mμ˜ L for simplicity. For most regions for Mχ˜ 0 ¼ 0 GeV; at 95% C:L:ðWh modeÞ: ð4:5Þ of the parameter space, the two searches are found to be 1 complementary.
0 0 0 The assumption of either BRðχ˜2 → Zχ˜1Þ¼1 or BRðχ˜2 → ≥ 2τ þ 0 exclusion contours, using the h ET search only, for hχ˜1Þ¼1 does not hold in most regions of the μ − M2 two different μ˜ mass values. The red (solid) and blue 0 0 0 L parameter space, and a combination of χ˜2 → Zχ˜1 and χ˜2 → (dashed) lines correspond to Mμ˜ ¼ 3000 GeV and Mμ˜ ¼ 0 L L hχ˜ decays take place depending upon the Higgsino 300 1 GeV respectively, while the other relevant parameters component of χ˜0 and χ˜0. We do not study this mass are the same as in Fig. 2. It is observed that for the winolike 2 1 0 hierarchy in this paper, and ideally a statistical combination χ˜ and χ˜ region, there is a decrease in the reach of the tau 0 0 0 1 2 Zχ˜ hχ˜ χ˜ χ˜ χ˜0 of the searches targeting the 1 and 1 decay modes of 2 search channel, since the winolike 1 = 2 will also have a should be performed in order to determine the current best significant decay branching to smuon and muon sneutrino constraints in the μ − M2 plane for this scenario. We note states, thereby reducing the BR to the multitau final state. that although this scenario leads to the weakest bounds on The region in which the ≥ 2τh þ ET search loses power, 3l þ the electroweakinos, making the sleptons, especially the the ET search becomes sensitive. In general, a left-smuon heavier, is not favorable to the chargino con- statistical combination of both these search channels should tribution to the ðg − 2Þμ. However, it is expected that a part lead to the strongest constraints in the μ − M2 plane. There of the ðg − 2Þ favored parameter space would be allowed is, however, a degree of complementarity to the power of μ these two searches. We demonstrate this fact in Fig. 7, which for this mass hierarchy, even after the 8 TeV LHC con- straints are taken into account. shows that we can separate different areas in the μ − M2 plane in which one of the two searches has a higher exclusion power. For reasons discussed above, in the lower μ and higher V. IMPACT OF LHC CONSTRAINTS ON THE M2 region, the multitau channel is stronger, while in the ðg − 2Þμ FAVORED PARAMETER SPACE lower M2 and higher μ region, the multilepton channel dominates. Along the diagonal, with μ ∼ M2, both searches We are now in a position to discuss the impact of the become less powerful, especially for M ˜ > 500 GeV. LHC constraints on the MSSM parameter space in which χ1 the ðg − 2Þμ anomaly can be explained within 1σ.As emphasized in Sec. II, we focus on the right-smuon D. Scenario-4: All sleptons heavier than chargino decoupled scenario, where the dominant contribution to Finally, we comment on the mass hierarchy in which Δaμ comes from the chargino-muon sneutrino loop. For our Mμ˜ ;Mτ˜ >Mχ˜ ;Mχ˜0 >Mχ˜0 . Since in this case all the L 1 1 2 1 numerical analysis, we have included all the relevant χ˜ χ˜0 Δ sleptons are heavier than 1 and 2, the latter can only chargino and neutralino contributions to aμ, with Mμ˜ R decay via W=Z=h bosons. Based on 20.3 fb−1 of data from fixed at 3 TeV.
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that for tan β values smaller than 50, the current LHC constraints on the ðg − 2Þμ favored region are even stronger. As discussed in Sec. IVA, the variation in M1 does not affect the LHC search constraints, and its impact on Δaμ through the neutralino-smuon loop is also small in the μ˜ R decoupled scenario. Furthermore, as explained in Sec. IVA, with a maximally mixed τ˜1, the LHC constraints are only slightly weaker compared to the right-stau NLSP case, while the constraints are very similar with a left-stau NLSP. Therefore, changing the stau mixing would not relax the constraints compared to the red solid line in Fig. 8.As far as the τ˜1 mass is concerned, within the assumptions of the above mass hierarchy, its impact should be minimal as 0 well, unless we encounter degeneracies between the χ˜1 =χ˜2 and τ˜1 mass values. Therefore, we can conclude that in the stau NLSP scenario, with the mass hierarchy, Mμ˜ >Mχ˜ ;Mχ˜0 >Mτ˜ > L 1 2 1 FIG. 8. Current 95% C.L. LHC constraints on the ðg − 2Þμ Mχ˜0 , the current 13 TeV LHC constraints already disfavor favored parameter region in the μ − M2 plane, for the mass 1 0 0 most of the parameter space in which the ðg − 2Þμ anomaly hierarchy Mμ˜ ;Mτ˜1 >Mχ˜ ;Mχ˜ >Mχ˜ . In the blue (violet) L 1 2 1 1σ shaded region, the ðg − 2Þμ anomaly can be explained at 1σ, can be accommodated within through the chargino ¼ 500 ð800 Þ contribution. with the choice Mμ˜ L GeV GeV . The values of other relevant MSSM parameters are fixed as in Fig. 2. B. Scenario-2: Selectron/smuon NLSP
A. Scenario-1: Stau NLSP We now consider the second mass hierarchy: Mτ˜1 > M ˜ ;M˜0 >Mμ˜ ;M˜ >M˜0 . Since the μ˜ is the NLSP in χ1 χ2 L eL χ1 L We start with the first mass hierarchy: Mμ˜ L > Mχ˜ ;Mχ˜0 >Mτ˜ >Mχ˜0 . In Fig. 8, we show two represen- this scenario, for our discussion, we choose the lowest 1 2 1 1 value of Mμ˜ allowed by the LHC8 search for left-smuons tative scenarios for the ðg − 2Þμ favored region at 1σ, with L described in Sec. III. In Fig. 9, we show the ðg − 2Þμ Mμ˜ ¼ 500 GeV (blue shaded) and 800 GeV (violet L 1σ ¼ 300 ¼ 500 favored region at with Mμ˜ L GeV (brown shaded shaded). As we can see in Fig. 8, for Mμ˜ L GeV, the above mass hierarchy assumption is not valid in a small region of the parameter space, in which Mμ˜
055035-9 HAGIWARA, MA, and MUKHOPADHYAY PHYS. REV. D 97, 055035 (2018) area), with tan β ¼ 50. As we can see from this figure, in a (brown shaded), with tan β ¼ 50. For discussing the substantial region of the μ − M2 plane, M ˜ is lower than LHC constraints, we choose, as in Fig. 7, Mτ˜ ¼ 100 GeV; χ1 1 ¼ 300 θ ¼ π 4 β ¼ 50 ¼ 300 GeV, which does not satisfy the hierarchy assumption Mτ˜2 GeV and τ˜ = , with tan and M1 50 of Mχ˜ ;Mχ˜0 >Mμ˜ ;Me˜ . However, the 3l þ ET search GeV (this choice of parameter values is motivated by 1 2 L L χ˜0 μ˜ results shown in this figure (blue dashed line) were the abundance for relic 1 DM). Thus, both the L and the τ˜ obtained with Mμ˜ ¼ 300 GeV in Sec. IV B, and therefore 1 masses are fixed close to their current lower limits (for L τ˜ the constraints shown remain valid in the entire region of the case of 1, the strongest bound from the LEP experi- the parameter space. In the region with Mχ˜ ;Mχ˜0 < ments is about 90 GeV [23,26]). Once again, as in the 1 2 ¼ 300 0 previous scenario, though taking Mμ˜ L GeV may Mμ˜ ;Me˜ , the trilepton events originate from χ˜1 =χ˜2 decays L L violate the hierarchy of Mχ˜ ;Mχ˜0 >Mμ˜ , the constraints to W =Z bosons. As we see from Fig. 9, even though the 1 2 L ≥ 2τ þ trilepton search is very powerful and strongly excludes shown in Fig. 10, namely that from the h ET (red solid line) and 3l þ E (blue dashed line) searches were most of the 1σ favored parameter space for ðg − 2Þμ with T 0 derived in Sec. IV C for the same value of Mμ˜ , and this mass hierarchy, in the Higgsino-like χ˜1 =χ˜2 region, we L can find a small window allowed by the current LHC search therefore they remain valid in the entire parameter space. As discussed in Sec. IV C, both the ≥ 2τh þ ET and the constraints. As discussed earlier, this is because of the 3l þ reduced coupling of a left-smuon or left-selectron to a ET searches provide important complementary con- 0 straints for this mass hierarchy, and taken together, they χ˜ =χ˜ , when the latter is mostly a Higgsino-like state. In 1 2 exclude bulk of the 1σ favored parameter region for the currently allowed region, the Higgsino mass parameter ðg − 2Þμ, with Mμ˜ ¼ 300 GeV. A small window remains (μ) is found to be around 500 GeV, with the wino- L allowed when M2 ∼ μ and 500 GeV
FIG. 10. Current 95% C.L. LHC constraints on the ðg − 2Þμ favored parameter region in the μ − M2 plane, for the mass hierarchy Mχ˜ ;Mχ˜0 >Mτ˜ ;Mμ˜ ˜ >Mχ˜0. In the brown shaded 1 2 1 L;eL 1 region, the ðg − 2Þμ anomaly can be explained at 1σ, with the FIG. 11. Parameter region in the μ − M2 plane in which the ¼ 300 ðg − 2Þ anomaly can be explained within 1σ: for Mμ˜ ¼ choice Mμ˜ L GeV. The values of other relevant MSSM μ L 300 ¼ 220 parameters are fixed as in Fig. 7. GeV (brown shaded) and Mμ˜ L GeV (green shaded).
055035-10 CLOSING IN ON THE CHARGINO CONTRIBUTION TO … PHYS. REV. D 97, 055035 (2018) the difference in the 1σ allowed regions for ðg − 2Þμ for the (μ − M2) plane. Particular attention is paid to the possible μ˜ ¼ 300 dependence of the LHC constraints on the LSP mass and two choices of L mass, Mμ˜ L GeV (brown shaded) and 220 GeV (green shaded). Focusing on the region below the mixing angle in the stau sector. It is observed that while the gray dashed line along which Mχ˜ < 300 GeV, we can the LSP mass does not play any significant role (unless we 1 encounter degeneracies between the sparticle masses), the see from this figure that the additional ðg − 2Þ favored μ bounds are weaker for a left-stau or maximally mixed stau parameter space gained by lowering Mμ˜ is for μ > L NLSP scenario, compared to a right-stau NLSP case. We 1500 300 GeV and M2 < GeV, where the lighter chargino note that the strongly mixed stau NLSP with a binolike LSP is winolike. However, from Figs. 9 and 10, we find that this is motivated by the DM relic density requirement [for additional parameter space is excluded by the current LHC ≥ Oð30 Þ MB˜ GeV ], or for accommodating the Galactic search results on electroweakinos. Therefore, the possible center gamma ray excess (for M ˜ ∼ 10 GeV). μ˜ B lowering of the L mass limit does not have any impact on While the LHC constraints are found to be slightly our conclusions. weaker in a region where the χ˜ =χ˜ 0 are Higgsino-like, due μ 1 2 We also note in passing that for very high M2 and low to lower values of χ˜ χ˜0 production rates, this difference is χ˜ 1 2 values, the smuon mass bound cannot be relaxed, as the 1 reduced by the opening of new substantial production μ˜ χ˜ 0 is Higgsino-like here, and thus the L cannot decay to a 1 . modes in the Higgsino-like region, such as that of χ˜ χ˜ . ð − 2Þ 1 3 Therefore, the additional g μ allowed parameter space With the left-smuon heavier than the χ˜ =χ˜0 for this mass 1700 μ 300 1 2 with M2 > GeV and < GeV in Fig. 11 is not hierarchy, we find that the ðg − 2Þμ favored region at 1σ is viable either. severely constrained even in the stau NLSP scenario, especially in the light of the recent 13 TeV data. Such VI. SUMMARY strong constraints are obtained on setting tan β values as high as 50, and the LHC constraints on the ðg − 2Þμ favored In this study, we revisit the current LHC constraints on parameter region become stronger for lower values of tan β. the ðg − 2Þ favored parameter space in the MSSM, μ When the left-smuon (and/or left-selectron) is the NLSP, focusing on the scenario where the chargino-muon sneu- we have the mass hierarchy Mτ˜ >Mχ˜ ;Mχ˜ 0 >Mμ˜ ; trino loop contribution largely accounts for the discrepancy. 1 1 2 L M˜ >Mχ˜0 . In such a case, the LHC constraints come Since the chargino-muon sneutrino loop leads to the eL 1 from the trilepton and E search channel, for which the dominant contribution to ðg − 2Þμ in most of the MSSM T parameter space (except in the region in which the left- and limits on the electroweakino sector are generically stronger, and using the recently analyzed 13 TeV LHC data, ATLAS right-scalar muons are light and there is a large mixing χ˜ χ˜0 between them), it is crucial to thoroughly probe this excludes 1 = 2 masses of up to 1 TeV. We estimate the μ − scenario at the LHC. current constraints in the M2 plane for this mass The most relevant LHC searches in this context are that hierarchy as well, taking into account the modification χ˜ χ˜0 of the left-smuon and electroweakinos, for which we to the 1 2 production cross section and the corresponding include constraints from both the 8 TeV (with 20.3 fb−1 decay BRs, in comparison to the simplified model based data) and 13 TeV (with up to 14.8 fb−1 data) LHC runs. In ATLAS study. With a left-smuon mass close to its current interpreting the LHC constraints from the above searches in lower bound of around 300 GeV, we find that a small region of the ðg − 2Þμ favored parameter space at 1σ is still viable the context of the ðg − 2Þμ, we organize our study by paying particular attention to the different possible mass in view of the current LHC13 exclusion estimate for this mass hierarchy. In the allowed region, the Higgsino mass hierarchies between the electroweakinos and the three μ generations of sleptons. parameter ( ) is found to be around 500 GeV, with the Since the LHC bounds on electroweakinos become wino-mass parameter (M2) taking values higher than weaker if they decay via an intermediate stau or a tau about 1 TeV, and the chargino mass falls in the range 300 GeV
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0 stronger limits due to the higher decay rate of χ˜1 =χ˜2 via an constraints, but also probe regions of parameter space yet intermediate stau, whereas for the winolike region unexplored, which still remain promising from the point of ð − 2Þ (μ ≫ M2) the 3l þ ET search leads to more stringent view of explaining the g μ anomaly within the MSSM constraints. In the intermediate region, where the χ˜1 and framework. 0 the χ˜2 are nearly a maximal mixture of wino and Higgsino states (μ ∼ M2), a small window of parameter space is ACKNOWLEDGMENTS found to be allowed based on the current constraints, in S. M. would like to thank Yasuhito Sakaki for help with which the ðg − 2Þ anomaly can still be explained within μ MATHEMATICA graphics. K. H. and S. M. are supported in 1σ, with 500 GeV 055035-12 CLOSING IN ON THE CHARGINO CONTRIBUTION TO … PHYS. REV. D 97, 055035 (2018) −1 FIG. 12. Updated LHC constraints on the ðg − 2Þμ favored parameter space using 36.1 fb of data in the multilepton þ ET search channel at the 13 TeV LHC [30]: for the selectron and/or smuon NLSP scenario (left column) and when all three generation sleptons are 0 lighter than χ˜1 and χ˜2 (right column). See text in the note added section for details. In the scenario with all three generation sleptons lighter algorithm [38] with radius parameter R ¼ 0.4 using χ˜ χ˜ 0 ¼ 500 FastJet [39]. We employ the CTEQ6L1 [40,41] parton than 1 and 2, we find that with Mμ˜ L GeV, the ðg − 2Þμ favored parameter region is now covered almost distribution functions, and the factorization and renormal- entirely by the 13 TeV LHC search in the ≥ 2τ þ E ization scales have been fixed at the default event-by-event h T MadGraph5 channel, as seen in Fig. 12, right column. We note that even choice of . though the ≥ 2τ þ E channel search results have also been The 8 TeV ATLAS search is divided into four different h T χ˜ χ˜0 χ˜ χ˜ updated by the ATLAS Collaboration including up to signal regions, primarily targeting the 1 2; 1 1 and −1 direct stau pair production processes. The 8 TeV results, 36.1 fb data [31], the small improvements in the χ˜1 and 0 however, are not sensitive to direct stau pair production χ˜ mass limits do not impact our conclusions on the ðg − 2Þ 2 μ exclusively [24], and most of the current sensitivity results favored parameter space, which are already disfavored in our from electroweakino pair production. The kinematic selec- analyses using the 14.8 fb−1 data set, following Ref. [25]. tion criteria used are as described in Ref. [24], see in particular the discussion in Secs. 6 and 7, with the APPENDIX: MC SIMULATION: SETUP AND definition of different signal regions in Table 1. For the VALIDATION three different MSSM reference points and the phenom- In this Appendix, we provide the details of our enological MSSM (pMSSM) parameter space in the Higgsino-wino mass (μ − M2) plane studied by ATLAS, Monte Carlo (MC) simulation framework for the χ˜1 and 0 we find that our event yields for the signal process are χ˜2 searches in the ≥ 2τh þ ET channel. We follow the ATLAS analyses in this regard, details of which can be somewhat larger than the numbers obtained by ATLAS. A found in Ref. [24] for the search using 20.3 fb−1 of data very likely origin of this difference is the simple modeling from the 8 TeV LHC, and in Ref. [25] for the search with of tau-jet identification and reconstruction efficiencies in 14.8 fb−1 of data from the 13 TeV run. our MC simulation. It is, however, encouraging that we can For our MC simulation of a general MSSM scenario, we approximately match the ATLAS results by multiplying our obtain the MSSM mass spectra from weak scale inputs of event yields with a constant fudge factor. After including an – the soft SUSY breaking parameters using SUSPECT2 [32]. average K-factor in the range of 1.2 1.3 to take into We then compute the decay branching ratios (BR) of the account the effects of higher order corrections to our supersymmetric particles using SDECAY [33], with the help leading order cross section computation (we compute the Prospino of the SUSY-HIT package [34]. The resulting mass spectra next-to-leading order cross sections using and decay BRs are used as inputs to MadGraph5 [35] for [42]), for the 8 TeV analysis, this fudge factor is found generating parton level events for electroweakino and stau to be around 0.4. In Fig. 13, we compare our 95% C.L. pair production, which are then passed onto PYTHIA6 [36] exclusion (blue solid contour) with the ATLAS pMSSM for including the effects of parton shower, hadronization exclusion (green dashed contour) in the μ − M2 plane, for ¼ 50 ¼ 90 and underlying events. We use DELPHES2 [37] for the parameter choices M1 GeV, Mτ˜1 GeV and including the effects of object reconstruction and detector tan β ¼ 50. For this analysis, the τ˜1 is taken to be a right- resolution. Jets are reconstructed using the anti-kT stau (see Fig. 10 in Ref. [24] for the corresponding ATLAS 055035-13 HAGIWARA, MA, and MUKHOPADHYAY PHYS. REV. D 97, 055035 (2018) FIG. 13. Comparison of the 95% C.L. exclusion contours FIG. 14. Comparison of the 95% C.L. exclusion contours obtained by our MC simulation (blue solid contour) with the obtained by our MC simulation (blue solid contour) with the corresponding ATLAS exclusion (green dashed contour) in a corresponding ATLAS pMSSM exclusion (green dashed con- 0 −1 −1 simplified model study of χ˜ χ˜ pair production, using 14.8 fb tour) in the μ − M2 plane, using 20.3 fb of data from the 8 TeV 1 2 ¼ 50 ¼ 90 of data from the 13 TeV LHC. The tau-slepton and tau-sneutrino LHC, for the parameter choices M1 GeV, Mτ˜1 GeV masses are set to be ðMχ˜ þ Mχ˜0 Þ=2, with Mχ˜ ¼ Mχ˜0 . See text and tan β ¼ 50. For this analysis, the τ˜1 is taken to be a right-stau. 1 1 1 2 See text for details. for details. result). As we can see in this figure, our results are broadly was necessary to normalize our signal yields by a fudge in agreement with the ATLAS limits, after the above fudge factor of around 0.14, after taking the K-factor correction factor is taken into account. In deriving the 8 TeVexclusion into account. This fudge factor is somewhat smaller than contours discussed in other sections of this study, we have the one required for the 8 TeVanalysis. This is possibly due adopted the same methodology. to the dependence of the tau reconstruction and identifi- For the 13 TeV LHC study, we follow the recent ATLAS cation efficiencies on the tau-jet kinematics, which can be note [25], see in particular Secs. 4 and 5 as well as Table 1 quite different depending upon the center of mass energy, in Ref. [25] for details on the object reconstruction, event and the difference in the kinematic selection criteria selection and the definition of the different signal regions. adopted. Once again, after taking the fudge factor into For the 13 TeV analysis, so far, ATLAS has reported their account, the overall agreement of our MC simulation with results in terms of simplified models, and the correspond- the ATLAS results is found to be reasonably good, χ˜ χ˜0 ing interpretations for the pMSSM parameter space is not especially in the intermediate 1 = 2 mass region, with yet available. We therefore compare our results with the our bounds being slightly weaker in the high mass region, 0 1 ATLAS limits on χ˜1 χ˜2 pair production, where the χ˜1 and and slightly stronger in the lower mass region. 0 χ˜2 decay via an intermediate tau-slepton and tau-sneutrino 1 of mass ðMχ˜ þ Mχ˜0 Þ=2, with Mχ˜ ¼ Mχ˜0 . We compare the 1 1 1 2 Without taking into account the fudge factor, the obtained 95% C.L. exclusion contours based on our MC simulation constraints from the multitau and missing transverse momentum channel would be stronger. However, since the ðg − 2Þμ favored (blue solid) with the corresponding ATLAS results (green parameter region where this search channel is important is dashed) in Fig. 14. As in the 8 TeV analysis, we found our already disfavored in our analyses even with the fudge factor, event yields to be larger than the ATLAS numbers, and it our conclusions would remain the same. [1] For a review, see, for example, F. Jegerlehner and moment measurement at BNL, Phys. Rev. D 73, 072003 A. Nyffeler, The Muon g − 2, Phys. Rep. 477, 1 (2009). (2006). [2] G. W. Bennett et al. (Muon g-2 Collaboration), Final [3] B. L. Roberts, Status of the Fermilab muon (g − 2) experi- report of the muon E821 anomalous magnetic ment, Chin. Phys. C 34, 741 (2010). 055035-14 CLOSING IN ON THE CHARGINO CONTRIBUTION TO … PHYS. REV. D 97, 055035 (2018) [4] K. Hagiwara, R. Liao, A. D. Martin, D. Nomura, and T. 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