PHYSICAL REVIEW D 97, 115002 (2018)
Muon g − 2 and dark matter suggest nonuniversal gaugino masses: SUð5Þ × A4 case study at the LHC
† ‡ Alexander S. Belyaev,1,2,* Steve F. King,1, and Patrick B. Schaefers1, 1School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom 2Particle Physics Department, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
(Received 25 January 2018; published 5 June 2018)
We argue that in order to account for the muon anomalous magnetic moment g − 2, dark matter and LHC data, nonuniversal gaugino masses Mi at the high scale are required in the framework of the minimal supersymmetric standard model. We also need a right-handed smuon μ˜ R with a mass around 100 GeV, 0 evading LHC searches due to the proximity of a neutralino χ˜1 several GeV lighter which allows successful dark matter. We discuss such a scenario in the framework of an SUð5Þ grand unified theory (GUT) ¯ combined with A4 family symmetry, where the three 5 representations form a single triplet of A4 with a unified soft mass mF, while the three 10 representations are singlets of A4 with independent soft masses mT1;mT2;mT3. Although mT2 (and hence μ˜ R) may be light, the muon g − 2 and relic density also requires light M1 ≃ 250 GeV, which is incompatible with universal gaugino masses due to LHC constraints on M2 and M3 arising from gaugino searches. After showing that universal gaugino masses M1=2 at the GUT scale are excluded by gluino searches, we provide a series of benchmarks which show that while M1 ¼ M2 ≪ M3 is in tension with 8 and 13 TeV LHC data, M1
DOI: 10.1103/PhysRevD.97.115002
I. INTRODUCTION An interesting possible signature of BSM physics is − 2 ¼ The minimal supersymmetric standard model (MSSM) the muon g or anomalous magnetic moment aμ ð − 2Þ 2 remains an attractive candidate for physics beyond the g μ= which differs from its standard model (SM) standard model (BSM) even in the absence of any signal at prediction by amount [4], the Large Hadron Collider (LHC). Despite the limits from −10 direct and indirect searches for dark matter (DM), the Δaμ ≡ aμðexpÞ − aμðSMÞ¼ð28.8 8.0Þ × 10 : ð1Þ lightest neutralino [1], whose stability is enforced by R parity, remains a prime candidate for the weakly interacting Although it is possible to account for the muon g − 2 within massive particle (WIMP). a supersymmetric framework [5–38], it is well known that it There are several constraints from the LHC that restrict cannot be achieved in the MSSM with universal soft masses the parameter space of the MSSM, in particular, the consistent with the above requirements, and therefore, requirement of a 125 GeV Higgs boson and stringent some degree of nonuniversality is required. For example, limits on the gluino mass [2,3]. nonuniversal gaugino masses have been shown to lead to an acceptable muon g − 2 [25,27,31,39], while for a universal high-scale gaugino mass M1 2 ≠ M3 one is forced into a *[email protected] ; † μ ∼ 2–5 [email protected] region of parameter space with large positive TeV ‡ [email protected] [37]. Based on fine-tuning considerations, one is motivated to consider smaller values of μ. In this paper we focus on Published by the American Physical Society under the terms of successful regions of parameter space with μ ≈−300 GeV, the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to which have not been well studied hitherto. the author(s) and the published article’s title, journal citation, It is well known that, to solve the muon g − 2 problem in and DOI. Funded by SCOAP3. supersymmetry (SUSY) models, various mass spectra,
2470-0010=2018=97(11)=115002(17) 115002-1 Published by the American Physical Society BELYAEV, KING, and SCHAEFERS PHYS. REV. D 97, 115002 (2018) including the general characteristics of the mass spectrum mF) [48]. In such a framework it was shown that the muon suggested in this paper, are preferred as discussed in the g − 2 and dark matter may both be explained successfully. papers[5–38] mentioned above. It is worth giving a more However, unlike our approach here, all SUð5Þ 5¯ and 10 detailed discussion about previous works, as well as the representations were assumed to have the same soft masses explanation of the difference between the previous works and for all three families, while here we allow only the second the present one. In general the sensitive parameters for family 10 to have a light soft mass, with all other representa- successful muon g − 2 are the low-energy values of the tions having large soft masses, as discussed above. Higgsino mass parameter μ, the bino soft mass M1, the wino In this paper, then, we argue that in order to account for soft mass M2, the smuon masses mμ˜ L and mμ˜ R ,thesmuon the muon anomalous magnetic moment and dark matter in neutrino mass mν˜μ and the ratio of Higgs vacuum expectation supersymmetry, in our studied region of parameter space for values tan β. Some subset of these masses must be quite light, μ ≈−300 GeV, nonuniversal gaugino masses are required. say of order 100 GeV, in order to explain the muon g − 2.On In particular, M1;2 ≪ M3, even for nonuniversal scalar the other hand there are stringent LHC limits on the colored masses. To achieve the desired pattern of nonuniversality, sparticles, say of order 1 TeV. In addition some heavy stop we consider an SUð5Þ GUT combined with an A4 family squarks are required in order to obtain a sufficiently large symmetry, where the three 5¯ representations form a single Higgs mass around 125 GeV. A common way to achieve this triplet of A4 with a unified soft mass mF, while the three 10 is if, at the grand unified theory (GUT) scale, M3 ≫ M1;2, representations are singlets of A4 with independent soft 1 which leads to all colored sparticles having large masses, masses mT1;mT2;mT3. Assuming that mT2 ≪ mT1;mT3,as while allowing at least some color singlet sparticles to remain discussed above, we show that it is not possible to account light. This is also what we assume in this paper. However the for the muon g − 2 with universal gaugino masses. Allowing novelty of our approach here is that we achieve this within the nonuniversal gaugino masses with M1;2 ≪ M3, we show framework of an SUð5Þ GUTwith a particular flavor structure that, with μ ≈−300 GeV, it is possible to successfully in which only one of the GUT matter representations, namely explain both the muon anomalous magnetic moment and the second family 10 representation has a light soft mass dark matter, while remaining consistent with all other ¼ 200–300 ∼100 mT2 GeV, leading to a light mass mμ˜ R GeV, experimental constraints. We present three benchmark points with all other squarks contained in this representation gaining in our favored region of parameter space involving a right- large mass from the large gluon corrections. All other GUT handed smuon mass around 100 GeV, which can decay into representations are assumed to have multi-TeV soft masses. a bino-dominated neutralino plus a muon. The remaining The resulting low-energy sparticle spectrum involving only a neutralino masses are all below about 300 GeV, while the light right-handed smuon, with all other squarks and sleptons rest of the SUSY spectrum has multi-TeV masses. being heavy, is one of the key distinguishing features of the The layout of the remainder of the paper is as follows. In present work. Sec. II, we present the SUð5Þ × A4 model and its symmetry In the framework of GUTs such as SUð5Þ and SOð10Þ, breaking to the MSSM. In Sec. III, we summarize the MSSM nonuniversal gaugino masses at MGUT can arise from specific one-loop contributions to Δaμ and give first predictions for nonsinglet F terms, or a linear combination of several such viable regions of parameter space of the model. All exper- terms [40–47]. In general the gaugino masses come from the imental constraints we take into account (both collider and following dimension five term in the Lagrangian: ðhFΦi= cosmological constraints) are listed and explained in Sec. IV. Þλ λ λ ð1Þ ð2Þ ð3Þ MPlanck i j where 1;2;3 are the U , SU and SU In Sec. V, we present scans of the model parameter space for gaugino fields (i.e., bino B˜ ,winoW˜ and gluino g˜,res- universal and nonuniversal gaugino masses, which also helps pectively). Since the gauginos belong to the adjoint repre- clarify the necessity of nonuniversal gaugino masses. Lastly, sentation of SUð5Þ, Φ and FΦ can belong to any of the we draw our conclusions in Sec. VI. irreducible representations appearing in their symmetric ð24 24Þ ¼ 1þ24þ75þ200 Φ product × sym .If is the singlet II. THE MODEL then this results in universal gaugino masses at the GUT scale. We first consider the gauge group SUð5Þ, which is rank 4 However if Φ belongs to one of the nonsinglet representations and has 24 gauge bosons which transform as the 24 adjoint of SUð5Þ then the gaugino masses are unequal, related to each representation. A left-handed lepton and quark fermion other by the representation invariants. If several such Φ fields family is neatly accommodated into the SUð5Þ representa- contribute in different representations then there is no longer ¼ 5¯ ¼ 10 any relation between the gaugino masses at the GUT scale. tions F and T , where The most general situation is when all the gaugino masses may be considered as effectively independent. Recently, an 1In this paper we ignore the induced off-diagonal elements of SUð5Þ model has been analyzed with completely nonuni- the sfermion mass matrices due to A4 symmetry breaking, which versal gaugino masses and two universal soft masses, namely become new sources of flavor violation. Such flavor violation has been studied in similar models based on S4 × SUð5Þ and found to 5¯ mF and mT, which accommodate the and 10 representa- be quite suppressed and within experimental limits; for example tions, respectively (with the two Higgs soft masses set equal to see [49,50].
115002-2 MUON g − 2 AND DARK MATTER SUGGEST … PHYS. REV. D 97, 115002 (2018) 0 1 0 1 c c c dr 0 ug −u ur dr singlets of A4 with independent soft masses mT1;mT2;mT3 B C B b C – B dc C B : 0 uc u d C [51 55]. For simplicity, we assume that at the GUT scale B b C B r b b C we have m ¼ m ¼ m , where m and m are the B c C B C F Hu Hd Hu Hd F ¼ B dg C ;T¼ B :: 0 ug dg C ; ð2Þ B C B C mass parameters of the MSSM Higgs doublets. − c @ e A @ :: : 0 e A In the considered SUð5Þ × A4 model we then have the −ν 0 soft scalar masses, e L :: : : L
m ¼ m ˜ c ¼ m ˜ ¼ m ¼ m ; where r, b, g are quark colors and c denotes CP conjugated F Di Li Hu Hd fermions. mT1 ¼ m ˜ ¼ m ˜ c ¼ m ˜ c ; The SUð5Þ gauge group may be broken to the SM by a Q1 U1 E1 ¼ ˜ ¼ ˜ c ¼ ˜ c Higgs multiplet in the 24 representation developing a mT2 mQ2 mU2 mE2 ; vacuum expectation value, ¼ ˜ ¼ ˜ c ¼ ˜ c ð Þ mT3 mQ3 mU3 mE3 : 6 ð5Þ → ð3Þ ð2Þ ð1Þ ð Þ SU SU C × SU L × U Y; 3 Notice that the stop mass parameters are completely contained in mT3, while the right-handed smuon mass with arises from mT2, and so on. 5¯ ¼ dcð3¯; 1; 1=3Þ ⊕ Lð1; 2¯; −1=2Þ; ð4Þ III. MSSM ONE-LOOP CONTRIBUTIONS TO Δaμ 10 ¼ ucð3¯; 1; −2=3Þ ⊕ Qð3; 2; 1=6Þ ⊕ ecð1; 1; 1Þ; ð5Þ The Feynman diagrams for the one-loop contributions to where ðQ; uc;dc;L;ecÞ is a complete quark and lepton SM Δaμ in the MSSM are shown in Fig. 1 with the respective – family. Higgs doublets Hu and Hd, which break electro- expression for each diagram given by Eqs. (7a) (7e) weak symmetry in a two Higgs doublet model, may arise [15,24]. ð5Þ from SU multiplets H5 and H5¯ , providing the color μ α m2 m2 triplet components can be made heavy. This is known as the ðAÞ M1 1 2 ðAÞ μ˜ L μ˜ R Δaμ ¼ mμ tan β · f ; ; ð7aÞ doublet-triplet splitting problem. m2 m2 4π N M2 M2 μ˜ L μ˜ R 1 1 When A4 family symmetry is combined with SUð5Þ,itis 5¯ ≡ ≡ quite common to unify the three families of F 1 α 2 μ2 ð c Þ Δ ðBÞ ¼ − 1 2 β ðBÞ M1 ð Þ d ;L into a triplet of A4, with a unified soft mass mF, aμ mμ tan · fN 2 ; 2 ; 7b 10 ≡ ≡ ð c cÞ M1μ 4π mμ˜ mμ˜ while the three i Ti Q; u ;e i representations are R R
(a) (b)
(c) (d)
(e)
FIG. 1. One-loop contributions to the anomalous magnetic moment of the muon for supersymmetric models with low-scale MSSM.
115002-3 BELYAEV, KING, and SCHAEFERS PHYS. REV. D 97, 115002 (2018)
1 α 2 μ2 positive contribution to Δaμ and this is the main reason Δ ðCÞ ¼ 1 2 β ðCÞ M1 ð Þ aμ mμ tan · fN 2 ; 2 ; 7c why we favor negative μ. In general, for negative μ, the M1μ 8π mμ˜ mμ˜ L L contribution from diagrams (B) and (D) is enhanced, while all contributions from diagrams (A), (C) and (E) (see 1 α 2 μ2 Δ ðDÞ ¼ − 2 2 β ðDÞ M2 ð Þ Sec. III) are simultaneously suppressed. Enhancing (B) aμ mμ tan · fN 2 ; 2 ; 7d M2μ 8π m m jμj μ˜ L μ˜ L and (D) requires small (not directly controllable), small M1 and M2 as well as light left- and right-handed smuon 2 2 ð Þ 1 α2 ð Þ M2 μ masses mμ˜ and mμ˜ (controlled by m or m 2 respectively). Δ E ¼ 2 β E ð Þ L R F T aμ mμ tan · f 2 ; 2 : 7e μ 4π C On the other hand, light mμ˜ would lead to unwanted large M2 mν˜μ mν˜μ L contributions from diagrams (A) and (C). This is one reason
to not have light mμ˜ L , but makes them rather heavy. Another α α ð1Þ ð2Þ reason for heavy mμ˜ comes from the model parameter space Here, 1 and 2 label the U Y and SU L fine L structure constants respectively and the functions itself. Since mμ˜ L is governed by mF, which also controls the ð Þ ð Þ A;B;C;D ð Þ E ð Þ muon sneutrino mass mν˜μ appearing in diagram (E), it is fN x; y and fC x; y are given by L possible to decrease contributions from diagrams (A), (C) ð Þ −3 þ x þ y þ xy 2x log x and (E) in one go by setting m large. f A;B;C;D ðx; yÞ¼xy þ F N ðx − 1Þ2ðy − 1Þ2 ðx − yÞðx − 1Þ3 In the next section we briefly summarize the experi- mental constraints, before discussing the full results in 2y log y − ; ð8aÞ detail in Sec. V. ðx − yÞðy − 1Þ3 IV. EXPERIMENTAL CONSTRAINTS ð Þ 5 − 3ðx þ yÞþxy 2 log x f E ðx; yÞ¼xy − C ðx − 1Þ2ðy − 1Þ2 ðx − yÞðx − 1Þ3 While the underlying model is proposed for the high- energy sector, it should nevertheless comprise any low- 2 log y þ ð Þ energy observations and limits coming from various ð − Þð − 1Þ3 ; 8b x y y experiments. In particular, we take into account the dark ð Þ matter relic density, dark matter direct detection (DD) cross where we use the superscripts A; B; C; D and (E)asa sections, the Higgs boson mass, constraints coming from short notation to allow omission of the mass ratio argu- þ − BrðBS → μ μ Þ as well as Brðb → sγÞ and several 8 and ments. Both fN and fC are monotonically increasing for all 13 TeV ATLAS and CMS searches at the LHC. Regarding 0 ≤ ð Þ ∞ 0 ≤ ≤ 1 x; y < and are defined in fN;C [24]. the DM relic density, the current combined best fit to data Δ One of the most important parameters influencing aμ is from PLANCK and WMAP is Ωh2 ¼ 0.1198 0.0026 [56] μ, or rather sgn μ. Having positive μ means positive 2 and we consider a parameter space with Ωh ≲ 0.1224. contributions from diagrams (A), (C) and (E), whereas The current best DM DD limit comes from the negative μ results in (B) and (E) giving positive contribu- σ ≤ 7 64 XENON1T experiment, reading DD-SI . × tions to Δaμ. Although it has been shown in the past that the −47 2 −11 10 cm ¼ 7.64 × 10 pb [57] for spin-independent constrained MSSM (cMSSM) with its usual five parame- β μ models and a WIMP mass of 36 GeV. Since WIMP masses ters (M1=2;m0; tan ;A0; sgn ) is able to yield the observed smaller or larger than 36 GeV lead to weaker limits, this Δ aμ, it cannot account simultaneously for further exper- choice is conservative. Concerning the Higgs boson mass, imental limits (see e.g., [15,24,26]), regardless of sgn μ but the current combined ATLAS and CMS measurement especially not for negative μ. Extending the cMSSM or is mh ¼ð125.09 0.21ðstat:Þ 0.11ðsys:ÞÞ GeV [58]. relaxing some of its constraints changes the picture and new However, due to the theoretical error in the radiative solutions without the need for fine-tuning arise—all while corrections to the Higgs mass inherent in the existing state being in conformity with all other low-energy observations of the art SUSY spectrum generators, we consider instead – – [5 17,19 38]. the larger range mh ¼ð125.09 1.5Þ GeV, which encom- In this work, we focus on regions in model parameter passes the much larger theoretical uncertainties. The space having viable Δaμ for negative μ together with an branching ratios Brðb → sγÞ¼ð3.29 0.19 0.48Þ × μ ∼ þ1 0 especially light mass spectrum. Solutions with positive 10−4 [59] and BrðB → μþμ−Þ¼3.0 . × 10−9 [60] are 2–5 s −0.9 TeV are possible for a universal high-scale gaugino directly applied to our results. mass M1;2 ≠ M3 [37]. However, motivated by fine-tuning considerations, we focus on negative and small μ in the V. RESULTS following. Negative μ infers that we are able to enhance the contribution from diagram (B) in which the right-handed Following the strategy to enhance Δaμ in Sec. III and the smuons (but not the left-handed smuons) appear. As already experimental constraints in Sec. V, we are left with the mentioned, negative μ results in diagram (B) giving a following desired choice of parameters:
115002-4 MUON g − 2 AND DARK MATTER SUGGEST … PHYS. REV. D 97, 115002 (2018)
TABLE I. Input parameters at the GUT scale in GeV (apart for tan β and sgnμ) for universal gaugino masses M1=2. β μ Parameter mF mT1 mT2 mT3 M1=2 Atri mH1;2 tan sgn Value 6000 7000 300 free free −6000 6000 30 −1
TABLE II. Input parameters at the GUT scale in GeV for nonuniversal gaugino masses M1;2 and M3. β μ Parameter mF mT1 mT2 mT3 M1;2 M3 Atri mH1;2 tan sgn Value 6000 7000 300 free 250 free −5000 6000 30 −1
(i) m large for large mμ˜ and mν˜μ , A. Universal gaugino masses F L L (ii) mT2 small for light mμ˜ , R The scan with universal gaugino masses M1=2 was (iii) mT1 and mT3 large for large squark masses, 0 performed with (iv) M1 small for light χ˜1, ∈ ½200 7000 (v) tan β large (affects all diagrams). mT3 ; GeV; All other parameters are, in principle, unconstrained, but in M1=2 ∈ ½200; 7000 GeV practice are constrained by experiment. To gather the data for this work, we used and all other parameters fixed with values as shown in SPheno_v4.0.3 [61,62] to generate the mass spectra Table I. An overview over the scanned mT3-M1=2 plane is based on input points chosen randomly as well as on fixed shown in Fig. 2, where the color coding indicates the value grids with variable grid spacing in the parameter space of Δaμ. The first thing to notice is that only a narrow stripe from Tables I and II below. Subsequently, we employ in the parameter space leads to radiative electroweak micrOMEGAs_v3.6.9.2 [63] to compute Δaμ and the symmetry breaking (REWSB). Following the stripe to Δ low-energy constraints listed in Sec. IV. In the following larger mT3 and smaller M1=2 gives larger aμ, before the two subsections, we present scans taking these consider- stripe eventually ends in a narrow peak around ations into account. Section VA holds data and results ðmT3;M3Þ¼ð5.3; 1.3Þ TeV. However, even in the peak −10 regarding fully universal gaugino masses, commonly Δaμ only reaches values up to 1.8 × 10 , which is about labeled as M1=2, whereas Sec. VB refers to the case of 10–20 times lower than observed. Before giving an Δ partially nonuniversal gaugino masses, labeled as M1;2 and explanation for why aμ is so small even with the M3, and Sec. VC refers to the case of fully nonuniversal assumptions made before, let us investigate the relic density gaugino masses labeled M1, M2 and M3. and μ behavior shown in Fig. 3. Regarding the relic density
FIG. 2. mT3-M1=2 plane with color-coded Δaμ with universal gaugino masses. The right panel is an excerpt of the full scan shown in the left panel.
115002-5 BELYAEV, KING, and SCHAEFERS PHYS. REV. D 97, 115002 (2018)
Δ σðpÞ Δ μ FIG. 3. Left: Relic density vs aμ with color-coded DD-SI with universal gaugino masses. Right: aμ vs with color-coded relic density Ωh2 with universal gaugino masses. shown in the left panel of Fig. 3, it turns out that DM is this Sec. V). It is also worth noticing that decreasing μ mostly Higgsino-like, thus yielding relic densities in the results in a decreased relic density due to the DM becoming right range or maximally 2 orders of magnitude smaller more and more Higgsino-like, as indicated by the color- 2 than the observed upper limit. With increasing Δaμ, the coded Ωh . relic density slightly converges to some central value In summary, the case of universal M1=2 at the GUT scale between its minimum and maximum reach. While the relic with negative μ does not yield any values of Δaμ in or close density thus is not a problem with this setup, the predicted to the 1σ reference bound. This is expected and can be DM DD cross sections turn out to be fully excluded (see reasoned by the following argument. With negative μ, only color coding). This can be readily understood since dark Eqs. (7b) and (7d) give positive contributions to Δaμ, while matter in this case is dominantly Higgsino-like and there- the major differences between (7b) and (7d) are simply the fore has a significant coupling to the Higgs boson, leading exchange of M1 and M2 as well as mμ˜ R and mμ˜ L . Since the to a large DM DD cross section. loop functions only run from 0 to 1, they are irrelevant The right panel of Fig. 3 shows Δaμ as a function of μ for our argument and we can conservatively assume for and it turns out that smaller values of μ yield larger values the moment that they both equal 1 and consider just the Δ of aμ, as was expected (see Sec. III and the beginning of remaining prefactors. With M1 and M2 unified at the GUT
FIG. 4. mT3-M3 plane with color-coded Δaμ with nonuniversal gaugino masses. The panel at the right is an excerpt of the full scan shown in the left panel.
115002-6 MUON g − 2 AND DARK MATTER SUGGEST … PHYS. REV. D 97, 115002 (2018) scale, their low-scale values are not much different either Δaμ. This setup is studied in detail in the following and allow us to focus solely on one of the two equations, Sec. VB. e.g., (7b). To get suitable Δaμ, M1 as well as μ need to be small [Oð200Þ GeV]. However, having M1 that light B. Partially nonuniversal gaugino masses results in a similar light M3 leading to light gluinos with Splitting M1=2 into M1;2 and M3 allows us to keep M3 masses mg˜ ≲ 1 TeV [18] which are already excluded by LHC searches [2,3] as we have checked in our study. heavy, while fixing M1;2 to some value light enough to strengthen rather than weaken Δaμ. We performed a scan Additionally, too small M1=2 prevents REWSB from happening, as can be seen in Fig. 2. taking this into account with Overall, in the case of unified gaugino masses M1=2,we m 3 ∈ ½500; 7000 ; did not find a region in parameter space able to explain Δaμ T GeV in harmony with the other experimental constraints con- M3 ∈ ½500; 7000 GeV sidered. However, a possible solution arises when the gaugino masses are split into M1;2 and M3, allowing for and all other parameters fixed with values as shown in heavy gluinos and light enough M1;2 to yield the correct Table II. Analogous to Fig. 2, we show the scanned over
Δ σðpÞ FIG. 5. Relic density vs aμ with color-coded DD-SI with nonuniversal gaugino masses. The grey shaded rectangle shows the 2 (extended) 1σ bound for Δaμ (Ωh ). The panel at the right is an excerpt of the full scan shown in the left panel.
σ Δ Ω 2 1σ FIG. 6. DD-SI vs aμ with color-coded relic density h with nonuniversal gaugino masses. The grey shaded rectangle shows the Δ σ bound for aμ and the upper limit for DD-SI. The panel at the right is an excerpt of the full scan shown in the left panel.
115002-7 BELYAEV, KING, and SCHAEFERS PHYS. REV. D 97, 115002 (2018)
2 FIG. 7. Δaμ vs μ with color-coded relic density Ωh with nonuniversal gaugino masses. The grey shaded rectangle shows the 1σ bound for Δaμ. The panel at the right is an excerpt of the full scan shown in the left panel.
2 FIG. 8. mμ˜ vs mχ˜ 0 with color-coded relic density Ωh with nonuniversal gaugino masses. The panel at the right is an excerpt of the full R 1 scan shown in the left panel. mT3-M3 plane in Fig. 4. Similar to the case of universal results to the case with universal gaugino masses, the large gaugino masses, a narrow, slightly elliptic stripe of solutions increase in Δaμ immediately becomes visible, therefore with larger Δaμ canbeseenforM3 ≲ 3.8 TeV and validating our assumptions made earlier. mT3 ≲ 4.5 TeV. Additionally, a wide band around this stripe In Fig. 5, we show the relic density-Δaμ plane with holds points where REWSB is happening, but Δaμ is close to color-coded DM direct detection cross sections, analogous 0. A second set of points with vanishingly small Δaμ is found to Fig. 3, left. This time, however, dark matter is mainly σ for M3 ≳ 3 TeV and mT3 ≳ 6.5 TeV (not shown here).When binolike and DD-SI is smaller than in Fig. 3 and increases zooming in on the interesting part of the scan with larger faster with increasing Δaμ. In the right panel of Fig. 5,a 2 σ values of Δaμ (see the right panel of Fig. 4), we notice that the zoomed excerpt without logarithmic scaling of DD-SI stripe extends into the nonphysical region without REWSB, shows that most of the 1σ reference bounds for Δaμ and although the points here are excluded by Large Electron- Ωh2 are excluded by DM direct detection, only leaving a Positron Collider (LEP) limits due to too light charginos or Δ smuons. Just before hitting the unphysical region, aμ peaks 2To allow for an easier comparison in the relevant range of 4 10−9 σ 1 10−11 7 64 at values around × before eventually vanishing DD-SI, i.e., approximately between × pb and . × 10−11 σ 10 10−11 abruptly in the non-REWSB region. Comparing these first pb, values of DD-SI > × pb are also colored red.
115002-8 MUON g − 2 AND DARK MATTER SUGGEST … PHYS. REV. D 97, 115002 (2018)
2 FIG. 9. mh vs Δaμ with color-coded Ωh (left) and σDD-SI (right) with nonuniversal gaugino masses. small range of solutions for the lower edge of the Δaμ 1σ Lastly, in Fig. 10 in the right panel we show a comparison bound. Nevertheless, in comparison to universal gaugino between Δaμ as a function of M3ðQÞ (lower horizontal axis) masses, there are solutions for nonuniversal gaugino and mg˜ (top horizontal axis) for both universal (purple masses that satisfy all experimental limits. diamonds) and nonuniversal (orange squares) gaugino Similar to Figs. 5 and 6 holds the same data but with Ωh2 masses. It is clearly visible that universal gaugino masses σ Δ — and DD-SI switched. Presenting the data this way allows for a cannot lead to viable aμ and even if there were a way to better understanding of the excluded and allowed parameter increase Δaμ further—the gluinos would become quite light, σ space with respect to DD-SI. As can be seen in Fig. 6, right, potentially violating existing collider constraints. In the case only a small fraction of points falls within the 1σ reference of nonuniversal gaugino masses, the Δaμ spectrum with Δ σ bounds of aμ and DD-SI (grey rectangle), although the respect to M3 is slightly squeezed, but approximately 1 order majority of these points provide a very good relic density. of magnitude larger. This leads to a large spectrum of points In Fig. 7, the μ dependence of Δaμ is shown and it turns out that μ needs to be between −300 and −100 GeV in order to yield the desired Δaμ. When μ goes closer to 0, the Higgsino components of the LSP start to dominate while simultaneously, the mass of the lightest chargino falls below approximately 100 GeV. Such light charginos are excluded by LEP [64], thus limiting our parameter space to values of μ smaller than −100 GeV. In Fig. 8,weshowthemμ˜ -mχ˜ 0 plane with color-coded R 1 relic density. As can be seen in the right panel, the pink benchmark point sits well above the line where the right- handed smuon and lightest supersymmetric particle (LSP) are mass degenerate. For this benchmark point, the LSP is predominantly binolike, but with a nonzero Higgsino 0 0 component. This allows for a significant amount of χ˜1-χ˜1 0 annihilation in addition to the dominant μ˜ R-χ˜1 coannihilation cross-section leading to the correct relic density. In Fig. 9, we show the Higgs mass mh as a function of Δaμ Ω 2 σ with color-coded h (left) and DD-SI (right). For small values of Δaμ, a broad range of Higgs masses is accessible with REWSB. This range shrinks drastically with FIG. 10. Influence of having universal (nonuniversal) gaugino masses M1=2 ðM1;2;M3Þ on Δaμ. The purple (red) points increasing Δaμ and eventually peaks at m ¼ 126.5 GeV h represent the universal (nonuniversal) case. The grey shaded Δ ≈ 4 10−9 for aμ × . The relic density generally decreases rectangle shows the 1σ bound for Δaμ. Note that, to allow for an with increasing Δaμ, while the DM DD cross sections easier comparison, the nonuniversal points were gathered with ¼ −6 ¼ −5 – increase, as discussed before. Atri TeV instead of Atri TeV as shown for Figs. 4 8.
115002-9 BELYAEV, KING, and SCHAEFERS PHYS. REV. D 97, 115002 (2018)
TABLE III. Input and output parameters for the benchmark points with partial gaugino nonuniversality M1 ¼ M2 ≪ M3. These points 2 0 have good Δaμ as well as Ωh but the wino dominated charginos χ˜1 and neutralinos χ˜2 are too light to have avoided 8 TeV LHC searches as discussed in the text. q˜ i labels the i-th generation of squarks.
Benchmark BP1 BP2 BP3 tan β 30 28 28 sgnðμÞ −1 −1 −1
Input at GUT scale mF 6000.0 6000.0 6200.0 [GeV] mT1 7000.0 6000.0 5700.0 mT2 300.0 300.0 290.0 mT3 4448.6 5572.0 5518.0 M1;2 250.0 250.0 250.0 M3 2521.2 2446.0 2790.0
Mh1 6000.0 6000.0 6200.0
Mh2 6000.0 6000.0 6200.0 Atri −5000.0 0 −500.0
Masses mh 126.4 124.3 124.7 [GeV] mg˜ 5457.7 5280.9 5963.4 m˜ 1 8248.5 7312.5 7433.2 qL ˜ muR 8250.1 7316.9 7439.2 m˜ 2 4350.1 4173.2 4764.6 qL
mc˜R 4377.1 4198.9 4788.7 ˜ mb1 4866.7 5884.2 6162.0
mt˜1 3944.4 5068.5 5340.8
mt˜2 4875.0 5887.4 6165.7 m˜ 7423.9 7320.6 7832.1 dR
ms˜R 7423.8 7320.5 7831.9 ˜ mb2 6934.5 6947.4 7453.3
me˜L 5987.1 5988.4 6188.8
me˜R 7001.2 5999.3 5699.4
mμ˜ L 5986.5 5988.0 6188.3
mμ˜ R 100.7 95.6 95.4
mτ˜1 3731.8 5175.0 5057.0
mτ˜2 5737.5 5789.7 5989.0 mχ˜ 0 93.2 91.1 89.2 1 mχ˜ 0 169.4 163.6 158.7 2 mχ˜ 0 −341.9 −336.2 −337.8 3 mχ˜ 0 353.9 347.8 348.6 4 mχ˜ 169.6 163.7 158.9 1 mχ˜ 356.8 350.7 351.5 2 mν˜e 5986.1 5987.5 6187.8 L mν˜μ 5985.6 5987.0 6187.3 L mν˜τ 5736.8 5788.7 5988.1 L Q 4287.9 5353.0 5609.8 μ −311.5 −302.1 −299.5 Constraints Brðb → sγÞ 3.40×10−4 3.35×10−4 3.34×10−4 [pb] þ − −9 −9 −9 BrðBs →μ μ Þ 3.03×10 3.04×10 3.04×10 σDD SI 7.23×10−11 7.59×10−11 6.89×10−11 Ωh2 1.04×10−1 4.65×10−2 7.55×10−2 −9 −9 −9 Δaμ 2.10×10 2.09×10 2.09×10
115002-10 MUON g − 2 AND DARK MATTER SUGGEST … PHYS. REV. D 97, 115002 (2018)
TABLE IV. CheckMATE analysis results for the benchmarks of Table III with partial gaugino nonuniversality M1 ¼ M2 ≪ M3.
Benchmark Quantity Unit BP1 BP2 BP3 rpmaxffiffiffi 7.38 9.16 9.30 s TeV888 Analysis ATLAS_1402_7029 ATLAS_1402_7029 ATLAS_1402_7029 Signal region SR0taua06 SR0taua02 SR0taua02 Ref. [69] [69] [69] σLO pb 1.65 1.85 2.14 ðχ˜0 → μ˜ μ∓Þ BR 2 R % 99.4 99.4 99.7 0 0 BRðχ˜2 → qq¯ χ˜1Þ % 0.4 0.4 0.2 0 ∓ 0 0 1 BRðχ˜2 → l l χ˜1Þ % 0.1 0.1 < . 0 0 0 1 0 1 0 1 BRðχ˜2 → ν¯lνlχ˜1Þ % < . < . < .
¯ 1;2 1;2 0 BRðχ˜1 → d u χ˜1Þ % 45.4 40.2 47.9 ðχ˜ → μ˜ ν Þ BR 1 R μ % 31.9 39.8 34.7 0 BRðχ˜1 → l νlχ˜1Þ % 22.7 20.0 17.4 Δmðχ˜1 ; μ˜ RÞ GeV 68.9 67.9 63.5 0 Δmðχ˜2; μ˜ RÞ GeV 68.7 67.7 63.3 0 Δmðμ˜ R; χ˜1Þ GeV 7.5 6.6 6.2
with Δaμ in the correct range while simultaneously keeping small (below a few GeV) since in this case the smuon decay 0 the gluinos fairly heavy. Overall, having nonuniversal products will be soft. The χ˜2 decay is characterized by the 0 gaugino masses allows for a variety of points with viable dominant χ˜2 → μ˜ Rνμ decay with not-so-soft leptons (the Δaμ, which then can be tested further against other exper- 0 energy of which is independent of μ˜ R-χ˜1 mass gap) provid- imental constraints, as was shown above. Based on these ing a very important contribution to the leptonic signature. findings, we provide three qualitatively different benchmark Thus, the only signature from the scenario under study is points, summarized in Table III below. BP2 differs from BP1 very specific and characterized by muon-dominated di- and β ¼ 28 ¼ 0 mainly in having tan and Atri , whereas BP3 has a trilepton signatures at the LHC. nonvanishing negative Atri and split mF and mT1. We have performed a CheckMATE 2.0.11 [65] The benchmark points in this region are characterized by analysis on these three benchmark points, including all χ˜0 (a) bino-dominated 1 LSP being the dark matter particlewith implemented 8 and 13 TeV ATLAS and CMS analyses on a mass below about 100 GeV; (b) a next-to-lightest right- chargino and neutralino searches with a light smuon, and handed smuon μ˜ R with mass several GeV heavier; (c) wino- χ˜0 χ˜ χ˜0 have verified that the LHC in fact is highly sensitive to this dominated 2 and 1 having a mass gap between them and 1 part of the parameter space. In particular, we used of less than the Z or W boson masses respectively; (d) non- MadGraph 5.2.3.3 [66] linked to CheckMATE to negligible μ˜ R − μ˜ L mixing (enhanced by not-so-small values generate 50000 events for SUSY final states consisting of tan β) and respectively non-negligible χ˜ → μ˜ νμ decay 0 0 1 R of μ˜ , χ˜ , χ˜ as well as χ˜ . Next, PYTHIA 8.2.30 [67] χ˜0 χ˜ R 1 2 1 branching fractions; (e) Higgsino-dominated 3 and 2 with was used to shower and hadronize the events and eventually masses below 400 GeV; and (f) all other SUSY partners CheckMATE together with Delphes 3.3.3 [68] was used having multi-TeV masses. to perform the event and detector analysis. While setting the Such a specific spectrum of light electroweak gauginos same cuts as were used for the experimental analyses, the and right-handed smuons predicts a rather characteristic CheckMATE χ˜ χ˜0 framework therefore allows us to examine signal at the LHC. The signal comes dominantly from 1 2 whether given points in the parameter space are allowed or χ˜þχ˜− χ˜0 and 1 1 -pair production followed by the dominant 2 ruled out by current experimental searches. For all three — — decay into a smuon which in its turn decays into a muon benchmarks, the ATLAS search ATLAS_1402_7029 [69] μ˜ μ˜ and DM. On the other hand, due to the non-negligible R- L aimed at three leptons plus missing E was most sensitive. χ˜ → μ˜ ν T mixing mentioned above, the branching ratio for R μ The r value defined by [65] ¯0 0 max becomes comparable to the three-body decay χ˜1 → ff χ˜1 S − 1.64 · ΔS via a virtual W boson. This Brðχ˜ → μ˜ νμÞ can be sub- ¼ 1 rmax 95 ; stantial (≃30%–50%) because of the significant Higgsino S component. The signal strength mμ˜ strongly depends on the where S is the number of predicted signal events with its 0 μ˜ R-χ˜1 mass gap and can be quite hidden if this mass gap is uncertainty ΔS and S95 is the experimental 95% upper limit
115002-11 BELYAEV, KING, and SCHAEFERS PHYS. REV. D 97, 115002 (2018)
TABLE V. Input and output parameters for the benchmark points with full gaugino nonuniversality M1 Benchmark BP4 BP5 BP6 tan β 30 28 30 sgnðμÞ −1 −1 −1 Input at GUT scale mF 5000.0 6200.0 5000.0 [GeV] mT1 5000.0 5700.0 5000.0 mT2 200.0 280.0 200.0 mT3 2995.0 5430.0 3005.0 M1 250.0 250.0 250.0 M2 400.0 550.0 500.0 M3 2600.0 2945.0 2595.0 Mh1 5000.0 6200.0 5000.0 Mh2 5000.0 6200.0 5000.0 −4000 0 −500 0 −4000 0 Atri . . . Masses mh 126.3 124.7 126.2 [GeV] mg˜ 5531.7 6235.3 5516.5 m˜ 1 6743.0 7589.2 6735.7 qL mu˜ R 6743.7 7589.9 6734.1 m˜ 2 4516.4 5003.3 4505.7 qL mc˜R 4529.2 5018.0 4514.9 ˜ mb1 4312.4 6262.8 4306.4 mt˜1 3601.6 5443.3 3588.2 mt˜2 4324.0 6266.7 4318.0 m˜ 6748.0 7975.4 6738.4 dR ms˜R 6747.9 7975.3 6738.3 ˜ mb2 6348.2 7597.3 6337.5 me˜L 4994.9 6196.1 4998.5 ˜ meR 5002.1 5699.9 5002.1 mμ˜ L 4994.4 6195.6 4998.0 mμ˜ R 98.9 96.8 99.4 mτ˜1 2282.9 4968.1 2293.7 mτ˜2 4802.1 5999.4 4805.3 mχ˜0 91.7 89.0 92.0 1 mχ˜0 266.9 303.3 302.2 2 mχ˜0 −335.1 −327.8 −335.9 3 mχ˜0 376.8 458.9 430.4 4 mχ˜ 267.4 303.7 302.8 1 m˜ 378.2 459.0 430.7 χ2 mν˜e 4993.8 6195.1 4997.4 L mν˜μ 4993.4 6194.6 4997.0 L mν˜τ 4800.9 5998.4 4804.1 L Q 3866.1 5705.8 3856.5 μ −313.0 −293.3 −314.3 Constraints Brðb → sγÞ 3.43 × 10−4 3.34 × 10−4 3.43 × 10−4 [pb] þ − −9 −9 −9 BrðBs → μ μ Þ 3.01 × 10 3.04 × 10 3.01 × 10 σDD SI 6.72 × 10−11 6.81 × 10−11 6.52 × 10−11 Ωh2 9.67 × 10−2 1.10 × 10−1 1.03 × 10−1 −9 −9 −9 Δaμ 2.17 × 10 2.14 × 10 2.16 × 10 115002-12 MUON g − 2 AND DARK MATTER SUGGEST … PHYS. REV. D 97, 115002 (2018) TABLE VI. CheckMATE analysis results for the benchmarks of Table V with full gaugino nonuniversality M1 Benchmark Quantity Unit BP4 BP5 BP6 prmaxffiffiffi 0.88 0.12 0.13 s TeV 13 13 13 Analysis ATLAS_CONF_2016_096 ATLAS_CONF_2016_096 ATLAS_CONF_2016_096 Signal region 3LI 2LADF 3LI Ref. [70] [70] [70] σLO pb 0.54 0.24 0.26 0 0 BRðχ˜2 → hχ˜1Þ % 51.0 55.5 55.4 0 0 BRðχ˜2 → Zχ˜1Þ % 30.5 30.2 30.1 ðχ˜0 → μ˜ μ∓Þ BR 2 R % 18.5 14.3 14.5 0 BRðχ˜1 → W χ˜1Þ % 99.4 99.5 99.5 ðχ˜ → μ˜ ν Þ BR 1 R μ % 0.6 0.5 0.5 Δmðχ˜1 ; μ˜ RÞ GeV 168.5 207.0 203.4 0 Δmðχ˜2; μ˜ RÞ GeV 168.0 206.5 202.7 0 Δmðμ˜ R; χ˜1Þ GeV 7.2 7.8 7.5 on the number of signal events, is shown below in Table IV arising from smuon decays. For solutions with positive μ ≥ 1 for all three benchmarks. Values of rmax indicate the such as in Ref. [37], the overall mass spectrum is slightly 1 signal is excluded, whereas rmax < indicates that the signal heavier and lies outside the sensitivity reach of the is not excluded or probed yet. 8 TeV LHC.3 It turns out that all benchmarks are strongly excluded, In this section, we show that, allowing fully nonuniversal 0 which is mainly due to the light χ˜1 and χ˜2 and their gaugino masses with M1 115002-13 BELYAEV, KING, and SCHAEFERS PHYS. REV. D 97, 115002 (2018) remaining Higgsino-dominated charginos and neutralinos the direct detection limits provided by XENON1T provide whose mass is governed by jμj cannot be pushed up beyond a strong constraint on this scenario. ≃300 GeV, since we need μ ∼−300 GeV to achieve a We have discussed such a scenario in the framework of successful muon g − 2. These charginos and neutralinos an SUð5Þ GUT combined with A4 family symmetry, where ¯ therefore remain a target for LHC searches. We have again the three 5 representations form a single triplet of A4 with a CheckMATE 2.0.11 performed a analysis on these three unified soft mass mF, while the three 10 representations are benchmark points, including all implemented 8 and 13 TeV singlets of A4 with independent soft masses mT1;mT2;mT3. ATLAS and CMS analyses on chargino and neutralino Although mT2 (and hence μ˜ R) may be light, the muon g − 2 searches with a light smuon and have verified that the LHC also requires M1 ≃ 250 GeV which we have shown to be in fact is highly sensitive to this part of the parameter space. incompatible with universal gaugino masses at the GUT Following the procedure described in detail in the previous scale due to LHC constraints on M2 and M3 arising from subsection, we have obtained the results shown in Table VI gaugino searches. Therefore, we have allowed nonuniversal for all three benchmarks. Contrary to the previous results, gaugino masses at the GUT scale, which is theoretically now we see that all three benchmark points are consistent allowed in SUð5Þ with nonsinglet F terms. One should with current LHC searches; however BP4 is on the verge of stress that this model is representative of a larger class of ¼ 0 88 being excluded with a value of rmax . , while BP5 and such nonuniversal MSSM scenarios, which can give ≈ 0 12 BP6 both have rmax . and require a substantial nonuniversal masses to left- and right-handed sfermions increase in luminosity to exclude them. The search chan- and which in particular allow a light right-handed smuon nels are di- and trilepton searches plus missing energy, as with mass around 100 GeV. After showing that universal before, but since the chargino and neutralino masses are gaugino masses M1=2 at the GUT scale are excluded by larger, the cross sections are now lower, as can be seen in gluino searches, we have provided a series of benchmarks Table VI. which demonstrate that while M1 ¼ M2 ≪ M3 for sgnμ ¼ – Another reason why the sensitivity of the LHC to BP4 −1 is also excluded by chargino searches, M1 115002-14 MUON g − 2 AND DARK MATTER SUGGEST … PHYS. REV. D 97, 115002 (2018) completion of this work. A. S. B., S. F. K. and P. B. S. Institute for Basic Science S. F. K. acknowledges partial acknowledge partial support from the InvisiblesPlus support from the STFC Grant No. ST/L000296/1. A. S. B. RISE from the European Union Horizon 2020 research also thanks the NExT Institute, Royal Society Leverhulme and innovation program under the Marie Sklodowska- Trust Senior Research Fellowship Grant No. LT140094, Curie Grant No. 690575. S. F. K. acknowledges partial Royal Society International Exchange Grant No. IE150682 support from the Elusives ITN from the European Union and the Soton-FAPESP grant. A. S. B. also acknowledges the Horizon 2020 research and innovation program under the support of the IBS center in Daejeon for the hospitality and Marie Sklodowska-Curie Grant No. 674896. A. S. B. and support. [1] G. Jungman, M. Kamionkowski, and K. Griest, Super- [15] T. Moroi, The muon anomalous magnetic dipole moment symmetric dark matter, Phys. Rep. 267, 195 (1996). in the minimal supersymmetric standard model, Phys. Rev. [2] ATLAS Collaboration, Search for pair-production of glui- D 53, 6565 (1996); Erratum, Phys. Rev. D 56, 4424(E) nos decaying via stop and sbottom in eventspffiffiffi with b-jets and (1997). large missing transverse momentum in s ¼ 13 TeV pp [16] S. P. Martin and J. D. Wells, Constraints on ultraviolet stable collisions with the ATLAS detector, CERN Report No. AT- fixed points in supersymmetric gauge theories, Phys. Rev. D LAS-CONF-2015-067, 2015. 64, 036010 (2001). [3] A. M. Sirunyan et al. (CMS Collaboration), Search for new [17] A. Czarnecki and W. J. Marciano, The muon anomalous phenomena with the MT2 variable in the all-hadronicpffiffiffi final magnetic moment: A harbinger for new physics, Phys. Rev. state produced in proton-proton collisions at s ¼ 13 TeV, D 64, 013014 (2001). Eur. Phys. J. C 77, 710 (2017). [18] H. Baer, A. Belyaev, T. Krupovnickas, and A. Mustafayev, [4] K. A. Olive et al. (Particle Data Group Collaboration) Re- SUSY normal scalar mass hierarchy reconciles ðg − 2Þμ, b → view of particle physics, Chin. Phys. C 38, 090001 (2014). sγ and relic density, J. High Energy Phys. 06 (2004) 044. [5] A. S. Belyaev, J. E. Camargo-Molina, S. F. King, D. J. [19] G.-C. Cho, K. Hagiwara, Y. Matsumoto, and D. Nomura, Miller, A. P. Morais, and P. B. Schaefers, A to Z of the The MSSM confronts the precision electroweak data and the muon anomalous magnetic moment in the MSSM with muon g − 2, J. High Energy Phys. 11 (2011) 068. Pati-Salam at the GUT scale, J. High Energy Phys. 06 [20] M. Endo, K. Hamaguchi, S. Iwamoto, and N. Yokozaki, (2016) 142. Higgs mass and muon anomalous magnetic moment in [6] J. A. Grifols and A. Mendez, Constraints on supersymmetric supersymmetric models with vectorlike matters, Phys. Rev. particle masses From (g − 2) μ, Phys. Rev. D 26, 1809 D 84, 075017 (2011). (1982). [21] M. Endo, K. Hamaguchi, S. Iwamoto, and N. Yokozaki, [7] J. R. Ellis, J. S. Hagelin, and D. V. Nanopoulos, Spin 0 Higgs mass, muon g − 2, and LHC prospects in gauge leptons and the anomalous magnetic moment of the muon, mediation models with vectorlike matters, Phys. Rev. D 85, Phys. Lett. 116B, 283 (1982). 095012 (2012). [8] J. Chakrabortty, S. Mohanty, and S. Rao, Nonuniversal [22] M. Endo, K. Hamaguchi, S. Iwamoto, K. Nakayama, and N. gaugino mass GUT models in the light of dark matter and Yokozaki, Higgs mass and muon anomalous magnetic LHC constraints, J. High Energy Phys. 02 (2014) 074. moment in the U(1) extended MSSM, Phys. Rev. D 85, [9] J. Chakrabortty, A. Choudhury, and S. Mondal, Nonuni- 095006 (2012). versal Gaugino mass models under the lamppost of muon [23] J. L. Evans, M. Ibe, S. Shirai, and T. T. Yanagida, A (g − 2), J. High Energy Phys. 07 (2015) 038. 125 GeV Higgs boson and muon g − 2 in more generic [10] R. Barbieri and L. Maiani, The muon anomalous magnetic gauge mediation, Phys. Rev. D 85, 095004 (2012). moment in broken supersymmetric theories, Phys. Lett. [24] M. Endo, K. Hamaguchi, S. Iwamoto, and T. Yoshinaga, 117B, 203 (1982). Muon g − 2 vs LHC in supersymmetric models, J. High [11] D. A. Kosower, L. M. Krauss, and N. Sakai, Low-energy Energy Phys. 01 (2014) 123. supergravity and the anomalous magnetic moment of the [25] S. Mohanty, S. Rao, and D. P. Roy, Reconciling the muon muon, Phys. Lett. 133B, 305 (1983). g − 2 and dark matter relic density with the LHC results in [12] T. C. Yuan, R. L. Arnowitt, A. H. Chamseddine, and P. Nath, nonuniversal gaugino mass models, J. High Energy Phys. 09 Supersymmetric electroweak effects on G-2 (mu), Z. Phys. (2013) 027. C 26, 407 (1984). [26] M. Ibe, T. T. Yanagida, and N. Yokozaki, Muon g − 2 and [13] J. C. Romao, A. Barroso, M. C. Bento, and G. C. Branco, 125 GeV Higgs in split-family supersymmetry, J. High Flavor violation in supersymmetric theories, Nucl. Phys. Energy Phys. 08 (2013) 067. B250, 295 (1985). [27] S. Akula and P. Nath, Gluino-driven radiative breaking, [14] J. L. Lopez, D. V. Nanopoulos, and X. Wang, Large (g − 2)- Higgs boson mass, muon g − 2, and the Higgs diphoton mu in SUð5Þ × Uð1Þ supergravity models, Phys. Rev. D 49, decay in supergravity unification, Phys. Rev. D 87, 115022 366 (1994). (2013). 115002-15 BELYAEV, KING, and SCHAEFERS PHYS. REV. D 97, 115002 (2018) [28] N. Okada, S. Raza, and Q. Shafi, Particle spectroscopy of [46] S. P. Martin, Nonuniversal gaugino masses and seminatural supersymmetric SU(5) in light of 125 GeV Higgs and muon supersymmetry in view of the Higgs boson discovery, Phys. g − 2 data, Phys. Rev. D 90, 015020 (2014). Rev. D 89, 035011 (2014). [29] M. Endo, K. Hamaguchi, T. Kitahara, and T. Yoshinaga, [47] A. Anandakrishnan and S. Raby, Yukawa Unification Probing bino contribution to muon g − 2, J. High Energy Predictions with Effective “Mirage” Mediation, Phys. Phys. 11 (2013) 013. Rev. Lett. 111, 211801 (2013). [30] G. Bhattacharyya, B. Bhattacherjee, T. T. Yanagida, and N. [48] M. A. Ajaib, SU(5) with nonuniversal gaugino masses, Int. Yokozaki, A practical GMSB model for explaining the J. Mod. Phys. A 33, 1850032 (2018). muon (g − 2) with gauge coupling unification, Phys. Lett. B [49] M. Dimou, S. F. King, and C. Luhn, Approaching minimal 730, 231 (2014). flavor violation from an SUð5Þ × S4 × Uð1Þ SUSY GUT, J. [31] I. Gogoladze, F. Nasir, Q. Shafi, and C. S. Un, Nonuniversal High Energy Phys. 02 (2016) 118. gaugino masses and muon g − 2, Phys. Rev. D 90, 035008 [50] M. Dimou, S. F. King, and C. Luhn, Phenomenological (2014). implications of an SUð5Þ × S4 × Uð1Þ SUSY GUT of [32] J. Kersten, J.-h. Park, D. Stöckinger, and L. VelascoSevilla, flavor, Phys. Rev. D 93, 075026 (2016). Understanding the correlation between ðg − 2Þμ and μ → eγ [51] B. D. Callen and R. R. Volkas, Large lepton mixing angles in the MSSM, J. High Energy Phys. 08 (2014) 118. from a 4 þ 1-dimensional SUð5Þ × Að4Þ domain-wall bra- [33] T. Li and S. Raza, Electroweak supersymmetry from the neworld model, Phys. Rev. D 86, 056007 (2012). generalized minimal supergravity model in the MSSM, [52] S. Antusch, S. F. King, and M. Spinrath, Spontaneous CP Phys. Rev. D 91, 055016 (2015). violation in A4 × SUð5Þ with constrained sequential domi- [34] W.-C. Chiu, C.-Q. Geng, and D. Huang, Correlation nance 2, Phys. Rev. D 87, 096018 (2013). between muon g − 2 and μ → eγ, Phys. Rev. D 91, [53] I. K. Cooper, S. F. King, and C. Luhn, A4 × SUð5Þ SUSY 013006 (2015). GUT of flavor with trimaximal neutrino mixing, J. High [35] M. Badziak, Z. Lalak, M. Lewicki, M. Olechowski, and Energy Phys. 06 (2012) 130. S. Pokorski, Upper bounds on sparticle masses from [54] I. K. Cooper, S. F. King, and C. Luhn, SUSY SU(5) with muon g − 2 and the Higgs mass and the complementarity singlet plus adjoint matter and A4 family symmetry, Phys. of future colliders, J. High Energy Phys. 03 (2015) 003. Lett. B 690, 396 (2010). [36] L. Calibbi, I. Galon, A. Masiero, P. Paradisi, and [55] F. Björkeroth, F. J. de Anda, I. de Medeiros Varzielas, and Y. Shadmi, Charged slepton flavor post the 8 TeV LHC: S. F. King, Towards a complete A4 × SUð5Þ SUSY GUT, J. A simplified model analysis of low-energy constraints High Energy Phys. 06 (2015) 141. and LHC SUSY searches, J. High Energy Phys. 10 [56] P. A. R. Ade et al. (Planck Collaboration), Planck 2013 (2015) 043. results. XVI. Cosmological parameters, Astron. Astrophys. [37] K. Kowalska, L. Roszkowski, E. M. Sessolo, and A. J. 571, A16 (2014). Williams, GUT-inspired SUSY and the muon g − 2 [57] E. Aprile et al. (XENON Collaboration), First Dark Matter anomaly: Prospects for LHC 14 TeV, J. High Energy Phys. Search Results from the XENON1T Experiment, Phys. Rev. 06 (2015) 020. Lett. 119, 181301 (2017). [38] F. Wang, W. Wang, and J. M. Yang, Reconcile muon [58] G. Aad et al. (ATLAS, CMS Collaboration), Combined g − 2 anomaly with LHC data in SUGRA with generalized Measurementpffiffiffi of the Higgs Boson Mass in pp Collisions at gravity mediation, J. High Energy Phys. 06 (2015) 079. s ¼ 7 and 8 TeV with the ATLAS and CMS Experiments, [39] J. Kawamura and Y. Omura, Study of dark matter physics in Phys. Rev. Lett. 114, 191803 (2015). nonuniversal gaugino mass scenario, J. High Energy Phys. [59] J. P. Lees et al. (BABAR Collaboration), Exclusive mea- 08 (2017) 072. surements of b → sγ transition rate and photon energy [40] A. Corsetti and P. Nath, Gaugino mass nonuniversality and spectrum, Phys. Rev. D 86, 052012 (2012). dark matter in SUGRA, strings and D-brane models, Phys. [60] S. Chatrchyan et al. (CMS Collaboration), Measurement of Rev. D 64, 125010 (2001). the B(s) to μþ μ− Branching Fraction and Search for B0 to [41] S. F. King, J. P. Roberts, and D. P. Roy, Natural dark matter μþμ− with the CMS Experiment, Phys. Rev. Lett. 111, in SUSY GUTs with nonuniversal gaugino masses, J. High 101804 (2013). Energy Phys. 10 (2007) 106. [61] W. Porod, SPheno, a program for calculating supersym- [42] U. Chattopadhyay, D. Das, and D. P. Roy, Mixed neutralino metric spectra, SUSY particle decays and SUSY particle dark matter in nonuniversal gaugino mass models, Phys. production at eþ e− colliders, Comput. Phys. Commun. Rev. D 79, 095013 (2009). 153, 275 (2003). [43] B. Ananthanarayan and P. N. Pandita, Sparticle mass spec- [62] W. Porod and F. Staub, SPheno 3.1: Extensions including trum in grand unified theories, Int. J. Mod. Phys. A 22, 3229 flavor, CP phases and models beyond the MSSM, Comput. (2007). Phys. Commun. 183, 2458 (2012). [44] S. Bhattacharya, A. Datta, and B. Mukhopadhyaya, [63] G. Belanger, F. Boudjema, A. Pukhov, and A. Semenov, Nonuniversal gaugino masses: A signal-based analysis micrOMEGAs_3: A program for calculating dark for the Large Hadron Collider, J. High Energy Phys. 10 matter observables, Comput. Phys. Commun. 185, 960 (2007) 080. (2014). [45] S. P. Martin, Nonuniversal gaugino masses from nonsinglet [64] G. Pasztor, Search for gauginos and gauge mediated SUSY F terms in nonminimal unified models, Phys. Rev. D 79, breaking scenarios at LEP, Proc. Sci., HEP20052006 (2006) 095019 (2009). 346 [arXiv:hep-ex/0512054]. 115002-16 MUON g − 2 AND DARK MATTER SUGGEST … PHYS. REV. D 97, 115002 (2018) [65] D. Dercks, N. Desai, J. S. Kim, K. Rolbiecki, J. Tattersall, Collaboration), A modular framework for fast simulation and T. Weber, CheckMATE 2: From the model to the limit, of a generic collider experiment, J. High Energy Phys. 02 Comput. Phys. Commun. 221, 383 (2017). (2014) 057. [66] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, [69] G. Aad et al. (ATLAS Collaboration), Search for direct O. Mattelaer, H.-S. Shao, T. Stelzer, P. Torrielli, and M. production of charginos and neutralinos in eventspffiffiffi with three Zaro, The automated computation of tree-level and next-to- leptons and missing transverse momentum in s ¼ 8 TeV leading order differential cross sections, and their matching pp collisions with the ATLAS detector, J. High Energy to parton shower simulations, J. High Energy Phys. 07 Phys. 04 (2014) 169. (2014) 079. [70] ATLAS Collaboration, Search for supersymmetry with two [67] T. Sjostrand, S. Mrenna, and P. Z. Skands, A brief intro- and three leptonspffiffiffi and missing transverse momentum in the duction to PYTHIA 8.1, Comput. Phys. Commun. 178,852 final state at s ¼ 13 TeV with the ATLAS detector, (2008). CERN Report No. ATLAS-CONF-2016-096, 2016. [68] J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaitre, A. Mertens, and M. Selvaggi (DELPHES 3 115002-17