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Smuon in the NMSSM confronted with the muon g–2 anomaly and SUSY searches

  • Motivated by recent supersymmetry (SUSY) search results, which prefer most SUSY particles to be heavy, and the muon g–2 anomaly, which prefers colorless SUSY particles to be light, we explore the status of a light smuon (the SUSY partner of a left-handed muon lepton) in the next-to-minimal supersymmetric standard model (NMSSM). Assuming colored SUSY particles to be heavy, and considering numerous experimental constraints, including muon g-2, SUSY searches, and dark matter, we scan the parameter space in the NMSSM with Z3-symmetry and check the status of colorless SUSY particles and their possible mass order, paying special attention to the smuon. After calculations and discussions, we find that the surviving samples can be divided into several scenarios, where the mass region and decay information of the smuon are given. Overall, the smuon mass can be approximately 0.1~1.8 TeV. These results may be useful for smuon searches at the LHC and future colliders.
  • In April 2021, a new result for the muon anomalous magnetic moment (muong2 or δaμ) was reported at Fermilab [1], revealing an exciting disparity compared to the standard model (SM) prediction. Combined with the previous result at Brookhaven [2], the discrepancy can be 4.2σ [1],

    δaμaexμaSMμ=(25.1±5.9)×1010,

    (1)

    where the combined experimental result aexμ [1] and SM prediction aSMμ [325] are given by

    aexμ=(11659206.1±4.1)×1010,

    (2)

    aSMμ=(11659181.0±4.3)×1010.

    (3)

    It is widely believed that the SM is not a complete description of nature. Besides the muong2 anomaly, the SM also cannot interpret problems such as hierarchy, grand unification, dark matter (DM), and baryogenesis. To interpret these problems, researchers have proposed many theories beyond the SM (BSM), among which supersymmetry (SUSY) is the most fascinating [2629]. SUSY assumes that every SM particle has a SUSY partner whose spin differs from that of the corresponding SM particle by half. These extra SUSY particles can significantly contribute to solving problems and anomalies, including muong2. The SUSY effects on muong2 were first calculated in the 1980s [3034] and comprehensively described in Refs. [3537]. In recent years, especially after the new result released at Fermilab, there have been numerous papers on interpreting the muong2 anomaly in the minimal supersymmetric SM (MSSM) and its extensions, such as the next-to MSSM (NMSSM) [3869]. In the MSSM and NMSSM, the main contributions to δaμ originate from chargino-sneutrino loops and neutralino-smuon loops. Thus, light SUSY particles, such as smuons, sneutrinos, charginos, and neutralinos, are generally required to interpret the distinct muong2 anomaly.

    However, the null results from the search for SUSY at the LHC in recent years have set strong constraints on SUSY particles. For gluino and the first two-generation squarks, the low mass bounds can be over 2 TeV [7072]. Even for colorless charginos and sleptons, including smuons, the low mass bounds can be hundreds of GeV in simple models, except for compressed-spectrum scenarios [7378]. Recent searches for smuons by the ATLAS collaboration with 139 fb1of data have demonstrated that the mass bound can be approximately 600 GeV, assuming that a smuon decays100% into a muon plus the lightest neutralino [77]. Thus, for constraints to SUSY models, the direct SUSY searches at the LHC and the muong2 anomaly may be at odds with each other. In this study, we consider the status of smuons in the NMSSM confronted with muong2 and SUSY searches and investigate their implications for DM.

    The added singlet scalar in the NMSSM and its partner singlino can introduce different phenomenology from those in the MSSM. In the Higgs sector, mixing between light singlet and doublet scalars can change the production and decay of the SM-like Higgs boson. In the neutralino sector, a light singlino-like neutralino can be a good candidate for DM and can change the decay of SUSY particles. Thus, the additional parts in the NMSSM can change the status of MSSM confronting Higgs data, DM detection, and SUSY searches and indirectly affect its muong2. Moreover, the lightest neutralino with a gaugino or higgsino component can get into neutralino-smuon loops and affect muong2 directly. In this study on the NMSSM, to obtain a more general result, we take the SUSY scale as the input scale of parameters, which differs from our former studies on the semi-constrained NMSSM [5355]. To ensure that surviving samples satisfy all types of experimental constraints, we impose them one by one (with the entire Higgs data as one), different from the likelihood method in most NMSSM references (e.g., Refs. [4245]).

    The rest of this paper is organized as follows. In Sec. II, we introduce the NMSSM, briefly presenting relevant analytic calculations onmuong2. In Sec. III, we present the numerical calculations and discussions. Finally, we summarize and draw our principal conclusions in Sec. IV.

    In contrast to the manual and large μ parameter used in the MSSM, the μ parameter in the NMSSM is effective and generated naturally when the additional singlet superfieldˆS obtains a vacuum expected value (VEV) [7981]. In the NMSSM of Z3-invariant vision, the superpotential can be expressed as

    WNMSSM=WMSSMμλˆS+κ3ˆS3,

    (4)

    where λ and κ are dimensionless couplings, WMSSM is the superpotential in the MSSM,

    WMSSM=μˆHuˆHd+yuˆuˆQˆHuydˆdˆQˆHdyeˆeˆLˆHd,

    (5)

    and in terms including quarks or leptons, the generation indexes being summed over are omitted.

    After electroweak symmetry breaking, several SUSY particles with the same quantum numbers mix, generating an equal number of mass eigenstates. The SUSY partners of left- and right-handed muon leptons have spin 0, denoted by ˜μL and ˜μR, both known as smuons. In the {˜μL,˜μR} basis, the smuon-mass matrix can be written as

    M2˜μ=(M2L2+(sin2θW12)m2Zcos2βmμ(AE2μtanβ)mμ(AE2μtanβ)M2E2m2Zsin2θWcos2β),

    (6)

    where ML2,E2 and AE2 are the soft masses of left- and right-handed smuons and the trilinear couplings of smuons, respectively, and when ML2,E2mZ,mμAE2 and mμμtanβ, the mixing between ˜μL and ˜μR is negligible. Because neutrinos are left-handed and massless in the NMSSM, the mass of the muon neutrino's partner muon sneutrino m˜ν is related to the left-handed smuon mass by

    m2˜ν=M2L+12m2Zcos2β.

    (7)

    When MLmZ, the masses are approximately equal.

    The SUSY partners of the gauge bosons W1,2,3,B0, doublet Higgs, and singlet scalars are called winos, binos, higgsinos, and singlinos, respectively, and all have spin 1/2 and are written with a tilde. Among them, the charged ones mix into two pairs of charginos, and the neutral ones mix to form five neutralinos. In the {˜W±,˜H±} base, the chargino-mass matrix can be written as

    M˜χ±=(M22mWsinβ2mWcosβμ).

    (8)

    In the {˜B0,˜W0,˜H0u,˜H0d,˜S} base, the neutralino-mass matrix can be written as

    M˜χ0=(M10mZcosβsinθWmZsinβsinθW00M2mZcosβcosθWmZsinβcosθW0mZcosβsinθWmZcosβcosθW0μλvdmZsinβsinθWmZsinβcosθWμ0λvu00λvdλvu2κμ/λ),

    (9)

    where vu and vd are the VEVs of Hu and Hd, respectively, with vu/vd=tanβ.

    The SUSY effects on muong2 at the one-loop level are mainly from chargino-sneutrino loops and neutralino-smuon loops, with summations performed over all corresponding mass eigenstates. The contributions of these two types of loops can be written as [35]

    δn=mμ16π2i,m[mμ12m2˜μm(|nLim|2+|nRim|2)FN1(xim)+m˜χ0i3m2˜μmRe(nLimnRim)FN2(xim)],

    (10)

    δc=mμ16π2k[mμ12m2˜νμ(|cLk|2+|cRk|2)FC1(xk)+2m˜χ±k3m2˜νμRe(cLkcRk)FC2(xk)],deltac

    (11)

    respectively, where the variables xim=m2˜χ0i/m2˜μmand xk=m2˜χ±k/m2˜νμ, with i=1,2,3,4,5 denoting five mass-eigenstate neutralino labels, and k=1,2 and m=1,2 denoting two mass-eigenstate chargino and smuon labels, respectively. Functions depending on xim,xk, which originate from loop integrals and are normalized, can be written as [35]

    FN1(x)=2(1x)4(16x+3x2+2x36x2lnx),

    (12)

    FN2(x)=3(1x)3(1x2+2xlnx),

    (13)

    FC1(x)=2(1x)4(2+3x6x2+x3+6xlnx),

    (14)

    FC2(x)=32(1x)3(34x+x2+2lnx).

    (15)

    With these functions, FN,C1,2(1)=1 corresponds to the case in which SUSY particles degenerate. In addition, the corresponding coefficients are written as

    nRim=2g1Ni1Xm2+yμNi3Xm1,

    (16)

    nLim=12(g2Ni2+g1Ni1)Xm1yμNi3Xm2,

    (17)

    cRk=yμUk2,

    (18)

    cLk=g2Vk1,

    (19)

    where Nij, {Ukl,Vkl}, and Xmn are the mixing matrix of neutralinos, charginos, and smuons, respectively, defined as

    NM˜χ0N=Diag{m˜χ01,m˜χ02,m˜χ03,m˜χ04},

    (20)

    UM˜χ±V=Diag{m˜χ±1,m˜χ±2},

    (21)

    XM2˜μX=Diag{m2˜μ1,m2˜μ2}.

    (22)

    Finally, g20.66 and g10.36 are the SU(2)L and U(1)Y gauge couplings, respectively, and yμg1,2 is the muon Yukawa coupling.

    Considering that the SUSY particles in the loops, which are the neutralinos ˜χ01,2,3,4,5 and smuons ˜μ1,2, or the charginos ˜χ±1,2 and muon sneutrino ˜νμ, approximately have the same masses, m˜χ0m˜μ or m˜χ±m˜νμ, their contributions to muong2 can be approximately written as [36]

    δn1192π2m2μm˜χ0m˜μ(g21g22)tanβ,

    (23)

    δc132π2m2μm˜χ±m˜νμg22tanβ.

    (24)

    In this study, we first scan the parameter space of the NMSSM with Z3-symmetry to obtain surviving samples under corresponding theoretical and experimental constraints. To focus on the light smuon, a light colorless SUSY particle preferred by the muong2 anomaly, we assume colored SUSY particles and heavy Higgs to be heavy and fix them to 5 TeV :

    MA,M3,MQi,MUi,MDi=5 TeV,AUi,ADi=0 TeV,

    (25)

    where MA,M3,MQi,MUi,MDi are the soft masses of the heavy Higgs, gluino, left-handed squarks, right-handed up-type squarks, and right-handed down-type squarks, respectively, and AUi,ADi are the trilinear couplings of up- and down-type squarks, respectively, with the generation index i=1,2,3. The other required parameters correlated with light and colorless SUSY particles are set as

    0<λ,|κ|<0.8,1<tanβ<100,0<μ,M1,M2,MP<1 TeV,0<MLi,MEi,|AEi|<10 TeV.

    (26)

    To considerably differ from former studies that used ˜τ1 as the lightest slepton, we also manually require m˜τ1>m˜μ1.

    The model spectrum, including masses and decay information, is calculated with NMSSMTools-5.5.4 [8284]. The corresponding constraints we consider in our scan are listed briefly as follows:

    ● Theoretical constraints from a stable vacuum (the effective scalar potential gets its least value when all scalar fields equal to their VEVs) and the inexistent Landau pole below the GUT scale [82, 83, 85].

    ● LEP constraints on chargino and slepton masses heavier than approximately 100 GeV.

    ● Flavor constraints, such as rare B-meson decays and the mass differences Δmdand Δms [8689].

    ● A Higgs boson of 122128 GeV with signal predictions consistent with Higgs data at the LHC [9092].

    ● Constraints from searches for additional Higgs and exotic decays of SM-like Higgs, imposed with HiggsBounds-5.10.1 [9599].

    ● Upper bounds of the DM relic density Ωh20.131 from WMAP/Planck [100, 101], with the relevant quantities calculated using micrOMEGAs 5.0 [102105].

    ● Constraints on direct searches for DM, the spin-independent case by XENON1T [106], and the spin-dependent case by LUX [107], XENON1T [108], and PICO-60 [109], where the original values are rescaled by Ω/Ω0 accordingly.

    ● The constraints from muong2 at the 2σ level, where we use the combined experimental value aexμ=(11659206.1±4.1)×1010 [1] and calculate the SM value aSMμ without the Higgs contribution, considering that the NMSSM contains a SM-like Higgs. Including the theoretical error on SUSY contributions, we obtain the range of δaμaexμaSMμ as (6.145.0)×1010 at the 2σ level.

    Moreover, in imposing constraints from SUSY searches, we exploit SModelS 2.1.1 [110118] with official database version 2.1.0 [119]. To focus on the status of the smuon, we pay special attention to the constraints on smuon searches in Refs. ATLAS-SUSY-2018-32 [77] and CMS-SUS-17-009 [78]. In these analyses of smuons, they were assumed to be produced in pairs and 100 % decay into a muon lepton and the lightest neutralino; thus, the final state is composed of two opposite-charge and same-flavor leptons (dimuon) and a large missing transverse momentum pT. However, no significant excess over the SM background was recorded in either report. The ATLAS analysis was based on 139 fb1 of data at the 13 TeV LHC, and smuon masses up to approximately 600 GeV were excluded with the massless lightest neutralino. For consistency with these analyses, we employ Resummino 3.0 [120126] to calculate the smuon production at the 13-TeV LHC at the next-to leading order (NLO).

    pp˜μ+L˜μL,pp˜μ+R˜μR,

    (27)

    where ˜μL and ˜μR are the SUSY partners of the left- and right-handed muon leptons, respectively, and the cross-section of the former is times larger than the latter. Thus, ˜μL is more constrained than ˜μR, and we mainly study ˜μL, denoting it as a muon or ˜μ in this paper. Because this is a real model NMSSM, we calculate the real branching ratios, including smuon decay into a muon lepton and the lightest neutralino, that is, Br(˜μ˜χ01+μ). We constrain our samples by requiring the cross-section timing branching ratio to be below the corresponding exclusion curves from the ATLAS and CMS collaborations.

    Finally, we obtain the surviving samples that satisfy all the above constraints and present them in the following figures.

    To study the dependence of muong2 on smuon mass, we display the surviving samples in Fig. 1, from which we determine the following facts:

    Figure 1

    Figure 1.  (color online) Surviving samples projected in the δn versus δc (left), m˜μμ versus m˜χ±1 (middle), and m˜χ01 versus m˜μ (right) planes, where ˜μ is the SUSY partner of the left-handed muon lepton, δaμ is the SUSY contribution to muong2, and δc and δn are the chargino-sneutrino and neutralino-smuon contributions to δaμ, respectively. In all the planes, colors indicate δaμ, and samples with larger δaμ are projected on top of smaller ones.

    ● The muong2 anomaly can be interpreted within 1σ. For 1σ samples, muon sneutrinos and left-handed smuons are lighter than 1000 GeV , the light charginos are lighter than 900 GeV, and the lightest neutralinos are lighter than 600 GeV.

    ● For most surviving samples, m˜χ±1m˜χ01 and m˜μm˜νμ; thus, their distributions in the middle and right planes have almost the same shapes. We verify that for most of these samples, the lightest neutralinos are wino- or higgsino-dominated, the same as the light chargino. For the other samples, m˜χ±1>m˜χ01, and the lightest neutralinos are bino- or singlino-dominated.

    ● The SUSY contribution tomuong2 is approximately equal to the sum of chargino-sneutrino and neutralino-smuon loops (δaμδc+δn), and for most samples, the former dominates (δc>δn), even when the lightest neutralinos and smuons are very light. From Eqs. (23) and (24), we know that this makes sense because g22/32(g21g22)/192. Furthermore, we check that the contributions are both proportional to tanβ and verify that δn can be both positive and negative because of the different masses of the five neutralinos and two smuons.

    To study the constraints on smuon searches at the LHC, we display the surviving samples in Fig. 2, where the solid and dotted curves denote the corresponding exclusion limits at the 95% confidence level from the ATLAS [77] and CMS collaborations [78]. From this figure we can find that

    Figure 2

    Figure 2.  (color online) Surviving samples projected in the m˜χ01 versus m˜μ planes, where ˜μ is the SUSY partner of the left-handed muon lepton. Colors indicate the branching ratios Br(˜μ˜χ01+μ) (left), the μ (middle), and M2 parameters (right). The dashed line of m˜χ01=m˜μ indicates that the smuon and ˜χ01 are mass-degenerate, and the solid and dotted curves are the exclusion limits at the 95 % CL from direct searches for smuons given by the ATLAS [77] and CMS collaborations [78], respectively. Samples with larger Br(˜μ˜χ01+μ) are projected on top of smaller ones.

    ● For surviving samples below the exclusion curve by ATLAS, all the branching ratios of Br(˜μ˜χ01+μ) are lower than 50 % because the large values are excluded in the experiments. We check that for these surviving samples, the lightest neutralinos are either higgsino-dominated, with masses approximating to the μ parameter, or wino-dominated, with masses approximating to the M2 parameter. Thus, m˜χ±1m˜χ01min{μ,M2}, and the smuon also decays with a sizable branching ratio to a light chargino plus muon sneutrino.

    ● For surviving samples with a mass-degenerate smuon and ˜χ01, all the branching ratios Br(˜μ˜χ01+μ) are nearly 100 % because the current experimental results of direct searches are powerless in the compressed SUSY spectrum.

    To illustrate the implication of light smuons for DM, we display the surviving samples in Fig. 3, where N211 denotes the bino component in the LSP dark matter ˜χ01, and N212denotes the corresponding wino component. From this figure, we can learn the following:

    Figure 3

    Figure 3.  (color online) Surviving samples projected in the m˜χ01 versus m˜μ planes, where ˜μ is the SUSY partner of the left-handed muon lepton. Colors indicate N211 (left), N212 (middle), and Ωh2 (right), where N211 and N212 indicate the ratios of the bino and wino components in ˜χ01, respectively, and Ωh2 indicates the relic density of the LSP dark matter ˜χ01. Samples with larger Ωh2 are projected on top of smaller ones.

    ● For most of the surviving samples with right relic density or Z- or h1-funnel annihilation, the LSP DM ˜χ01 is bino-dominated. Some others are singlino-dominated.

    ● For most of the surviving samples with a mass-degenerate smuon and ˜χ01, the LSP DM ˜χ01 is bino-dominated, and we check that the dominating annihilation mechanism is slepton annihilation. These samples constitute a large part of samples with right relic density only with the LSP ˜χ01.

    ● For all the surviving samples with wino-dominated ˜χ01, the relic density is insufficient because of mass-degenerate charginos; however, it is larger than that of higgsino-dominated-˜χ01samples (in all three planes, samples with largerΩh2 are projected on top of smaller ones, and in the middle plane, wino-dominated-˜χ01 samples are covered by higgsino-dominated-˜χ01samples).

    In addition, we also list detailed information on six benchmark points for further study in Table 1.

    Table 1

    Table 1.  Detailed information on six benchmark points, where N2i1, N2i2, N2i3+N2i4, and N2i5 indicate the ratios of the bino, wino, higgsino, and singlino components in the neutralinos ˜χ0i, respectively. Moreover, ˜μL (˜μR) is the SUSY partner of the left-handed (right-handed) muon lepton, and ˜μLis the smuon that we investigate in this study.
    BP1 BP2 BP3 BP4 BP5 BP6
    λ0.08030.00150.03670.02600.1870.0363
    κ0.667–0.6630.553–0.0047–0.606–0.630
    tanβ706946135543
    μ796567440310699479
    M14643460931340198
    M2689448941150337890
    ML2471709119143638217
    ME2640148012503682160575
    AE277–1190–150032–5245.0
    m˜χ01/GeV4613459115336196
    m˜χ02/GeV712463449150361489
    m˜χ±1/GeV712463449151361488
    m˜χ±2/GeV8466101010346727957
    N2110.990.990.990.000.980.99
    N2120.000.000.000.000.010.00
    N213+N2140.010.010.010.000.010.01
    N2150.000.000.001.000.000.00
    N2210.000.000.010.000.020.01
    N2220.760.810.010.870.960.02
    N223+N2240.240.190.980.130.020.97
    m˜μL/GeV470709119143638217
    m˜μR/GeV640148012503682160575
    m˜νμ/GeV46470592121633203
    Br(˜μ˜χ01+μ)1.000.281.001.000.071.00
    Br(˜μ˜χ02+μ)0.000.240.000.000.340.00
    Br(˜μ˜χ±1+νμ)0.000.440.000.000.590.00
    δaμ[×1010]21.822.828.241.720.524.3
    Ωh20.1260.1200.1150.1200.1090.117
    ph0.9230.9280.8490.9280.9200.920
    DownLoad: CSV
    Show Table

    In this study, motivated by recent SUSY search results, which prefer most SUSY particles to be heavy, and the muong2 anomaly, which prefers colorless SUSY particles to be light, we explore the status of the smuon (the SUSY partner of the left-handed muon lepton) in the NMSSM. Assuming that colored SUSY particles are heavy, and considering numerous experimental constraints, including the muong2, SUSY searches, and DM, we scan the parameter space in the NMSSM with Z3-symmetry and check the status of colorless SUSY particles and their possible mass order, paying special attention to the status of a smuon confronted withmuong2 and direct SUSY searches. We also investigate their implication for DM.

    We draw the following conclusions regarding the smuon, muong2, SUSY searches, and DM in the NMSSM:

    ● The dominated SUSY contributions to muong2 originate from chargino-sneutrino loops; however, the muong2 anomaly can also constrain the mass of smuons seriously because of the mass-degenerate relationship between smuons and muon sneutrinos. To interpret the muong2 anomaly at the 1σ (2σ) level, the smuon must be lighter than 1 TeV (1.8 TeV).

    ● When ˜χ01 is wino- or higgsino-dominated, the smuon and muon sneutrino, ˜χ±1 and ˜χ01, respectively, are usually mass-degenerate. Thus, the branching ratio Br(˜μ˜χ01+μ) is suppressed to lower than 50 %, and the smuon can escape from direct searches with low mass, e.g., 300 GeV.

    ● When the smuon and ˜χ01 are mass-degenerate, the smuon can be as light as 200 GeV, whereas the ˜χ01is usually bino-dominated or sometimes singlino-dominated, and its relic density can most likely reach the observed value. The dominating annihilation mechanism is slepton annihilation.

    Moreover, we emphasize again that this study is performed in the NMSSM with Z3 symmetry, which includes no large free parameters in the superpotential but may cause the so-called 'domain wall' problem in cosmology. This problem can be solved by introducing Z3-breaking terms, such as ξm3sS [127]. This term may have an effect on the singlino sector and DM phenomenology when it is singlino-dominated. Because the chargino-sneutrino contribution to muong2 dominates in our study, and κ/λ is arbitrary in the singlino or DM sector, the Z3-breaking terms from the singlet field have little effect on the mass region of the smuon.

    Note added: The uncertainty on the SM theoretical value of muong2 is dominated by hadronic vacuum polarization (HVP), which can be calculated using the data-driven method, as quoted in the experimental report of the muong2 collaboration [1] and this paper, or the lattice method. In 2020, the BMW collaboration released their lattice result for the HVP contribution [128], which was considerably different from the quoted data-driven result. Recently, another group released a new lattice result [129], independently showing agreement with the 2020 BMW value. Employing the two lattice results for the HVP contribution, the muong2 anomaly can change to δaμ=10.4±7.0×1010, with the significance changing to 1.5σ. We verified that there are still samples in the smuon mass region as low as 0.1 TeV that can satisfy thisδaμ value at the 2σ level, and the surviving samples can have smuon masses higher than 1.8 TeV.

    The experimental uncertainty of Higgs mass is only 0.14 GeV, but we have considered a dominated theoretical uncertainty from the calculation of Higgs mass in the NMSSM. We calculated the Higgs signals and impose their constraints with \begin{document}$\textsf{NMSSMTools-5.5.4}$\end{document}

    , and calculate a global p-value (\begin{document}$ p_h $\end{document}
    ) for the 111 datasets of Higgs signals with \begin{document}$\textsf{HiggsSignals-2.6.2}$\end{document}
    [93, 94].

    [1] B. Abi et al. (Muon g-2 Collaboration), Phys. Rev. Lett. 126, 141801 (2021), arXiv:2104.03281[hep-ex doi: 10.1103/PhysRevLett.126.141801
    [2] G. W. Bennett et al. (Muon g-2 Collaboration), Phys. Rev. D 73, 072003 (2006), arXiv:hep-ex/0602035 doi: 10.1103/PhysRevD.73.072003
    [3] T. Aoyama et al., Phys. Rept. 887, 1 (2020), arXiv:2006.04822[hep-ph doi: 10.1016/j.physrep.2020.07.006
    [4] T. Aoyama, M. Hayakawa, T. Kinoshita, et al., Phys. Rev. Lett. 109, 111808 (2012), arXiv:1205.5370[hep-ph doi: 10.1103/PhysRevLett.109.111808
    [5] T. Aoyama, T. Kinoshita, and M. Nio, Atoms 7, 28 (2019) doi: 10.3390/atoms7010028
    [6] A. Czarnecki, W. J. Marciano, and A. Vainshtein, Phys. Rev. D 67, 073006 (2003), [Erratum: Phys. Rev. D 73, 119901 (2006)], arXiv: hep-ph/0212229
    [7] C. Gnendiger, D. Stöckinger, and H. Stöckinger-Kim, Phys. Rev. D 88, 053005 (2013), arXiv:1306.5546[hep-ph doi: 10.1103/PhysRevD.88.053005
    [8] M. Davier, A. Hoecker, B. Malaescu et al., Eur. Phys. J. C 77, 827 (2017), arXiv:1706.09436[hep-ph doi: 10.1140/epjc/s10052-017-5161-6
    [9] A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 97, 114025 (2018), arXiv:1802.02995[hep-ph doi: 10.1103/PhysRevD.97.114025
    [10] G. Colangelo, M. Hoferichter, and P. Stoffer, JHEP 2019, 006 (2019), arXiv:1810.00007[hep-ph doi: 10.1007/JHEP02(2019)006
    [11] M. Hoferichter, B.-L. Hoid, and B. Kubis, JHEP 2019, 137 (2019), arXiv:1907.01556[hep-ph doi: 10.1007/JHEP08(2019)137
    [12] M. Davier, A. Hoecker, B. Malaescu et al., Eur. Phys. J. C 80, 241 (2020), [Erratum: Eur. Phys. J. C 80, 410 (2020)], arXiv: 1908.00921
    [13] A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 101, 014029 (2020), arXiv:1911.00367[hep-ph doi: 10.1103/PhysRevD.101.014029
    [14] A. Kurz, T. Liu, P. Marquardet al., Phys. Lett. B 734, 144 (2014), arXiv:1403.6400[hep-ph doi: 10.1016/j.physletb.2014.05.043
    [15] K. Melnikov and A. Vainshtein, Phys. Rev. D 70, 113006 (2004), arXiv:hep-ph/0312226 doi: 10.1103/PhysRevD.70.113006
    [16] P. Masjuan and P. Sanchez-Puertas, Phys. Rev. D 95, 054026 (2017), arXiv:1701.05829[hep-ph doi: 10.1103/PhysRevD.95.054026
    [17] G. Colangelo, M. Hoferichter, M. Procura et al., JHEP 04, 161 (2017), arXiv:1702.07347[hep-ph
    [18] M. Hoferichter, B.-L. Hoid, B. Kubis et al., JHEP 2018, 141 (2018), arXiv:1808.04823[hep-ph doi: 10.1007/JHEP10(2018)141
    [19] A. Gérardin, H. B. Meyer, and A. Nyffeler, Phys. Rev. D 100, 034520 (2019), arXiv:1903.09471[hep-lat doi: 10.1103/PhysRevD.100.034520
    [20] J. Bijnens, N. Hermansson-Truedsson, and A. Rodríguez-Sánchez, Phys. Lett. B 798, 134994 (2019), arXiv:1908.03331[hep-ph doi: 10.1016/j.physletb.2019.134994
    [21] G. Colangelo, F. Hagelstein, M. Hoferichter et al., JHEP 2020, 101 (2020), arXiv:1910.13432[hep-ph doi: 10.1007/JHEP03(2020)101
    [22] T. Blum, N. Christ, M. Hayakawa et al., Phys. Rev. Lett. 124, 132002 (2020), arXiv:1911.08123[hep-lat doi: 10.1103/PhysRevLett.124.132002
    [23] G. Colangelo, M. Hoferichter, A. Nyffeler et al., Phys. Lett. B 735, 90 (2014), arXiv:1403.7512[hep-ph doi: 10.1016/j.physletb.2014.06.012
    [24] M. Davier, A. Hoecker, B. Malaescu et alEur. Phys. J. C 71, 1515 (2011), [Erratum: Eur.Phys.J.C 72, 1874 (2012)], arXiv: 1010.4180
    [25] H. Terazawa, Prog. Theor. Phys. 39, 1326 (1968) doi: 10.1143/ptp/39.5.1326
    [26] P. Fayet, Phys. Lett. B 64, 159 (1976) doi: 10.1016/0370-2693(76)90319-1
    [27] P. Fayet, Phys. Lett. B 69, 489 (1977) doi: 10.1016/0370-2693(77)90852-8
    [28] H. E. Haber and G. L. Kane, Phys. Rept. 117, 75 (1985) doi: 10.1016/0370-1573(85)90051-1
    [29] S. P. Martin, Adv. Ser. Direct. High Energy Phys. 18, 1 (1998), arXiv:hep-ph/9709356 doi: 10.1142/9789812839657_0001
    [30] P. Fayet, Phys. Lett. B 84, 416 (1979) doi: 10.1016/0370-2693(79)91229-2
    [31] P. Fayet, Ettore Majorana Int. Sci. Ser. Phys. Sci. 7, 587 (1980)
    [32] J. A. Grifols and A. Mendez, Phys. Rev. D 26, 1809 (1982) doi: 10.1103/PhysRevD.26.1809
    [33] J. R. Ellis, J. S. Hagelin, and D. V. Nanopoulos, Phys. Lett. B 116, 283 (1982) doi: 10.1016/0370-2693(82)90343-4
    [34] R. Barbieri and L. Maiani, Phys. Lett. B 117, 203 (1982) doi: 10.1016/0370-2693(82)90547-0
    [35] T. Moroi, Phys. Rev. D 53, 6565 (1996), arXiv:hep-ph/9512396 doi: 10.1103/PhysRevD.53.6565
    [36] S. P. Martin and J. D. Wells, Phys. Rev. D 64, 035003 (2001), arXiv:hep-ph/0103067 doi: 10.1103/PhysRevD.64.035003
    [37] D. Stockinger, J. Phys. G 34, R45 (2007), arXiv:hep-ph/0609168 doi: 10.1088/0954-3899/34/2/R01
    [38] P. Athron, C. Balázs, D. H. Jacob et al., JHEP 2021, 080 (2021), arXiv:2104.03691[hep-ph doi: 10.1007/JHEP09(2021)080
    [39] Q. Shafi and C. S. Ün, Sparticle Spectroscopy at LHC-Run3 and LSP Dark Matter in light of Muon g-2, (2021), arXiv: 2107.04563
    [40] S. Li, Y. Xiao, and J. M. Yang, Eur. Phys. J. C 82, 276 (2021) doi: 10.1140/epjc/s10052-022-10242-y
    [41] S. Li, Y. Xiao, and J. M. Yang, Nucl. Phys. B 974, 115629 (2022), arXiv:2108.00359[hep-ph doi: 10.1016/j.nuclphysb.2021.115629
    [42] Z. Li, G.-L. Liu, F. Wang et al., JHEP 2021, 219 (2021) doi: 10.1007/JHEP12(2021)219
    [43] J. Cao, J. Lian, Y. Pan et al., JHEP 2021, 175 (2021), arXiv:2104.03284[hep-ph doi: 10.1007/JHEP09(2021)175
    [44] F. Wang, L. Wu, Y. Xiao et al., Nucl. Phys. B 970, 115486 (2021), arXiv:2104.03262[hep-ph doi: 10.1016/j.nuclphysb.2021.115486
    [45] M. Abdughani, Y.-Z. Fan, L. Feng et al., Sci. Bull. 66, 2170 (2021), arXiv:2104.03274[hep-ph doi: 10.1016/j.scib.2021.07.029
    [46] C. Han, (2021), Muon g-2 and CP violation in MSSM, arXiv: 2104.03292
    [47] P. Cox, C. Han, and T. T. Yanagida, Phys. Rev. D 104, 075035 (2021), arXiv:2104.03290[hep-ph doi: 10.1103/PhysRevD.104.075035
    [48] W. Ahmed, I. Khan, J. Li et al., Phys. Lett. B 827, 136879 (2022) doi: 10.1016/j.physletb.2022.136879
    [49] S. Iwamoto, T. T. Yanagida, and N. Yokozaki, Phys. Lett. B 823, 136768 (2021), arXiv:2104.03223[hep-ph doi: 10.1016/j.physletb.2021.136768
    [50] M.-D. Zheng and H.-H. Zhang, Phys. Rev. D 104, 115023 (2021), arXiv:2105.06954[hep-ph doi: 10.1103/PhysRevD.104.115023
    [51] S.-M. Zhao, L.-H. Su, X.-X. Dong et al., JHEP 2022, 101 (2022) doi: 10.1007/JHEP03(2022)101
    [52] L.-H. Su, S.-M. Zhao, X.-X. Dong et al., Eur. Phys. J. C 81, 433 (2021), arXiv:2012.04824[hep-ph doi: 10.1140/epjc/s10052-021-09219-0
    [53] K. Wang and J. Zhu, JHEP 2020, 078 (2020), arXiv:2002.05554[hep-ph doi: 10.1007/JHEP06(2020)078
    [54] K. Wang and J. Zhu, Phys. Rev. D 101, 095028 (2020), arXiv:2003.01662[hep-ph doi: 10.1103/PhysRevD.101.095028
    [55] K. Wang, F. Wang, J. Zhu et al., Chin. Phys. C 42, 103109 (2018), arXiv:1811.04435[hep-ph doi: 10.1088/1674-1137/42/10/103109
    [56] M. Badziak and K. Sakurai, JHEP 2019, 024 (2019), arXiv:1908.03607[hep-ph doi: 10.1007/JHEP10(2019)024
    [57] M. Abdughani, K.-I. Hikasa, L. Wu et al., JHEP 2019, 095 (2019), arXiv:1909.07792[hep-ph doi: 10.1007/JHEP11(2019)095
    [58] F. Wang, K. Wang, J. M. Yang et al., JHEP 2018, 041 (2018), arXiv:1808.10851[hep-ph doi: 10.1007/JHEP12(2018)041
    [59] A. Kobakhidze, M. Talia, and L. Wu, PoS EPS-HEP2017, 343 (2017), https://pos.sissa.it/314/343/pdf
    [60] F. Wang, W. Wang, and J. M. Yang, Phys. Rev. D 96, 075025 (2017), arXiv:1703.10894[hep-ph doi: 10.1103/PhysRevD.96.075025
    [61] M. Badziak, Z. Lalak, M. Lewicki et al., JHEP 2015, 003 (2015), arXiv:1411.1450[hep-ph doi: 10.1007/JHEP03(2015)003
    [62] J.-J. Cao, Z.-X. Heng, J. M. Yang et al., JHEP 03, 086 (2012), arXiv:1202.5821[hep-ph doi: 10.1007/JHEP03(2012)086
    [63] J. Cao, Z. Heng, J. M. Yang et al., JHEP 10, 079 (2012), arXiv:1207.3698[hep-ph doi: 10.1007/JHEP10(2012)079
    [64] J. Cao, Z. Heng, D. Li et al., Phys. Lett. B 710, 665 (2012), arXiv:1112.4391[hep-ph doi: 10.1016/j.physletb.2012.03.052
    [65] W. Yin, JHEP 2021, 029 (2021), arXiv:2104.03259[hep-ph doi: 10.1007/JHEP06(2021)029
    [66] W. Yin and M. Yamaguchi, (2020), arXiv: 2012.03928
    [67] W. Yin and N. Yokozaki, Phys. Lett. B 762, 72 (2016), arXiv:1607.05705[hep-ph doi: 10.1016/j.physletb.2016.09.024
    [68] M. Yamaguchi and W. Yin, PTEP 2018, 023B06 (2018), arXiv:1606.04953[hep-ph doi: 10.1093/ptep/pty002
    [69] D. Sabatta, A. S. Cornell, A. Goyal et al., Chin. Phys. C 44, 063103 (2020), arXiv:1909.03969[hep-ph doi: 10.1088/1674-1137/44/6/063103
    [70] G. Aad et al. (ATLAS Collaboration), JHEP 06, 046 (2020), arXiv:1909.08457[hep-ex doi: 10.1007/JHEP06(2020)046
    [71] T. A. Vami (ATLAS and CMS Collaborations), PoS LHCP2019, 168 (2019), arXiv:1909.11753
    [72] G. Aad et al. (ATLAS collaboration), Eur. Phys. J. C 81, 600 (2021), arXiv:2101.01629[hep-ex doi: 10.1140/epjc/s10052-021-09344-w
    [73] G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 104, 112010 (2021) doi: 10.1103/PhysRevD.104.112010
    [74] A.Tumasyan et al. (CMS Collaboration), JHEP 2022, 147 (2022) doi: 10.1007/JHEP04(2022)147
    [75] A. M. Sirunyan et al. (CMS Collaboration), JHEP 2018, 166 (2018), arXiv:1709.05406[hep-ex doi: 10.1007/JHEP03(2018)166
    [76] M. Aaboud et al. (ATLAS Collaboration), Eur. Phys. J. C 78, 995 (2018), arXiv:1803.02762[hep-ex doi: 10.1140/epjc/s10052-018-6423-7
    [77] G. Aad et al. (ATLAS Collaboration), Eur. Phys. J. C 80, 123 (2020), arXiv:1908.08215[hep-ex doi: 10.1140/epjc/s10052-019-7594-6
    [78] A. M. Sirunyan et al. (CMS Collaboration), Phys. Lett. B 790, 140 (2019), arXiv:1806.05264[hep-ex doi: 10.1016/j.physletb.2019.01.005
    [79] P. Fayet, Nucl. Phys. B 90, 104 (1975) doi: 10.1016/0550-3213(75)90636-7
    [80] U. Ellwanger, C. Hugonie, and A. M. Teixeira, Phys. Rept. 496, 1 (2010), arXiv:0910.1785[hep-ph doi: 10.1016/j.physrep.2010.07.001
    [81] M. Maniatis, Int. J. Mod. Phys. A 25, 3505 (2010), arXiv:0906.0777[hep-ph doi: 10.1142/S0217751X10049827
    [82] U. Ellwanger, J. F. Gunion, and C. Hugonie, JHEP 02, 066 (2005), arXiv:hep-ph/0406215 doi: 10.1088/1126-6708/2005/02/066FocustolearnmoreSubmissionhistory
    [83] U. Ellwanger and C. Hugonie, Comput. Phys. Commun. 175, 290 (2006), arXiv:hep-ph/0508022 doi: 10.1016/j.cpc.2006.04.004
    [84] D. Das, U. Ellwanger, and A. M. Teixeira, Comput. Phys. Commun. 183, 774 (2012), arXiv:1106.5633[hep-ph doi: 10.1016/j.cpc.2011.11.021
    [85] U. Ellwanger and C. Hugonie, Comput. Phys. Commun. 177, 399 (2007), arXiv:hep-ph/0612134 doi: 10.1016/j.cpc.2007.05.001
    [86] M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) doi: 10.1103/PhysRevD.98.030001
    [87] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 110, 021801 (2013), arXiv:1211.2674[hep-ex doi: 10.1103/PhysRevLett.110.021801
    [88] J. P. Lees et al. (BABAR Collaboration), Phys. Rev. Lett. 109, 101802 (2012), arXiv:1205.5442[hep-ex doi: 10.1103/PhysRevLett.109.101802
    [89] J. P. Lees et al. (BABAR Collaboration), Phys. Rev. Lett. 109, 191801 (2012), arXiv:1207.2690[hep-ex doi: 10.1103/PhysRevLett.109.191801
    [90] G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 101, 012002 (2020), arXiv:1909.02845[hep-ex doi: 10.1103/PhysRevD.101.012002
    [91] A. M. Sirunyan et al. (CMS Collaboration), Eur. Phys. J. C 79, 421 (2019), arXiv:1809.10733[hep-ex doi: 10.1140/epjc/s10052-019-6909-y
    [92] G. Aad et al. (ATLAS and CMS Collaborations), JHEP 2016, 045 (2016), arXiv:1606.02266[hep-ex doi: 10.1007/JHEP08(2016)045
    [93] P. Bechtle, S. Heinemeyer, T. Klingl et al., Eur. Phys. J. C 81, 145 (2021), arXiv:2012.09197[hep-ph doi: 10.1140/epjc/s10052-021-08942-y
    [94] P. Bechtle, S. Heinemeyer, O. Stål et al., Eur. Phys. J. C 74, 2711 (2014), arXiv:1305.1933[hep-ph doi: 10.1140/epjc/s10052-013-2711-4
    [95] P. Bechtle, S. Heinemeyer, O. Stal et al., Eur. Phys. J. C 75, 421 (2015), arXiv:1507.06706[hep-ph doi: 10.1140/epjc/s10052-015-3650-z
    [96] P. Bechtle, O. Brein, S. Heinemeyer et al., Eur. Phys. J. C 74, 2693 (2014), arXiv:1311.0055[hep-ph doi: 10.1140/epjc/s10052-013-2693-2
    [97] P. Bechtle, O. Brein, S. Heinemeyer et al., PoS CHARGED2012, 024 (2012), arXiv: 1301.2345[hep-ph]
    [98] P. Bechtle, O. Brein, S. Heinemeyer et al., Comput. Phys. Commun. 182, 2605 (2011), arXiv:1102.1898[hep-ph doi: 10.1016/j.cpc.2011.07.015
    [99] P. Bechtle, O. Brein, S. Heinemeyer et al., Comput. Phys. Commun. 181, 138 (2010), arXiv:0811.4169[hep-ph doi: 10.1016/j.cpc.2009.09.003
    [100] G. Hinshaw, D. Larson, E. Komatsu et al., Astrophys. J. Suppl. 208, 19 (2013), arXiv:1212.5226[astro-ph.CO doi: 10.1088/0067-0049/208/2/19
    [101] P. A. R. Ade et al. (Planck Collaboration), Astron. Astrophys. 571, A16 (2014), arXiv:1303.5076[astro-ph.CO doi: 10.1051/0004-6361/201321591
    [102] G. Belanger, F. Boudjema, A. Pukhov et al., Comput. Phys. Commun. 176, 367 (2007), arXiv:hep-ph/0607059 doi: 10.1016/j.cpc.2006.11.008
    [103] G. Belanger, F. Boudjema, A. Pukhov et al., Comput. Phys. Commun. 180, 747 (2009), arXiv:0803.2360[hep-ph doi: 10.1016/j.cpc.2008.11.019
    [104] G. Belanger, F. Boudjema, A. Pukhov et al., Nuovo Cim. C 033N2, 111 (2010), arXiv:1005.4133[hep-ph doi: 10.1393/ncc/i2010-10591-3
    [105] G. Belanger, F. Boudjema, A. Pukhov et al., Comput. Phys. Commun. 185, 960 (2014), arXiv:1305.0237[hep-ph doi: 10.1016/j.cpc.2013.10.016
    [106] E. Aprile et al. (XENON Collaboration), Phys. Rev. Lett. 121, 111302 (2018), arXiv:1805.12562[astro-ph.CO doi: 10.1103/PhysRevLett.121.111302
    [107] D. S. Akerib et al. (LUX Collaboration), Phys. Rev. Lett. 116, 161302 (2016), arXiv:1602.03489[hep-ex doi: 10.1103/PhysRevLett.116.161302
    [108] E. Aprile et al. (XENON Collaboration), Phys. Rev. Lett. 122, 141301 (2019), arXiv:1902.03234[astro-ph.CO doi: 10.1103/PhysRevLett.122.141301
    [109] C. Amole et al. (PICO Collaboration), Phys. Rev. D 100, 022001 (2019), arXiv:1902.04031[astro-ph.CO doi: 10.1103/PhysRevD.100.022001
    [110] S. Kraml, S. Kulkarni, U. Laa et al., Eur. Phys. J. C 74, 2868 (2014), arXiv:1312.4175[hep-ph doi: 10.1140/epjc/s10052-014-2868-5
    [111] F. Ambrogi, S. Kraml, S. Kulkarni et al., Comput. Phys. Commun. 227, 72 (2018), arXiv:1701.06586[hep-ph doi: 10.1016/j.cpc.2018.02.007
    [112] F. Ambrogi et al., Comput. Phys. Commun. 251, 106848 (2020), arXiv:1811.10624[hep-ph doi: 10.1016/j.cpc.2019.07.013
    [113] J. Dutta, S. Kraml, A. Lessa et al., LHEP 1, 5 (2018), arXiv:1803.02204[hep-ph doi: 10.48550/arXiv.1803.02204
    [114] A. Buckley, Eur. Phys. J. C 75, 467 (2015), arXiv:1305.4194[hep-ph doi: 10.1140/epjc/s10052-015-3638-8
    [115] T. Sjostrand, S. Mrenna, and P. Z. Skands, JHEP 2006, 026 (2006), arXiv:hep-ph/0603175 doi: 10.1088/1126-6708/2006/05/026
    [116] T. Sjöstrand, S. Ask, J. R. Christiansen et al., Comput. Phys. Commun. 191, 159 (2015), arXiv:1410.3012[hep-ph doi: 10.1016/j.cpc.2015.01.024
    [117] G. Alguero, S. Kraml, and W. Waltenberger, Comput. Phys. Commun. 264, 107909 (2021), arXiv:2009.01809[hep-ph doi: 10.1016/j.cpc.2021.107909
    [118] C. K. Khosa, S. Kraml, A. Lessa et al., LHEP 2020, 158 (2020), arXiv:2005.00555[hep-ph doi: 10.31526/lhep.2020.158
    [119] G. Alguero, J. Heisig, C. Khosa et al., JHEP 2022, 68 (2022) doi: 10.1007/JHEP08(2022)068
    [120] J. Fiaschi, M. Klasen, and M. Sunder, (2020), Slepton pair production with aNNLO+NNLL precision, arXiv:1911.02419[hep-ph]
    [121] J. Fiaschi and M. Klasen, Phys. Rev. D 98, 055014 (2018), arXiv:1805.11322[hep-ph doi: 10.1103/PhysRevD.98.055014
    [122] B. Fuks, M. Klasen, D. R. Lamprea et al., Eur. Phys. J. C 73, 2480 (2013), arXiv:1304.0790[hep-ph doi: 10.1140/epjc/s10052-013-2480-0
    [123] G. Bozzi, B. Fuks, and M. Klasen, Phys. Rev. D 74, 015001 (2006), arXiv:hep-ph/0603074 doi: 10.1103/PhysRevD.74.015001
    [124] G. Bozzi, B. Fuks, and M. Klasen, Nucl. Phys. B 777, 157 (2007), arXiv:hep-ph/0701202 doi: 10.1016/j.nuclphysb.2007.03.052
    [125] B. Fuks, M. Klasen, D. R. Lamprea et al., JHEP 2014, 168 (2014), arXiv:1310.2621[hep-ph doi: 10.1007/JHEP01(2014)168
    [126] J. Fiaschi and M. Klasen, JHEP 2018, 094 (2018), arXiv:1801.10357[hep-ph doi: 10.1007/JHEP03(2018)094
    [127] C. Panagiotakopoulos and K. Tamvakis, Phys. Lett. B 446, 224 (1999), arXiv:hep-ph/9809475 doi: 10.1016/S0370-2693(98)01493-2
    [128] S. Borsanyi et al., Nature 593, 51 (2021), arXiv:2002.12347[hep-lat doi: 10.1038/s41586-021-03418-1
    [129] M. Cè et al., (2022), arXiv: 2206.06582
  • [1] B. Abi et al. (Muon g-2 Collaboration), Phys. Rev. Lett. 126, 141801 (2021), arXiv:2104.03281[hep-ex doi: 10.1103/PhysRevLett.126.141801
    [2] G. W. Bennett et al. (Muon g-2 Collaboration), Phys. Rev. D 73, 072003 (2006), arXiv:hep-ex/0602035 doi: 10.1103/PhysRevD.73.072003
    [3] T. Aoyama et al., Phys. Rept. 887, 1 (2020), arXiv:2006.04822[hep-ph doi: 10.1016/j.physrep.2020.07.006
    [4] T. Aoyama, M. Hayakawa, T. Kinoshita, et al., Phys. Rev. Lett. 109, 111808 (2012), arXiv:1205.5370[hep-ph doi: 10.1103/PhysRevLett.109.111808
    [5] T. Aoyama, T. Kinoshita, and M. Nio, Atoms 7, 28 (2019) doi: 10.3390/atoms7010028
    [6] A. Czarnecki, W. J. Marciano, and A. Vainshtein, Phys. Rev. D 67, 073006 (2003), [Erratum: Phys. Rev. D 73, 119901 (2006)], arXiv: hep-ph/0212229
    [7] C. Gnendiger, D. Stöckinger, and H. Stöckinger-Kim, Phys. Rev. D 88, 053005 (2013), arXiv:1306.5546[hep-ph doi: 10.1103/PhysRevD.88.053005
    [8] M. Davier, A. Hoecker, B. Malaescu et al., Eur. Phys. J. C 77, 827 (2017), arXiv:1706.09436[hep-ph doi: 10.1140/epjc/s10052-017-5161-6
    [9] A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 97, 114025 (2018), arXiv:1802.02995[hep-ph doi: 10.1103/PhysRevD.97.114025
    [10] G. Colangelo, M. Hoferichter, and P. Stoffer, JHEP 2019, 006 (2019), arXiv:1810.00007[hep-ph doi: 10.1007/JHEP02(2019)006
    [11] M. Hoferichter, B.-L. Hoid, and B. Kubis, JHEP 2019, 137 (2019), arXiv:1907.01556[hep-ph doi: 10.1007/JHEP08(2019)137
    [12] M. Davier, A. Hoecker, B. Malaescu et al., Eur. Phys. J. C 80, 241 (2020), [Erratum: Eur. Phys. J. C 80, 410 (2020)], arXiv: 1908.00921
    [13] A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 101, 014029 (2020), arXiv:1911.00367[hep-ph doi: 10.1103/PhysRevD.101.014029
    [14] A. Kurz, T. Liu, P. Marquardet al., Phys. Lett. B 734, 144 (2014), arXiv:1403.6400[hep-ph doi: 10.1016/j.physletb.2014.05.043
    [15] K. Melnikov and A. Vainshtein, Phys. Rev. D 70, 113006 (2004), arXiv:hep-ph/0312226 doi: 10.1103/PhysRevD.70.113006
    [16] P. Masjuan and P. Sanchez-Puertas, Phys. Rev. D 95, 054026 (2017), arXiv:1701.05829[hep-ph doi: 10.1103/PhysRevD.95.054026
    [17] G. Colangelo, M. Hoferichter, M. Procura et al., JHEP 04, 161 (2017), arXiv:1702.07347[hep-ph
    [18] M. Hoferichter, B.-L. Hoid, B. Kubis et al., JHEP 2018, 141 (2018), arXiv:1808.04823[hep-ph doi: 10.1007/JHEP10(2018)141
    [19] A. Gérardin, H. B. Meyer, and A. Nyffeler, Phys. Rev. D 100, 034520 (2019), arXiv:1903.09471[hep-lat doi: 10.1103/PhysRevD.100.034520
    [20] J. Bijnens, N. Hermansson-Truedsson, and A. Rodríguez-Sánchez, Phys. Lett. B 798, 134994 (2019), arXiv:1908.03331[hep-ph doi: 10.1016/j.physletb.2019.134994
    [21] G. Colangelo, F. Hagelstein, M. Hoferichter et al., JHEP 2020, 101 (2020), arXiv:1910.13432[hep-ph doi: 10.1007/JHEP03(2020)101
    [22] T. Blum, N. Christ, M. Hayakawa et al., Phys. Rev. Lett. 124, 132002 (2020), arXiv:1911.08123[hep-lat doi: 10.1103/PhysRevLett.124.132002
    [23] G. Colangelo, M. Hoferichter, A. Nyffeler et al., Phys. Lett. B 735, 90 (2014), arXiv:1403.7512[hep-ph doi: 10.1016/j.physletb.2014.06.012
    [24] M. Davier, A. Hoecker, B. Malaescu et alEur. Phys. J. C 71, 1515 (2011), [Erratum: Eur.Phys.J.C 72, 1874 (2012)], arXiv: 1010.4180
    [25] H. Terazawa, Prog. Theor. Phys. 39, 1326 (1968) doi: 10.1143/ptp/39.5.1326
    [26] P. Fayet, Phys. Lett. B 64, 159 (1976) doi: 10.1016/0370-2693(76)90319-1
    [27] P. Fayet, Phys. Lett. B 69, 489 (1977) doi: 10.1016/0370-2693(77)90852-8
    [28] H. E. Haber and G. L. Kane, Phys. Rept. 117, 75 (1985) doi: 10.1016/0370-1573(85)90051-1
    [29] S. P. Martin, Adv. Ser. Direct. High Energy Phys. 18, 1 (1998), arXiv:hep-ph/9709356 doi: 10.1142/9789812839657_0001
    [30] P. Fayet, Phys. Lett. B 84, 416 (1979) doi: 10.1016/0370-2693(79)91229-2
    [31] P. Fayet, Ettore Majorana Int. Sci. Ser. Phys. Sci. 7, 587 (1980)
    [32] J. A. Grifols and A. Mendez, Phys. Rev. D 26, 1809 (1982) doi: 10.1103/PhysRevD.26.1809
    [33] J. R. Ellis, J. S. Hagelin, and D. V. Nanopoulos, Phys. Lett. B 116, 283 (1982) doi: 10.1016/0370-2693(82)90343-4
    [34] R. Barbieri and L. Maiani, Phys. Lett. B 117, 203 (1982) doi: 10.1016/0370-2693(82)90547-0
    [35] T. Moroi, Phys. Rev. D 53, 6565 (1996), arXiv:hep-ph/9512396 doi: 10.1103/PhysRevD.53.6565
    [36] S. P. Martin and J. D. Wells, Phys. Rev. D 64, 035003 (2001), arXiv:hep-ph/0103067 doi: 10.1103/PhysRevD.64.035003
    [37] D. Stockinger, J. Phys. G 34, R45 (2007), arXiv:hep-ph/0609168 doi: 10.1088/0954-3899/34/2/R01
    [38] P. Athron, C. Balázs, D. H. Jacob et al., JHEP 2021, 080 (2021), arXiv:2104.03691[hep-ph doi: 10.1007/JHEP09(2021)080
    [39] Q. Shafi and C. S. Ün, Sparticle Spectroscopy at LHC-Run3 and LSP Dark Matter in light of Muon g-2, (2021), arXiv: 2107.04563
    [40] S. Li, Y. Xiao, and J. M. Yang, Eur. Phys. J. C 82, 276 (2021) doi: 10.1140/epjc/s10052-022-10242-y
    [41] S. Li, Y. Xiao, and J. M. Yang, Nucl. Phys. B 974, 115629 (2022), arXiv:2108.00359[hep-ph doi: 10.1016/j.nuclphysb.2021.115629
    [42] Z. Li, G.-L. Liu, F. Wang et al., JHEP 2021, 219 (2021) doi: 10.1007/JHEP12(2021)219
    [43] J. Cao, J. Lian, Y. Pan et al., JHEP 2021, 175 (2021), arXiv:2104.03284[hep-ph doi: 10.1007/JHEP09(2021)175
    [44] F. Wang, L. Wu, Y. Xiao et al., Nucl. Phys. B 970, 115486 (2021), arXiv:2104.03262[hep-ph doi: 10.1016/j.nuclphysb.2021.115486
    [45] M. Abdughani, Y.-Z. Fan, L. Feng et al., Sci. Bull. 66, 2170 (2021), arXiv:2104.03274[hep-ph doi: 10.1016/j.scib.2021.07.029
    [46] C. Han, (2021), Muon g-2 and CP violation in MSSM, arXiv: 2104.03292
    [47] P. Cox, C. Han, and T. T. Yanagida, Phys. Rev. D 104, 075035 (2021), arXiv:2104.03290[hep-ph doi: 10.1103/PhysRevD.104.075035
    [48] W. Ahmed, I. Khan, J. Li et al., Phys. Lett. B 827, 136879 (2022) doi: 10.1016/j.physletb.2022.136879
    [49] S. Iwamoto, T. T. Yanagida, and N. Yokozaki, Phys. Lett. B 823, 136768 (2021), arXiv:2104.03223[hep-ph doi: 10.1016/j.physletb.2021.136768
    [50] M.-D. Zheng and H.-H. Zhang, Phys. Rev. D 104, 115023 (2021), arXiv:2105.06954[hep-ph doi: 10.1103/PhysRevD.104.115023
    [51] S.-M. Zhao, L.-H. Su, X.-X. Dong et al., JHEP 2022, 101 (2022) doi: 10.1007/JHEP03(2022)101
    [52] L.-H. Su, S.-M. Zhao, X.-X. Dong et al., Eur. Phys. J. C 81, 433 (2021), arXiv:2012.04824[hep-ph doi: 10.1140/epjc/s10052-021-09219-0
    [53] K. Wang and J. Zhu, JHEP 2020, 078 (2020), arXiv:2002.05554[hep-ph doi: 10.1007/JHEP06(2020)078
    [54] K. Wang and J. Zhu, Phys. Rev. D 101, 095028 (2020), arXiv:2003.01662[hep-ph doi: 10.1103/PhysRevD.101.095028
    [55] K. Wang, F. Wang, J. Zhu et al., Chin. Phys. C 42, 103109 (2018), arXiv:1811.04435[hep-ph doi: 10.1088/1674-1137/42/10/103109
    [56] M. Badziak and K. Sakurai, JHEP 2019, 024 (2019), arXiv:1908.03607[hep-ph doi: 10.1007/JHEP10(2019)024
    [57] M. Abdughani, K.-I. Hikasa, L. Wu et al., JHEP 2019, 095 (2019), arXiv:1909.07792[hep-ph doi: 10.1007/JHEP11(2019)095
    [58] F. Wang, K. Wang, J. M. Yang et al., JHEP 2018, 041 (2018), arXiv:1808.10851[hep-ph doi: 10.1007/JHEP12(2018)041
    [59] A. Kobakhidze, M. Talia, and L. Wu, PoS EPS-HEP2017, 343 (2017), https://pos.sissa.it/314/343/pdf
    [60] F. Wang, W. Wang, and J. M. Yang, Phys. Rev. D 96, 075025 (2017), arXiv:1703.10894[hep-ph doi: 10.1103/PhysRevD.96.075025
    [61] M. Badziak, Z. Lalak, M. Lewicki et al., JHEP 2015, 003 (2015), arXiv:1411.1450[hep-ph doi: 10.1007/JHEP03(2015)003
    [62] J.-J. Cao, Z.-X. Heng, J. M. Yang et al., JHEP 03, 086 (2012), arXiv:1202.5821[hep-ph doi: 10.1007/JHEP03(2012)086
    [63] J. Cao, Z. Heng, J. M. Yang et al., JHEP 10, 079 (2012), arXiv:1207.3698[hep-ph doi: 10.1007/JHEP10(2012)079
    [64] J. Cao, Z. Heng, D. Li et al., Phys. Lett. B 710, 665 (2012), arXiv:1112.4391[hep-ph doi: 10.1016/j.physletb.2012.03.052
    [65] W. Yin, JHEP 2021, 029 (2021), arXiv:2104.03259[hep-ph doi: 10.1007/JHEP06(2021)029
    [66] W. Yin and M. Yamaguchi, (2020), arXiv: 2012.03928
    [67] W. Yin and N. Yokozaki, Phys. Lett. B 762, 72 (2016), arXiv:1607.05705[hep-ph doi: 10.1016/j.physletb.2016.09.024
    [68] M. Yamaguchi and W. Yin, PTEP 2018, 023B06 (2018), arXiv:1606.04953[hep-ph doi: 10.1093/ptep/pty002
    [69] D. Sabatta, A. S. Cornell, A. Goyal et al., Chin. Phys. C 44, 063103 (2020), arXiv:1909.03969[hep-ph doi: 10.1088/1674-1137/44/6/063103
    [70] G. Aad et al. (ATLAS Collaboration), JHEP 06, 046 (2020), arXiv:1909.08457[hep-ex doi: 10.1007/JHEP06(2020)046
    [71] T. A. Vami (ATLAS and CMS Collaborations), PoS LHCP2019, 168 (2019), arXiv:1909.11753
    [72] G. Aad et al. (ATLAS collaboration), Eur. Phys. J. C 81, 600 (2021), arXiv:2101.01629[hep-ex doi: 10.1140/epjc/s10052-021-09344-w
    [73] G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 104, 112010 (2021) doi: 10.1103/PhysRevD.104.112010
    [74] A.Tumasyan et al. (CMS Collaboration), JHEP 2022, 147 (2022) doi: 10.1007/JHEP04(2022)147
    [75] A. M. Sirunyan et al. (CMS Collaboration), JHEP 2018, 166 (2018), arXiv:1709.05406[hep-ex doi: 10.1007/JHEP03(2018)166
    [76] M. Aaboud et al. (ATLAS Collaboration), Eur. Phys. J. C 78, 995 (2018), arXiv:1803.02762[hep-ex doi: 10.1140/epjc/s10052-018-6423-7
    [77] G. Aad et al. (ATLAS Collaboration), Eur. Phys. J. C 80, 123 (2020), arXiv:1908.08215[hep-ex doi: 10.1140/epjc/s10052-019-7594-6
    [78] A. M. Sirunyan et al. (CMS Collaboration), Phys. Lett. B 790, 140 (2019), arXiv:1806.05264[hep-ex doi: 10.1016/j.physletb.2019.01.005
    [79] P. Fayet, Nucl. Phys. B 90, 104 (1975) doi: 10.1016/0550-3213(75)90636-7
    [80] U. Ellwanger, C. Hugonie, and A. M. Teixeira, Phys. Rept. 496, 1 (2010), arXiv:0910.1785[hep-ph doi: 10.1016/j.physrep.2010.07.001
    [81] M. Maniatis, Int. J. Mod. Phys. A 25, 3505 (2010), arXiv:0906.0777[hep-ph doi: 10.1142/S0217751X10049827
    [82] U. Ellwanger, J. F. Gunion, and C. Hugonie, JHEP 02, 066 (2005), arXiv:hep-ph/0406215 doi: 10.1088/1126-6708/2005/02/066FocustolearnmoreSubmissionhistory
    [83] U. Ellwanger and C. Hugonie, Comput. Phys. Commun. 175, 290 (2006), arXiv:hep-ph/0508022 doi: 10.1016/j.cpc.2006.04.004
    [84] D. Das, U. Ellwanger, and A. M. Teixeira, Comput. Phys. Commun. 183, 774 (2012), arXiv:1106.5633[hep-ph doi: 10.1016/j.cpc.2011.11.021
    [85] U. Ellwanger and C. Hugonie, Comput. Phys. Commun. 177, 399 (2007), arXiv:hep-ph/0612134 doi: 10.1016/j.cpc.2007.05.001
    [86] M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) doi: 10.1103/PhysRevD.98.030001
    [87] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 110, 021801 (2013), arXiv:1211.2674[hep-ex doi: 10.1103/PhysRevLett.110.021801
    [88] J. P. Lees et al. (BABAR Collaboration), Phys. Rev. Lett. 109, 101802 (2012), arXiv:1205.5442[hep-ex doi: 10.1103/PhysRevLett.109.101802
    [89] J. P. Lees et al. (BABAR Collaboration), Phys. Rev. Lett. 109, 191801 (2012), arXiv:1207.2690[hep-ex doi: 10.1103/PhysRevLett.109.191801
    [90] G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 101, 012002 (2020), arXiv:1909.02845[hep-ex doi: 10.1103/PhysRevD.101.012002
    [91] A. M. Sirunyan et al. (CMS Collaboration), Eur. Phys. J. C 79, 421 (2019), arXiv:1809.10733[hep-ex doi: 10.1140/epjc/s10052-019-6909-y
    [92] G. Aad et al. (ATLAS and CMS Collaborations), JHEP 2016, 045 (2016), arXiv:1606.02266[hep-ex doi: 10.1007/JHEP08(2016)045
    [93] P. Bechtle, S. Heinemeyer, T. Klingl et al., Eur. Phys. J. C 81, 145 (2021), arXiv:2012.09197[hep-ph doi: 10.1140/epjc/s10052-021-08942-y
    [94] P. Bechtle, S. Heinemeyer, O. Stål et al., Eur. Phys. J. C 74, 2711 (2014), arXiv:1305.1933[hep-ph doi: 10.1140/epjc/s10052-013-2711-4
    [95] P. Bechtle, S. Heinemeyer, O. Stal et al., Eur. Phys. J. C 75, 421 (2015), arXiv:1507.06706[hep-ph doi: 10.1140/epjc/s10052-015-3650-z
    [96] P. Bechtle, O. Brein, S. Heinemeyer et al., Eur. Phys. J. C 74, 2693 (2014), arXiv:1311.0055[hep-ph doi: 10.1140/epjc/s10052-013-2693-2
    [97] P. Bechtle, O. Brein, S. Heinemeyer et al., PoS CHARGED2012, 024 (2012), arXiv: 1301.2345[hep-ph]
    [98] P. Bechtle, O. Brein, S. Heinemeyer et al., Comput. Phys. Commun. 182, 2605 (2011), arXiv:1102.1898[hep-ph doi: 10.1016/j.cpc.2011.07.015
    [99] P. Bechtle, O. Brein, S. Heinemeyer et al., Comput. Phys. Commun. 181, 138 (2010), arXiv:0811.4169[hep-ph doi: 10.1016/j.cpc.2009.09.003
    [100] G. Hinshaw, D. Larson, E. Komatsu et al., Astrophys. J. Suppl. 208, 19 (2013), arXiv:1212.5226[astro-ph.CO doi: 10.1088/0067-0049/208/2/19
    [101] P. A. R. Ade et al. (Planck Collaboration), Astron. Astrophys. 571, A16 (2014), arXiv:1303.5076[astro-ph.CO doi: 10.1051/0004-6361/201321591
    [102] G. Belanger, F. Boudjema, A. Pukhov et al., Comput. Phys. Commun. 176, 367 (2007), arXiv:hep-ph/0607059 doi: 10.1016/j.cpc.2006.11.008
    [103] G. Belanger, F. Boudjema, A. Pukhov et al., Comput. Phys. Commun. 180, 747 (2009), arXiv:0803.2360[hep-ph doi: 10.1016/j.cpc.2008.11.019
    [104] G. Belanger, F. Boudjema, A. Pukhov et al., Nuovo Cim. C 033N2, 111 (2010), arXiv:1005.4133[hep-ph doi: 10.1393/ncc/i2010-10591-3
    [105] G. Belanger, F. Boudjema, A. Pukhov et al., Comput. Phys. Commun. 185, 960 (2014), arXiv:1305.0237[hep-ph doi: 10.1016/j.cpc.2013.10.016
    [106] E. Aprile et al. (XENON Collaboration), Phys. Rev. Lett. 121, 111302 (2018), arXiv:1805.12562[astro-ph.CO doi: 10.1103/PhysRevLett.121.111302
    [107] D. S. Akerib et al. (LUX Collaboration), Phys. Rev. Lett. 116, 161302 (2016), arXiv:1602.03489[hep-ex doi: 10.1103/PhysRevLett.116.161302
    [108] E. Aprile et al. (XENON Collaboration), Phys. Rev. Lett. 122, 141301 (2019), arXiv:1902.03234[astro-ph.CO doi: 10.1103/PhysRevLett.122.141301
    [109] C. Amole et al. (PICO Collaboration), Phys. Rev. D 100, 022001 (2019), arXiv:1902.04031[astro-ph.CO doi: 10.1103/PhysRevD.100.022001
    [110] S. Kraml, S. Kulkarni, U. Laa et al., Eur. Phys. J. C 74, 2868 (2014), arXiv:1312.4175[hep-ph doi: 10.1140/epjc/s10052-014-2868-5
    [111] F. Ambrogi, S. Kraml, S. Kulkarni et al., Comput. Phys. Commun. 227, 72 (2018), arXiv:1701.06586[hep-ph doi: 10.1016/j.cpc.2018.02.007
    [112] F. Ambrogi et al., Comput. Phys. Commun. 251, 106848 (2020), arXiv:1811.10624[hep-ph doi: 10.1016/j.cpc.2019.07.013
    [113] J. Dutta, S. Kraml, A. Lessa et al., LHEP 1, 5 (2018), arXiv:1803.02204[hep-ph doi: 10.48550/arXiv.1803.02204
    [114] A. Buckley, Eur. Phys. J. C 75, 467 (2015), arXiv:1305.4194[hep-ph doi: 10.1140/epjc/s10052-015-3638-8
    [115] T. Sjostrand, S. Mrenna, and P. Z. Skands, JHEP 2006, 026 (2006), arXiv:hep-ph/0603175 doi: 10.1088/1126-6708/2006/05/026
    [116] T. Sjöstrand, S. Ask, J. R. Christiansen et al., Comput. Phys. Commun. 191, 159 (2015), arXiv:1410.3012[hep-ph doi: 10.1016/j.cpc.2015.01.024
    [117] G. Alguero, S. Kraml, and W. Waltenberger, Comput. Phys. Commun. 264, 107909 (2021), arXiv:2009.01809[hep-ph doi: 10.1016/j.cpc.2021.107909
    [118] C. K. Khosa, S. Kraml, A. Lessa et al., LHEP 2020, 158 (2020), arXiv:2005.00555[hep-ph doi: 10.31526/lhep.2020.158
    [119] G. Alguero, J. Heisig, C. Khosa et al., JHEP 2022, 68 (2022) doi: 10.1007/JHEP08(2022)068
    [120] J. Fiaschi, M. Klasen, and M. Sunder, (2020), Slepton pair production with aNNLO+NNLL precision, arXiv:1911.02419[hep-ph]
    [121] J. Fiaschi and M. Klasen, Phys. Rev. D 98, 055014 (2018), arXiv:1805.11322[hep-ph doi: 10.1103/PhysRevD.98.055014
    [122] B. Fuks, M. Klasen, D. R. Lamprea et al., Eur. Phys. J. C 73, 2480 (2013), arXiv:1304.0790[hep-ph doi: 10.1140/epjc/s10052-013-2480-0
    [123] G. Bozzi, B. Fuks, and M. Klasen, Phys. Rev. D 74, 015001 (2006), arXiv:hep-ph/0603074 doi: 10.1103/PhysRevD.74.015001
    [124] G. Bozzi, B. Fuks, and M. Klasen, Nucl. Phys. B 777, 157 (2007), arXiv:hep-ph/0701202 doi: 10.1016/j.nuclphysb.2007.03.052
    [125] B. Fuks, M. Klasen, D. R. Lamprea et al., JHEP 2014, 168 (2014), arXiv:1310.2621[hep-ph doi: 10.1007/JHEP01(2014)168
    [126] J. Fiaschi and M. Klasen, JHEP 2018, 094 (2018), arXiv:1801.10357[hep-ph doi: 10.1007/JHEP03(2018)094
    [127] C. Panagiotakopoulos and K. Tamvakis, Phys. Lett. B 446, 224 (1999), arXiv:hep-ph/9809475 doi: 10.1016/S0370-2693(98)01493-2
    [128] S. Borsanyi et al., Nature 593, 51 (2021), arXiv:2002.12347[hep-lat doi: 10.1038/s41586-021-03418-1
    [129] M. Cè et al., (2022), arXiv: 2206.06582
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Kun Wang and Jingya Zhu. Smuon in the NMSSM confronted with the muon g–2 anomaly and SUSY searches[J]. Chinese Physics C. doi: 10.1088/1674-1137/ac9896
Kun Wang and Jingya Zhu. Smuon in the NMSSM confronted with the muon g–2 anomaly and SUSY searches[J]. Chinese Physics C.  doi: 10.1088/1674-1137/ac9896 shu
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Smuon in the NMSSM confronted with the muon g–2 anomaly and SUSY searches

  • 1. Joint Center for Theoretical Physics, Henan University, Kaifeng 475004, China
  • 2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • 3. School of Physics and Electronics, Henan University, Kaifeng 475004, China

Abstract: Motivated by recent supersymmetry (SUSY) search results, which prefer most SUSY particles to be heavy, and the muon g–2 anomaly, which prefers colorless SUSY particles to be light, we explore the status of a light smuon (the SUSY partner of a left-handed muon lepton) in the next-to-minimal supersymmetric standard model (NMSSM). Assuming colored SUSY particles to be heavy, and considering numerous experimental constraints, including muon g-2, SUSY searches, and dark matter, we scan the parameter space in the NMSSM with Z3-symmetry and check the status of colorless SUSY particles and their possible mass order, paying special attention to the smuon. After calculations and discussions, we find that the surviving samples can be divided into several scenarios, where the mass region and decay information of the smuon are given. Overall, the smuon mass can be approximately 0.1~1.8 TeV. These results may be useful for smuon searches at the LHC and future colliders.

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    I.   INTRODUCTION
    • In April 2021, a new result for the muon anomalous magnetic moment (muong2 or δaμ) was reported at Fermilab [1], revealing an exciting disparity compared to the standard model (SM) prediction. Combined with the previous result at Brookhaven [2], the discrepancy can be 4.2σ [1],

      δaμaexμaSMμ=(25.1±5.9)×1010,

      (1)

      where the combined experimental result aexμ [1] and SM prediction aSMμ [325] are given by

      aexμ=(11659206.1±4.1)×1010,

      (2)

      aSMμ=(11659181.0±4.3)×1010.

      (3)

      It is widely believed that the SM is not a complete description of nature. Besides the muong2 anomaly, the SM also cannot interpret problems such as hierarchy, grand unification, dark matter (DM), and baryogenesis. To interpret these problems, researchers have proposed many theories beyond the SM (BSM), among which supersymmetry (SUSY) is the most fascinating [2629]. SUSY assumes that every SM particle has a SUSY partner whose spin differs from that of the corresponding SM particle by half. These extra SUSY particles can significantly contribute to solving problems and anomalies, including muong2. The SUSY effects on muong2 were first calculated in the 1980s [3034] and comprehensively described in Refs. [3537]. In recent years, especially after the new result released at Fermilab, there have been numerous papers on interpreting the muong2 anomaly in the minimal supersymmetric SM (MSSM) and its extensions, such as the next-to MSSM (NMSSM) [3869]. In the MSSM and NMSSM, the main contributions to δaμ originate from chargino-sneutrino loops and neutralino-smuon loops. Thus, light SUSY particles, such as smuons, sneutrinos, charginos, and neutralinos, are generally required to interpret the distinct muong2 anomaly.

      However, the null results from the search for SUSY at the LHC in recent years have set strong constraints on SUSY particles. For gluino and the first two-generation squarks, the low mass bounds can be over 2 TeV [7072]. Even for colorless charginos and sleptons, including smuons, the low mass bounds can be hundreds of GeV in simple models, except for compressed-spectrum scenarios [7378]. Recent searches for smuons by the ATLAS collaboration with 139 fb1of data have demonstrated that the mass bound can be approximately 600 GeV, assuming that a smuon decays100% into a muon plus the lightest neutralino [77]. Thus, for constraints to SUSY models, the direct SUSY searches at the LHC and the muong2 anomaly may be at odds with each other. In this study, we consider the status of smuons in the NMSSM confronted with muong2 and SUSY searches and investigate their implications for DM.

      The added singlet scalar in the NMSSM and its partner singlino can introduce different phenomenology from those in the MSSM. In the Higgs sector, mixing between light singlet and doublet scalars can change the production and decay of the SM-like Higgs boson. In the neutralino sector, a light singlino-like neutralino can be a good candidate for DM and can change the decay of SUSY particles. Thus, the additional parts in the NMSSM can change the status of MSSM confronting Higgs data, DM detection, and SUSY searches and indirectly affect its muong2. Moreover, the lightest neutralino with a gaugino or higgsino component can get into neutralino-smuon loops and affect muong2 directly. In this study on the NMSSM, to obtain a more general result, we take the SUSY scale as the input scale of parameters, which differs from our former studies on the semi-constrained NMSSM [5355]. To ensure that surviving samples satisfy all types of experimental constraints, we impose them one by one (with the entire Higgs data as one), different from the likelihood method in most NMSSM references (e.g., Refs. [4245]).

      The rest of this paper is organized as follows. In Sec. II, we introduce the NMSSM, briefly presenting relevant analytic calculations onmuong2. In Sec. III, we present the numerical calculations and discussions. Finally, we summarize and draw our principal conclusions in Sec. IV.

    II.   MODEL AND ANALYTICCALCULATIONS
    • In contrast to the manual and large μ parameter used in the MSSM, the μ parameter in the NMSSM is effective and generated naturally when the additional singlet superfieldˆS obtains a vacuum expected value (VEV) [7981]. In the NMSSM of Z3-invariant vision, the superpotential can be expressed as

      WNMSSM=WMSSMμλˆS+κ3ˆS3,

      (4)

      where λ and κ are dimensionless couplings, WMSSM is the superpotential in the MSSM,

      WMSSM=μˆHuˆHd+yuˆuˆQˆHuydˆdˆQˆHdyeˆeˆLˆHd,

      (5)

      and in terms including quarks or leptons, the generation indexes being summed over are omitted.

      After electroweak symmetry breaking, several SUSY particles with the same quantum numbers mix, generating an equal number of mass eigenstates. The SUSY partners of left- and right-handed muon leptons have spin 0, denoted by ˜μL and ˜μR, both known as smuons. In the {˜μL,˜μR} basis, the smuon-mass matrix can be written as

      M2˜μ=(M2L2+(sin2θW12)m2Zcos2βmμ(AE2μtanβ)mμ(AE2μtanβ)M2E2m2Zsin2θWcos2β),

      (6)

      where ML2,E2 and AE2 are the soft masses of left- and right-handed smuons and the trilinear couplings of smuons, respectively, and when ML2,E2mZ,mμAE2 and mμμtanβ, the mixing between ˜μL and ˜μR is negligible. Because neutrinos are left-handed and massless in the NMSSM, the mass of the muon neutrino's partner muon sneutrino m˜ν is related to the left-handed smuon mass by

      m2˜ν=M2L+12m2Zcos2β.

      (7)

      When MLmZ, the masses are approximately equal.

      The SUSY partners of the gauge bosons W1,2,3,B0, doublet Higgs, and singlet scalars are called winos, binos, higgsinos, and singlinos, respectively, and all have spin 1/2 and are written with a tilde. Among them, the charged ones mix into two pairs of charginos, and the neutral ones mix to form five neutralinos. In the {˜W±,˜H±} base, the chargino-mass matrix can be written as

      M˜χ±=(M22mWsinβ2mWcosβμ).

      (8)

      In the {˜B0,˜W0,˜H0u,˜H0d,˜S} base, the neutralino-mass matrix can be written as

      M˜χ0=(M10mZcosβsinθWmZsinβsinθW00M2mZcosβcosθWmZsinβcosθW0mZcosβsinθWmZcosβcosθW0μλvdmZsinβsinθWmZsinβcosθWμ0λvu00λvdλvu2κμ/λ),

      (9)

      where vu and vd are the VEVs of Hu and Hd, respectively, with vu/vd=tanβ.

      The SUSY effects on muong2 at the one-loop level are mainly from chargino-sneutrino loops and neutralino-smuon loops, with summations performed over all corresponding mass eigenstates. The contributions of these two types of loops can be written as [35]

      δn=mμ16π2i,m[mμ12m2˜μm(|nLim|2+|nRim|2)FN1(xim)+m˜χ0i3m2˜μmRe(nLimnRim)FN2(xim)],

      (10)

      δc=mμ16π2k[mμ12m2˜νμ(|cLk|2+|cRk|2)FC1(xk)+2m˜χ±k3m2˜νμRe(cLkcRk)FC2(xk)],deltac

      (11)

      respectively, where the variables xim=m2˜χ0i/m2˜μmand xk=m2˜χ±k/m2˜νμ, with i=1,2,3,4,5 denoting five mass-eigenstate neutralino labels, and k=1,2 and m=1,2 denoting two mass-eigenstate chargino and smuon labels, respectively. Functions depending on xim,xk, which originate from loop integrals and are normalized, can be written as [35]

      FN1(x)=2(1x)4(16x+3x2+2x36x2lnx),

      (12)

      FN2(x)=3(1x)3(1x2+2xlnx),

      (13)

      FC1(x)=2(1x)4(2+3x6x2+x3+6xlnx),

      (14)

      FC2(x)=32(1x)3(34x+x2+2lnx).

      (15)

      With these functions, FN,C1,2(1)=1 corresponds to the case in which SUSY particles degenerate. In addition, the corresponding coefficients are written as

      nRim=2g1Ni1Xm2+yμNi3Xm1,

      (16)

      nLim=12(g2Ni2+g1Ni1)Xm1yμNi3Xm2,

      (17)

      cRk=yμUk2,

      (18)

      cLk=g2Vk1,

      (19)

      where Nij, {Ukl,Vkl}, and Xmn are the mixing matrix of neutralinos, charginos, and smuons, respectively, defined as

      NM˜χ0N=Diag{m˜χ01,m˜χ02,m˜χ03,m˜χ04},

      (20)

      UM˜χ±V=Diag{m˜χ±1,m˜χ±2},

      (21)

      XM2˜μX=Diag{m2˜μ1,m2˜μ2}.

      (22)

      Finally, g20.66 and g10.36 are the SU(2)L and U(1)Y gauge couplings, respectively, and yμg1,2 is the muon Yukawa coupling.

      Considering that the SUSY particles in the loops, which are the neutralinos ˜χ01,2,3,4,5 and smuons ˜μ1,2, or the charginos ˜χ±1,2 and muon sneutrino ˜νμ, approximately have the same masses, m˜χ0m˜μ or m˜χ±m˜νμ, their contributions to muong2 can be approximately written as [36]

      δn1192π2m2μm˜χ0m˜μ(g21g22)tanβ,

      (23)

      δc132π2m2μm˜χ±m˜νμg22tanβ.

      (24)
    III.   NUMERICAL CALCULATIONS ANDDISCUSSIONS
    • In this study, we first scan the parameter space of the NMSSM with Z3-symmetry to obtain surviving samples under corresponding theoretical and experimental constraints. To focus on the light smuon, a light colorless SUSY particle preferred by the muong2 anomaly, we assume colored SUSY particles and heavy Higgs to be heavy and fix them to 5 TeV :

      MA,M3,MQi,MUi,MDi=5 TeV,AUi,ADi=0 TeV,

      (25)

      where MA,M3,MQi,MUi,MDi are the soft masses of the heavy Higgs, gluino, left-handed squarks, right-handed up-type squarks, and right-handed down-type squarks, respectively, and AUi,ADi are the trilinear couplings of up- and down-type squarks, respectively, with the generation index i=1,2,3. The other required parameters correlated with light and colorless SUSY particles are set as

      0<λ,|κ|<0.8,1<tanβ<100,0<μ,M1,M2,MP<1 TeV,0<MLi,MEi,|AEi|<10 TeV.

      (26)

      To considerably differ from former studies that used ˜τ1 as the lightest slepton, we also manually require m˜τ1>m˜μ1.

      The model spectrum, including masses and decay information, is calculated with NMSSMTools-5.5.4 [8284]. The corresponding constraints we consider in our scan are listed briefly as follows:

      ● Theoretical constraints from a stable vacuum (the effective scalar potential gets its least value when all scalar fields equal to their VEVs) and the inexistent Landau pole below the GUT scale [82, 83, 85].

      ● LEP constraints on chargino and slepton masses heavier than approximately 100 GeV.

      ● Flavor constraints, such as rare B-meson decays and the mass differences Δmdand Δms [8689].

      ● A Higgs boson of 122128 GeV with signal predictions consistent with Higgs data at the LHC [9092].

      ● Constraints from searches for additional Higgs and exotic decays of SM-like Higgs, imposed with HiggsBounds-5.10.1 [9599].

      ● Upper bounds of the DM relic density Ωh20.131 from WMAP/Planck [100, 101], with the relevant quantities calculated using micrOMEGAs 5.0 [102105].

      ● Constraints on direct searches for DM, the spin-independent case by XENON1T [106], and the spin-dependent case by LUX [107], XENON1T [108], and PICO-60 [109], where the original values are rescaled by Ω/Ω0 accordingly.

      ● The constraints from muong2 at the 2σ level, where we use the combined experimental value aexμ=(11659206.1±4.1)×1010 [1] and calculate the SM value aSMμ without the Higgs contribution, considering that the NMSSM contains a SM-like Higgs. Including the theoretical error on SUSY contributions, we obtain the range of δaμaexμaSMμ as (6.145.0)×1010 at the 2σ level.

      Moreover, in imposing constraints from SUSY searches, we exploit SModelS 2.1.1 [110118] with official database version 2.1.0 [119]. To focus on the status of the smuon, we pay special attention to the constraints on smuon searches in Refs. ATLAS-SUSY-2018-32 [77] and CMS-SUS-17-009 [78]. In these analyses of smuons, they were assumed to be produced in pairs and 100 % decay into a muon lepton and the lightest neutralino; thus, the final state is composed of two opposite-charge and same-flavor leptons (dimuon) and a large missing transverse momentum pT. However, no significant excess over the SM background was recorded in either report. The ATLAS analysis was based on 139 fb1 of data at the 13 TeV LHC, and smuon masses up to approximately 600 GeV were excluded with the massless lightest neutralino. For consistency with these analyses, we employ Resummino 3.0 [120126] to calculate the smuon production at the 13-TeV LHC at the next-to leading order (NLO).

      pp˜μ+L˜μL,pp˜μ+R˜μR,

      (27)

      where ˜μL and ˜μR are the SUSY partners of the left- and right-handed muon leptons, respectively, and the cross-section of the former is times larger than the latter. Thus, ˜μL is more constrained than ˜μR, and we mainly study ˜μL, denoting it as a muon or ˜μ in this paper. Because this is a real model NMSSM, we calculate the real branching ratios, including smuon decay into a muon lepton and the lightest neutralino, that is, Br(˜μ˜χ01+μ). We constrain our samples by requiring the cross-section timing branching ratio to be below the corresponding exclusion curves from the ATLAS and CMS collaborations.

      Finally, we obtain the surviving samples that satisfy all the above constraints and present them in the following figures.

      To study the dependence of muong2 on smuon mass, we display the surviving samples in Fig. 1, from which we determine the following facts:

      Figure 1.  (color online) Surviving samples projected in the δn versus δc (left), m˜μμ versus m˜χ±1 (middle), and m˜χ01 versus m˜μ (right) planes, where ˜μ is the SUSY partner of the left-handed muon lepton, δaμ is the SUSY contribution to muong2, and δc and δn are the chargino-sneutrino and neutralino-smuon contributions to δaμ, respectively. In all the planes, colors indicate δaμ, and samples with larger δaμ are projected on top of smaller ones.

      ● The muong2 anomaly can be interpreted within 1σ. For 1σ samples, muon sneutrinos and left-handed smuons are lighter than 1000 GeV , the light charginos are lighter than 900 GeV, and the lightest neutralinos are lighter than 600 GeV.

      ● For most surviving samples, m˜χ±1m˜χ01 and m˜μm˜νμ; thus, their distributions in the middle and right planes have almost the same shapes. We verify that for most of these samples, the lightest neutralinos are wino- or higgsino-dominated, the same as the light chargino. For the other samples, m˜χ±1>m˜χ01, and the lightest neutralinos are bino- or singlino-dominated.

      ● The SUSY contribution tomuong2 is approximately equal to the sum of chargino-sneutrino and neutralino-smuon loops (δaμδc+δn), and for most samples, the former dominates (δc>δn), even when the lightest neutralinos and smuons are very light. From Eqs. (23) and (24), we know that this makes sense because g22/32(g21g22)/192. Furthermore, we check that the contributions are both proportional to tanβ and verify that δn can be both positive and negative because of the different masses of the five neutralinos and two smuons.

      To study the constraints on smuon searches at the LHC, we display the surviving samples in Fig. 2, where the solid and dotted curves denote the corresponding exclusion limits at the 95% confidence level from the ATLAS [77] and CMS collaborations [78]. From this figure we can find that

      Figure 2.  (color online) Surviving samples projected in the m˜χ01 versus m˜μ planes, where ˜μ is the SUSY partner of the left-handed muon lepton. Colors indicate the branching ratios Br(˜μ˜χ01+μ) (left), the μ (middle), and M2 parameters (right). The dashed line of m˜χ01=m˜μ indicates that the smuon and ˜χ01 are mass-degenerate, and the solid and dotted curves are the exclusion limits at the 95 % CL from direct searches for smuons given by the ATLAS [77] and CMS collaborations [78], respectively. Samples with larger Br(˜μ˜χ01+μ) are projected on top of smaller ones.

      ● For surviving samples below the exclusion curve by ATLAS, all the branching ratios of Br(˜μ˜χ01+μ) are lower than 50 % because the large values are excluded in the experiments. We check that for these surviving samples, the lightest neutralinos are either higgsino-dominated, with masses approximating to the μ parameter, or wino-dominated, with masses approximating to the M2 parameter. Thus, m˜χ±1m˜χ01min{μ,M2}, and the smuon also decays with a sizable branching ratio to a light chargino plus muon sneutrino.

      ● For surviving samples with a mass-degenerate smuon and ˜χ01, all the branching ratios Br(˜μ˜χ01+μ) are nearly 100 % because the current experimental results of direct searches are powerless in the compressed SUSY spectrum.

      To illustrate the implication of light smuons for DM, we display the surviving samples in Fig. 3, where N211 denotes the bino component in the LSP dark matter ˜χ01, and N212denotes the corresponding wino component. From this figure, we can learn the following:

      Figure 3.  (color online) Surviving samples projected in the m˜χ01 versus m˜μ planes, where ˜μ is the SUSY partner of the left-handed muon lepton. Colors indicate N211 (left), N212 (middle), and Ωh2 (right), where N211 and N212 indicate the ratios of the bino and wino components in ˜χ01, respectively, and Ωh2 indicates the relic density of the LSP dark matter ˜χ01. Samples with larger Ωh2 are projected on top of smaller ones.

      ● For most of the surviving samples with right relic density or Z- or h1-funnel annihilation, the LSP DM ˜χ01 is bino-dominated. Some others are singlino-dominated.

      ● For most of the surviving samples with a mass-degenerate smuon and ˜χ01, the LSP DM ˜χ01 is bino-dominated, and we check that the dominating annihilation mechanism is slepton annihilation. These samples constitute a large part of samples with right relic density only with the LSP ˜χ01.

      ● For all the surviving samples with wino-dominated ˜χ01, the relic density is insufficient because of mass-degenerate charginos; however, it is larger than that of higgsino-dominated-˜χ01samples (in all three planes, samples with largerΩh2 are projected on top of smaller ones, and in the middle plane, wino-dominated-˜χ01 samples are covered by higgsino-dominated-˜χ01samples).

      In addition, we also list detailed information on six benchmark points for further study in Table 1.

      BP1 BP2 BP3 BP4 BP5 BP6
      λ0.08030.00150.03670.02600.1870.0363
      κ0.667–0.6630.553–0.0047–0.606–0.630
      tanβ706946135543
      μ796567440310699479
      M14643460931340198
      M2689448941150337890
      ML2471709119143638217
      ME2640148012503682160575
      AE277–1190–150032–5245.0
      m˜χ01/GeV4613459115336196
      m˜χ02/GeV712463449150361489
      m˜χ±1/GeV712463449151361488
      m˜χ±2/GeV8466101010346727957
      N2110.990.990.990.000.980.99
      N2120.000.000.000.000.010.00
      N213+N2140.010.010.010.000.010.01
      N2150.000.000.001.000.000.00
      N2210.000.000.010.000.020.01
      N2220.760.810.010.870.960.02
      N223+N2240.240.190.980.130.020.97
      m˜μL/GeV470709119143638217
      m˜μR/GeV640148012503682160575
      m˜νμ/GeV46470592121633203
      Br(˜μ˜χ01+μ)1.000.281.001.000.071.00
      Br(˜μ˜χ02+μ)0.000.240.000.000.340.00
      Br(˜μ˜χ±1+νμ)0.000.440.000.000.590.00
      δaμ[×1010]21.822.828.241.720.524.3
      Ωh20.1260.1200.1150.1200.1090.117
      ph0.9230.9280.8490.9280.9200.920

      Table 1.  Detailed information on six benchmark points, where N2i1, N2i2, N2i3+N2i4, and N2i5 indicate the ratios of the bino, wino, higgsino, and singlino components in the neutralinos ˜χ0i, respectively. Moreover, ˜μL (˜μR) is the SUSY partner of the left-handed (right-handed) muon lepton, and ˜μLis the smuon that we investigate in this study.

    IV.   CONCLUSIONS
    • In this study, motivated by recent SUSY search results, which prefer most SUSY particles to be heavy, and the muong2 anomaly, which prefers colorless SUSY particles to be light, we explore the status of the smuon (the SUSY partner of the left-handed muon lepton) in the NMSSM. Assuming that colored SUSY particles are heavy, and considering numerous experimental constraints, including the muong2, SUSY searches, and DM, we scan the parameter space in the NMSSM with Z3-symmetry and check the status of colorless SUSY particles and their possible mass order, paying special attention to the status of a smuon confronted withmuong2 and direct SUSY searches. We also investigate their implication for DM.

      We draw the following conclusions regarding the smuon, muong2, SUSY searches, and DM in the NMSSM:

      ● The dominated SUSY contributions to muong2 originate from chargino-sneutrino loops; however, the muong2 anomaly can also constrain the mass of smuons seriously because of the mass-degenerate relationship between smuons and muon sneutrinos. To interpret the muong2 anomaly at the 1σ (2σ) level, the smuon must be lighter than 1 TeV (1.8 TeV).

      ● When ˜χ01 is wino- or higgsino-dominated, the smuon and muon sneutrino, ˜χ±1 and ˜χ01, respectively, are usually mass-degenerate. Thus, the branching ratio Br(˜μ˜χ01+μ) is suppressed to lower than 50 %, and the smuon can escape from direct searches with low mass, e.g., 300 GeV.

      ● When the smuon and ˜χ01 are mass-degenerate, the smuon can be as light as 200 GeV, whereas the ˜χ01is usually bino-dominated or sometimes singlino-dominated, and its relic density can most likely reach the observed value. The dominating annihilation mechanism is slepton annihilation.

      Moreover, we emphasize again that this study is performed in the NMSSM with Z3 symmetry, which includes no large free parameters in the superpotential but may cause the so-called 'domain wall' problem in cosmology. This problem can be solved by introducing Z3-breaking terms, such as ξm3sS [127]. This term may have an effect on the singlino sector and DM phenomenology when it is singlino-dominated. Because the chargino-sneutrino contribution to muong2 dominates in our study, and κ/λ is arbitrary in the singlino or DM sector, the Z3-breaking terms from the singlet field have little effect on the mass region of the smuon.

      Note added: The uncertainty on the SM theoretical value of muong2 is dominated by hadronic vacuum polarization (HVP), which can be calculated using the data-driven method, as quoted in the experimental report of the muong2 collaboration [1] and this paper, or the lattice method. In 2020, the BMW collaboration released their lattice result for the HVP contribution [128], which was considerably different from the quoted data-driven result. Recently, another group released a new lattice result [129], independently showing agreement with the 2020 BMW value. Employing the two lattice results for the HVP contribution, the muong2 anomaly can change to δaμ=10.4±7.0×1010, with the significance changing to 1.5σ. We verified that there are still samples in the smuon mass region as low as 0.1 TeV that can satisfy thisδaμ value at the 2σ level, and the surviving samples can have smuon masses higher than 1.8 TeV.

Reference (129)

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