Likelihood Analysis of the Sub-GUT MSSM in Light

of LHC 13-TeV Data

J.C. Costaa, E. Bagnaschib, K. Sakuraic, M. Borsatod, O. Buchmuellera M. Citrona,A. De Roecke, M.J. Dolanf , J.R. Ellisg, H. Flacherh, S. Heinemeyeri, M. Luciod,D. Martınez Santosd, K.A. Olivej, A. Richardsa, G. Weigleinb

aHigh Energy Physics Group, Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2AZ, UK

bDESY, Notkestraße 85, D–22607 Hamburg, Germany

cInstitute of Theoretical Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL–02–093Warsaw, Poland

dInstituto Galego de Fısica de Altas Enerxıas, Universidade de Santiago de Compostela, Spain

eExperimental Physics Department, CERN, CH–1211 Geneva 23, Switzerland;Antwerp University, B–2610 Wilrijk, Belgium

fARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, University ofMelbourne, 3010, Australia

gTheoretical Particle Physics and Cosmology Group, Department of Physics, King’s College London,London WC2R 2LS, UK;National Institute of Chemical Physics and Biophysics, Ravala 10, 10143 Tallinn, Estonia;Theoretical Physics Department, CERN, CH–1211 Geneva 23, Switzerland

hH.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK

iCampus of International Excellence UAM+CSIC, Cantoblanco, E–28049 Madrid, Spain;Instituto de Fısica Teorica UAM-CSIC, C/ Nicolas Cabrera 13-15, E–28049 Madrid, Spain;Instituto de Fısica de Cantabria (CSIC-UC), Avda. de Los Castros s/n, E–39005 Santander, Spain

jWilliam I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University ofMinnesota, Minneapolis, Minnesota 55455, USA

We describe a likelihood analysis using MasterCode of variants of the MSSM in which the soft supersymmetry-breaking parameters are assumed to have universal values at some scale Min below the supersymmetric grandunification scale MGUT, as can occur in mirage mediation and other models. In addition to Min, such ‘sub-GUT’ models have the 4 parameters of the CMSSM, namely a common gaugino mass m1/2, a common softsupersymmetry-breaking scalar mass m0, a common trilinear mixing parameter A and the ratio of MSSM Higgsvevs tanβ, assuming that the Higgs mixing parameter µ > 0. We take into account constraints on strongly-and electroweakly-interacting sparticles from ∼ 36/fb of LHC data at 13 TeV and the LUX and 2017 PICO,XENON1T and PandaX-II searches for dark matter scattering, in addition to the previous LHC and dark matterconstraints as well as full sets of flavour and electroweak constraints. We find a preference for Min ∼ 105 to109 GeV, with Min ∼MGUT disfavoured by ∆χ2 ∼ 3 due to the BR(Bs,d → µ+µ−) constraint. The lower limitson strongly-interacting sparticles are largely determined by LHC searches, and similar to those in the CMSSM.We find a preference for the LSP to be a Bino or Higgsino with mχ0

1∼ 1 TeV, with annihilation via heavy Higgs

bosons H/A and stop coannihilation, or chargino coannihilation, bringing the cold dark matter density into thecosmological range. We find that spin-independent dark matter scattering is likely to be within reach of theplanned LUX-Zeplin and XENONnT experiments. We probe the impact of the (g−2)µ constraint, finding similarresults whether or not it is included.

KCL-PH-TH/2017-45, CERN-PH-TH/2017-197, DESY 17-156, IFT-UAM/CSIC-17-089

FTPI-MINN-17/19, UMN-TH-3703/17

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1. Introduction

Models invoking the appearance of supersym-metry (SUSY) at the TeV scale are being sorelytested by the negative results of high-sensitivitysearches for sparticles at the LHC [1,2] and for thescattering of dark matter particles [3–6]. Therehave been many global analyses of the impli-cations of these experiments for specific SUSYmodels, mainly within the minimal supersymmet-ric extension of the Standard Model (MSSM),in which the lightest supersymmetric particle(LSP) is stable and a candidate for dark matter(DM). This may well be the lightest neutralino,χ01 [7], as we assume here. Some of these stud-

ies have assumed universality of the soft SUSY-breaking parameters at the GUT scale, e.g., inthe constrained MSSM (the CMSSM) [8–11] andin models with non-universal Higgs masses (theNUHM1,2) [9, 12]. Other analyses have taken aphenomenological approach, allowing free varia-tion in the soft SUSY-breaking parameters at theelectroweak scale (the pMSSM) [13–16].

A key issue in the understanding of the im-plications of the LHC searches for SUSY is theexploration of regions of parameter space wherecompressed spectra may reduce the sensitivity ofsearches for missing transverse energy, /ET . Theseregions also have relevance to cosmology, sincemodels with sparticles that are nearly degener-ate with the LSP allow for important coannihila-tion processes that suppress the relic LSP numberdensity, allowing heavier values of mχ0

1. The ac-

companying heavier SUSY spectra are also morechallenging for the LHC /ET searches.

The CMSSM offers limited prospects for coan-nihilation, and examples that have been studiedin some detail include coannihilation with thelighter stau slepton, τ1 [17, 18], or the lighterstop squark, t1 [19]. Other models offer thepossibilities of different coannihilation partners,such as the lighter chargino, χ±

1 [14, 20], someother slepton [16] or squark flavour [21], or thegluino [22, 23]. In particular, the pMSSM allowsfor all these possibilities, potentially also in com-bination [16].

In this paper we study the implications of LHCand DM searches for an intermediate class of

SUSY models, in which universality of the softSUSY-breaking parameters is imposed at someinput scale Min below the GUT scale MGUT butabove the electroweak scale [24, 25], which weterm ‘sub-GUT’ models. Models in this class arewell motivated theoretically, since the soft SUSY-breaking parameters in the visible sector may beinduced by some dynamical mechanism such asgluino condensation that kicks in below the GUTscale. Specific examples of sub-GUT models in-clude warped extra dimensions [26] and miragemediation [27].

Mirage mediation can occur when two sourcesof supersymmetry breaking play off each other,such as moduli mediation based, e.g., on mod-uli stabilization as in [28] and anomaly me-diation [29]. The relative contributions ofeach source of supersymmetry breaking can beparametrized by the strength of the moduli me-diation, α, and allows one to interpolate be-tween nearly pure moduli mediation (large α) andnearly pure anomaly mediation (α → 0). Forexample, gaugino masses, Mi, can be written asMi = Ms(α + big

2i ) where Ms is related to the

gravitino mass in anomaly mediation (m3/2 =16π2Ms), and bi, gi are the beta functions andgauge couplings. This leads to a renormaliza-tion scale, Min = MGUT e

−8π2/α at which gauginomasses and soft scalar masses take unified values,although there is no physical threshold at Min inthis model. We are not concerned here with thedetailed origin of Min, simply postulating thatthere is a scale below the GUT scale where thesupersymmetry breaking masses are unified.

Sub-GUT models are of particular phenomeno-logical interest, since the reduction in the amountof renormalization-group (RG) running belowMin, compared to that below MGUT in theCMSSM and related models, leads naturally toSUSY spectra that are more compressed [24].These may offer extended possibilities for ‘hiding’SUSY via suppressed /ET signatures, as well asoffering enhanced possibilities for different coan-nihilation processes. Other possible effects ofthe reduced RG running include a stronger lowerlimit on mχ0

1because of the smaller hierarchy

with the gluino mass, a stronger lower limit on theDM scattering cross section because of a smaller

2

3

hierarchy between mχ01

and the squark masses,and greater tension between LHC searches and apossible SUSY explanation of the measurementof (g− 2)µ [30,31], because of the smaller hierar-chies between the gluino and squark masses andthe smuon and χ0

1 masses.We use the MasterCode framework [8,9,12,14,

16, 21, 32–35] to study these issues in the sub-GUT generalization of the CMSSM, which has5 free parameters, comprising Min as well asa common gaugino mass m1/2, a common softSUSY-breaking scalar mass m0, a common trilin-ear mixing parameter A and the ratio of MSSMHiggs vevs tanβ, assuming that the Higgs mix-ing parameter µ > 0, as may be suggested by(g − 2)µ

1. Our global analysis takes into ac-count the relevant CMS searches for strongly-andelectroweakly-interacting sparticles with the full2016 sample of ∼ 36/fb of data at 13 TeV [36–38],and also considers the available results of searchesfor long-lived charged particles [39,40] 2. We alsoinclude a complete set of direct DM searches pub-lished in 2017, including the PICO limit on thespin-dependent scattering cross section, σSD

p [4],as well as the first XENON1T limit [5] and themost recent PandaX-II limit [6] on the spin-independent scattering cross section, σSI

p , as wellas the previous LUX search [3]. We also includefull sets of relevant electroweak and flavour con-straints.

We find in our global sub-GUT analysis a dis-tinct preference for MW Min MGUT, withvalues of Min ∼ 105 or ∼ 108 to 109 GeV beingpreferred by ∆χ2 ∼ 3 compared to the CMSSM(where Min = MGUT). This preference is drivenprincipally by the ability of the sub-GUT MSSMto accommodate a value of BR(Bs,d → µ+µ−)smaller than in the Standard Model (SM), aspreferred by the current data [41–43]. As dis-cussed later, this effect can be traced to thedifferent RGE evolution of At in the sub-GUTmodel, which enables it have a different signfrom that in the CMSSM. The lower limits on

1We have also made an exploratory study for µ < 0 witha limited sample, finding quite similar results within thestatistical uncertainties.2The ATLAS SUSY searches with ∼ 36/fb of data at13 TeV [2] yield similar constraints.

strongly-interacting sparticles are similar to thosein the CMSSM, being largely determined by LHCsearches. The favoured DM scenario is that theLSP is a Bino or Higgsino with mχ0

1∼ 1 TeV,

with the cold DM being brought into the cos-mological range by annihilation via heavy Higgsbosons H/A and stop coannihilation, or charginocoannihilation. In contrast to the CMSSM andpMSSM11, the possibility that mχ0

1 1 TeV is

strongly disfavoured in the sub-GUT model, sothe LHC constraints have insignificant impact.The same is true of the LHC searches for long-lived charged particles.

The likelihood functions for fits with and with-out the (g − 2)µ constraint are quite similar, re-flecting the anticipated difficulty in accounting forthe (g − 2)µ anomaly in the sub-GUT MSSM.Encouragingly, we find a preference for a rangeof σSI

p just below the current upper limits, andwithin the prospective sensitivities of the LUX-Zeplin (LZ) [44] and XENONnT [45] experiments.

The outline of this paper is as follows. In Sec-tion 2 we summarize the experimental and astro-physical constraints we apply. Since we followexactly our treatments in [16], we refer the in-terested reader there for details. Then, in Sec-tion 3 we summarize the MasterCode frameworkand how we apply it to the sub-GUT models. Ourresults are presented in Section 4. Finally, Sec-tion 5 summarizes our conclusions and discussesfuture perspectives for the sub-GUT MSSM.

2. Experimental and Astrophysical Con-straints

2.1. Electroweak and Flavour ConstraintsOur treatments of these constraints are identi-

cal to those in [16], which were based on Table 1of [21] with the updates listed in Table 2 of [16].Since we pay particular attention in this paperto the impact on the sub-GUT parameter spaceof the (g − 2)µ constraint [30], we note that weassume

aEXPµ −aSMµ = (30.2±8.8±2.0MSSM)×10−10 (1)

to be the possible discrepancy with SM calcula-tions [31] that may be explained by SUSY. Aswe shall see, the BR(Bs,d → µ+µ−) measure-

4

ment [41–43] plays an important role in indicat-ing a preferred region of the sub-GUT parameterspace.

2.2. Higgs ConstraintsIn the absence of published results on the Higgs

boson based on Run 2 data, we use in this globalfit the published results from Run 1 [46], as in-corporated in the HiggsSignals code [47].

Searches for heavy MSSM Higgs bosons areincorporated using the HiggsBounds code [48],which uses the results from Run 1 of the LHC.We also include the ATLAS limit from ∼ 36/fbof data from the LHC at 13 TeV [49].

2.3. Dark Matter Constraints andMechanisms

Cosmological densitySince R-parity is conserved in the MSSM,

the LSP is a candidate to provide the coldDM (CDM). We assume that the LSP is thelightest neutralino χ0

1 [7], and that it domi-nates the total CDM density. For the latterwe assume the Planck 2015 value: ΩCDMh

2 =0.1186± 0.0020EXP ± 0.0024TH [50].

Density mechanismsAs in [16], we use the following set of mea-

sures related to particle masses to indicate whenspecific mechanisms are important for bringingΩCDMh

2 into the Planck 2015 range, which havebeen validated by checks using Micromegas [51].

•Chargino coannihilationThis may be important if the χ0

1 is not muchlighter than the lighter chargino, χ±

1 , and we in-troduce the following coannihilation measure:

chargino coann. :

(mχ±

1

mχ01

− 1

)< 0.25 . (2)

We shade green in the 2-dimensional plots inSection 4 the parts of the 68 and 95% CL regionswhere (2) is satisfied.

•Rapid annihilation via direct-channel H/A polesWe find that LSP annihilation is enhanced sig-

nificantly if the following condition is satisfied:

H/A funnel :

∣∣∣∣∣MA

mχ01

− 2

∣∣∣∣∣ < 0.1 , (3)

and shade in blue the parts of the 68 and 95% CLregions of the two-dimensional plots in Section 4where (3) is satisfied.

•Stau coannihilationWe introduce the following measure for stau

coannihilation:

τ coann. :

(mτ1

mχ01

− 1

)< 0.15 , (4)

and shade in pink the corresponding area of the68 and 95% CL regions of the two-dimensionalsub-GUT parameter planes. We do not find re-gions where coannihilation with other chargedslepton species, or with sneutrinos, is important.

•Stop coannihilationWe introduce the following measure for stop

coannihilation:

t1 coann. :

(mt1

mχ01

− 1

)< 0.15 , (5)

and shade in yellow the corresponding area of the68 and 95% CL regions of the two-dimensionalsub-GUT parameter planes. We do not findregions where coannihilation with other squarkspecies, or with gluinos, is important.

•Focus-point regionThe sub-GUT parameter space has a focus-

point region where the DM annihilation rate is en-hanced because the LSP χ0

1 has an enhanced Hig-gsino component as a result of near-degeneracyin the neutralino mass matrix. We introduce thefollowing measure to characterize this possibility:

focus point :

(µ

mχ01

)− 1 < 0.3 , (6)

and shade in cyan the corresponding area of the68 and 95% CL regions of the two-dimensional

5

sub-GUT parameter planes.

•Hybrid regionsIn addition to regions where one of the above

DM mechanisms is dominant, there are alsovarious ‘hybrid’ regions where more than onemechanism is important. These are indicatedin the two-dimensional planes below by shad-ings in mixtures of the ‘primary’ colours above,which are shown in the corresponding figure leg-ends. For example, there are prominent regionswhere both chargino coannihilation and direct-channel H/A poles are important, whose shadingis darker than the blue of regions where H/Apoles are dominant.

Direct DM searchesWe apply the constraints from direct searches

for weakly-interacting dark matter particles viaboth spin-independent and -dependent scat-tering on nuclei. In addition to the 2016LUX constraint on σSI

p [3], we use the 2017XENON1T [5] and PandaX-II [6] constraintson the spin-independent DM scattering, whichwe combine in a joint two-dimensional likeli-hood function in the (mχ0

1, σSIp ) plane. We es-

timate the spin-independent nuclear scatteringmatrix element assuming σ0 = 36 ± 7 MeV andΣπN = 50± 7 MeV as in [52,53] 3, and the spin-dependent nuclear scattering matrix elementassuming ∆u = +0.84± 0.03,∆d = −0.43± 0.03and ∆s = −0.09±0.03 [52,53]. We implement therecent PICO [4] constraint on the spin-dependentdark matter scattering cross-section on protons,σSDp .

Indirect astrophysical searches for DMAs discussed in [16], there are considerable un-certainties in the use of IceCube data [56] toconstrain σSD

p and, as we discuss below, theglobal fit yields a prediction that lies well belowthe current PICO [4] constraint on σSD

p and the

3We note that a recent analysis using covariant baryon chi-ral perturbation theory yields a very similar central valueof ΣπN [54]. However, we emphasize that there are stillconsiderable uncertainties in the estimates of σ0 and ΣπNand hence the 〈N |ss|N〉 matrix element that is importantfor σSI

p [55].

current IceCube sensitivity, so we do not includethe IceCube data in our global fit.

2.4. 13 TeV LHC ConstraintsSearches for gluinos and squarks

We implement the CMS simplified modelsearches with ∼ 36/fb of data at 13 TeV forevents with jets and /ET but no leptons [36]and for events with jets, /ET and a single lep-ton [37], using the Fastlim approach [57]. Weuse [36] to constrain gg → [qqχ0

1]2 and [bbχ01]2,

and q ˜q → [qχ01][qχ0

1], and use [37] to constraingg → [ttχ0

1]2. Details are given in [16].

Stop and sbottom searchesWe also implement the CMS simplified model

searches with ∼ 36/fb of data at 13 TeV inthe jets + 0 [36] and 1 [37] lepton final states

to constrain t1˜t1 → [tχ01][tχ0

1], [cχ01][cχ0

1] in thecompressed-spectrum region, [bW+χ0

1][bW−χ01]

via χ±1 intermediate states and b1

˜b1 → [bχ01][bχ0

1],again using Fastlim as described in detail in [16].

Searches for electroweak inosWe also consider the CMS searches for elec-

troweak inos in multilepton final states with∼ 36/fb of data at 13 TeV [38], constrainingχ±1 χ

02 → [Wχ0

1][Zχ01], 3`± + 2χ0

1 via ˜±/ν in-termediate states, and 3τ± + 2χ0

1 via τ± inter-mediate states using Fastlim [57] as describedin [16]. These analyses can also be used to con-strain the production of electroweak inos in thedecays of coloured sparticles, since these searchesdo not impose conditions on the number of jets.However, as we discuss below, in the sub-GUTmodel the above-mentioned searches for strongly-interacting sparticles impose such strong limitson the mχ0

1and mχ±

1that the searches for elec-

troweak inos do not have significant impact onthe preferred parameter regions.

Searches for long-lived or stable charged particlesWe also consider a posteriori the search for

long-lived charged particles published in [39],which are sensitive to lifetimes & ns, and thesearch for massive charged particles that escapefrom the detector without decaying [40]. How-

6

ever, these also do not have significant impact onthe preferred parameter regions, as we discuss indetail below, and are not included in our globalfit.

3. Analysis Framework

3.1. Model ParametersAs mentioned above, the five-dimensional sub-

GUT MSSM parameter space we consider in thispaper comprises a gaugino mass parameter m1/2,a soft SUSY-breaking scalar mass parameter m0

and a trilinear soft SUSY-breaking parameter A0

that are assumed to be universal at some inputmass scale Min, and the ratio of MSSM Higgsvevs, tanβ. Table 1 displays the ranges of theseparameters sampled in our analysis, as well astheir divisions into segments, which define boxesin the five-dimensional parameter space.

Parameter Range # ofsegments

Min (103, 1016) GeV 6m1/2 (0, 6) TeV 2m0 (0, 6) TeV 2A0 (−15, 10) TeV 2

tanβ ( 1 , 60) 2Total # of boxes 96

Table 1The ranges of the sub-GUT MSSM parameterssampled, together with the numbers of segmentsinto which they are divided, together with the to-tal number of sample boxes shown in the last row.This sample is for positive values of the Higgsmixing parameter, µ. As already noted, a smallersample for µ < 0 gives similar results. Note thatour sign convention for A is opposite to that usedin SoftSusy [58].

3.2. Sampling ProcedureWe sample the boxes in the five-dimensional

sub-GUT MSSM parameter space using the

MultiNest package [59], choosing for each box aprior such that 80% of the sample has a flat dis-tribution within the nominal box, and 20% of thesample is in normally-distributed tails extendingoutside the box. This eliminates features asso-ciated with the boundaries of the 96 boxes, byproviding a smooth overlap between them. In to-tal, our sample includes ∼ 112 million points with∆χ2 < 100.

3.3. The MasterCode

The MasterCode framework [8, 9, 12, 14, 16,21, 32–35], interfaces and combines consis-tently various private and public codes usingthe SUSY Les Houches Accord (SLHA) [60].This analysis uses the following codes:SoftSusy 3.7.2 [58] for the MSSM spectrum,FeynWZ [61] for the electroweak precision observ-ables, SuFla [62] and SuperIso [63] for flavourobservables, FeynHiggs 2.12.1-beta [64]for (g − 2)µ and calculating Higgs prop-erties, HiggsSignals 1.4.0 [47] andHiggsBounds 4.3.1 [48] for experimental con-straints on the Higgs sector, Micromegas 3.2 [51]for the DM relic density, SSARD [53] for the spin-independent and -dependent elastic scatteringcross-sections σSI

p and σSDp , SDECAY 1.3b [65]

for sparticle branching ratios and (as alreadymentioned) Fastlim [57] to recast LHC 13 TeVconstraints on events with /ET .

4. Results

4.1. Results for Min,m0 and m1/2

The top left panel of Fig. 1 displays the one-dimensional profile χ2 likelihood function for Min,as obtained under various assumptions 4. In thisand subsequent one-dimensional plots, the solidlines represent the results of a fit including resultsfrom ∼ 36/fb of data from the LHC at 13 TeV(LHC13), whereas the dashed lines omit these re-sults, and the blue lines include (g−2)µ, whereasthe green lines are obtained when this constraintis dropped.

We observe in the top left panel of Fig. 1 a pref-erence for Min ' 4.2 × 108 GeV when the LHC

4This and subsequent figures were made usingMatplotlib [66], unless otherwise noted.

7

3 4 5 6 7 8 9 10 11 12 13 14 15 16Log Min[GeV]

0

1

2

3

4

5

6

7

8

9

∆χ

2

sub-GUTLHC13, (g− 2)µ

LHC8, (g− 2)µ

LHC13, w/o (g− 2)µ

LHC8, w/o (g− 2)µ

0 1000 2000 3000 4000 5000 6000

m0[GeV]

0

1000

2000

3000

4000

5000

6000

m1/2

[GeV

]

sub-GUT MSSM: best fit, 1σ, 2σ, 3σ

3 4 5 6 7 8 9 10 11 12 13 14 15 16

Log Min[GeV]

0

1000

2000

3000

4000

5000

6000

m0[G

eV

]

sub-GUT MSSM: best fit, 1σ, 2σ, 3σ

3 4 5 6 7 8 9 10 11 12 13 14 15 16

Log Min[GeV]

0

1000

2000

3000

4000

5000

6000

m1/

2[G

eV

]

sub-GUT MSSM: best fit, 1σ, 2σ, 3σ

0 1000 2000 3000 4000 5000 6000m0[GeV]

0

1

2

3

4

5

6

7

8

9

∆χ

2

sub-GUTLHC13, (g− 2)µ

LHC8, (g− 2)µ

LHC13, w/o (g− 2)µ

LHC8, w/o (g− 2)µ

0 1000 2000 3000 4000 5000 6000m1/2[GeV]

0

1

2

3

4

5

6

7

8

9

∆χ

2

sub-GUTLHC13, (g− 2)µ

LHC8, (g− 2)µ

LHC13, w/o (g− 2)µ

LHC8, w/o (g− 2)µ

χ ±1 coann.

A/H funnel

t1 coann.

τ1 coann.

focus point

t1 coann. + H/A funnel

τ1 + t1 coann.

t1 + χ ±1 coann.

τ1 coann. + t1 coann. + H/A

Figure 1. Profile likelihood functions in the sub-GUT MSSM. Top left: One-dimensional profile likelihoodfunction for Min. Top right: Two-dimensional projection of the likelihood function in the (m0,m1/2)plane. Middle left: Two-dimensional projection of the likelihood function in the (Min,m0) plane. Middleright: Two-dimensional projection of the likelihood function in the (Min,m1/2) plane. Bottom left: One-dimensional profile likelihood function for m0. Bottom right: One-dimensional profile likelihood functionfor m1/2. Here and in subsequent one-dimensional plots, the solid lines include the constraints from∼ 36/fb of LHC data at 13 TeV and the dashed lines drop them, and the blue lines include (g − 2)µ,whereas the green lines drop these constraints. Here and in subsequent two-dimensional plots, the red(blue) (green) contours are boundaries of the 1-, 2- and 3-σ regions, and the shadings correspond to theDM mechanisms indicated in the legend.

8

13-TeV data and (g−2)µ are both included (solidblue line), falling to ' 5.9×105 GeV when the 13-TeV data are dropped (dashed blue line). Thereis little difference between the global χ2 values atthese two minima, but values of Min < 105 GeVare strongly disfavoured. The rise in ∆χ2 whenMin increases to ∼ 106 GeV and the LHC 13-TeVdata are included (solid lines) is largely due to thecontribution of BR(Bs,d → µ+µ−). At lower Min,the H → τ+τ− constraint allows a larger valueof tanβ, which leads (together with an increasein the magnitude of A) to greater negative in-terference in the supersymmetric contribution toBR(Bs,d → µ+µ−), as preferred by the data.

For both fits including the LHC 13-TeV data(solid lines), the ∆χ2 function ∼ 1 for most ofthe range Min ∈ (105, 1011) GeV, apart fromlocalized dips, whereas ∆χ2 rises to & 2 forMin & 1012 GeV. As already mentioned and dis-cussed in more detail later, the reduction in theglobal χ2 function for Min . 1012 GeV arisesbecause for these values of Min the sub-GUTmodel can accommodate better the measurementof BR(Bs,d → µ+µ−), whose central experimen-tal value is somewhat lower than in the SM.

When the (g − 2)µ constraint is dropped, asshown by the green lines in top left panel ofFig. 1, there is a minimum of χ2 around Min '1.6 × 105 GeV, whether the LHC 13-TeV con-straint is included, or not. The values of theother input parameters at the best-fit points withand without these data are also very similar, asare the values of ∆χ2. On the other hand, thevalues of ∆χ2 for Min ∈ (105, 108) GeV are gen-erally smaller when the LHC 13-TeV constraintsare dropped, the principal effect being due to theH/A→ τ+τ− constraint.

In contrast, when Min & 109 GeV the ∆χ2

function in the top left panel of Fig. 1 is quitesimilar whether the LHC 13-TeV and (g − 2)µconstraints are included or not, though ∆χ2 & 0.5lower when the (g− 2)µ constraint is dropped, asseen by comparing the green and blue lines. Thisis because the tension between (g− 2)µ and LHCdata is increased when M3/M1 is reduced, as oc-curs because of the smaller RGE running whenMin < MGUT. Conversely, lower Min is relativelymore favoured when (g − 2)µ is dropped, leading

to this increase in ∆χ2 at high Min though thetotal χ2 is reduced.

We list in Table 2 the parameters of the best-fitpoints when we drop one or both of the (g − 2)µand LHC13 constraints, as well as the values ofthe global χ2 function at the best-fit points. Wesee that the best-fit points without (g − 2)µ arevery similar with and without the LHC 13-TeVconstraint. On the other hand, the best-fit pointswith (g − 2)µ have quite different values of theother input parameters, as well as larger valuesof Min, particularly when the LHC 13-TeV dataare included.

The top right panel of Fig. 1 displays the(m0,m1/2) plane when the (g − 2)µ and LHC13constraints are applied. Here and in subsequentplanes, the green star indicates the best-fit point,whose input parameters are listed in Table 2: itlies in a hybrid stop coannihilation and rapidH/Aannihilation region.

This parameter plane and others in Fig. 1 andsubsequent figures also display the 68% CL (1-σ), 95% CL (2-σ) and 99.7% (3-σ) contours inthe fit including both (g − 2)µ and the LHC13data as red, blue and green lines, respectively.We note, here and subsequently, that the green3-σ contours are generally close to the blue 2-σcontours, indicating a relatively rapid increase inχ2, and that the χ2 function is relatively flat form0,m1/2 & 1 TeV. The regions inside the 95%CL contours are colour-coded according to thedominant DM mechanisms, as shown in the leg-end beneath Fig. 1 5. Similar results for this andother planes are obtained when either or both ofthe (g− 2)µ and LHC13 constraints are dropped.

We see that chargino coannihilation is impor-tant in the upper part of the (m0,m1/2) planeshown in the top right panel of Fig. 1, but rapidannihilation via the H/A bosons becomes im-portant for lower m1/2, often hybridized withother mechanisms including stop and stau coan-nihilation. We also note smaller regions withm1/2 ∼ 1.5 to 3 TeV where stop coannihilationand focus-point mechanisms are dominant.

The middle left panel of Fig. 1 shows the cor-

5In regions left uncoloured none of the DM mechanismdominance criteria are satisfied.

9

m0 [GeV] m1/2 [GeV] A0 [GeV] tanβ Min [GeV] χ2

With (g − 2)µWith 13-TeV 1940 1370 - 6860 36 4.1× 108 99.56

Without 13-TeV 1620 6100 - 8670 45 5.7× 105 99.38Without (g − 2)µ

With 13-TeV 3550 6560 - 14400 45 1.6× 105 88.73Without 13-TeV 3340 6390 - 14260 45 1.6× 105 88.67

Table 2Values of the sub-GUT input parameters at the best-fit points with and without (g − 2)µ and the LHC13-TeV data.

responding (Min,m0) plane, where we see a sig-nificant positive correlation between the variablesthat is particularly noticeable in the 68% CL re-gion. In most of this and the 95% CL region withMin . 1013 GeV the relic LSP density is con-trolled by chargino coannihilation, though withpatches where rapid annihilation via the A/Hbosons is important, partly in hybrid combina-tions. In contrast, the (Min,m1/2) plane shownin the middle right panel of Fig. 1 does not ex-hibit a strong correlation between the variables.We see again the importance of chargino coan-nihilation, with the A/H mechanism becomingmore important for lower m1/2 and larger Min,and for all values of m1/2 for Min & 1014 GeV.

Also visible in the middle row of planes aresmall regions with Min ∼ 1013 to 1014 GeVwhere stau coannihilation is dominant, partly hy-bridized with stop coannihilation. The reductionin the global χ2 function for Min . 1012 GeV visi-ble in the top left panel of Fig. 1 is associated withthe 68% CL regions in this range of Min visiblein the two middle planes of Fig. 1.

The one-dimensional profile likelihood func-tions for m0 and m1/2 are shown in the bottompanels of Fig. 1. We note once again the similar-ities between the results with/without (g − 2)µ(blue/green lines) and the LHC13 constraints(solid/dashed lines). The flattening of the χ2

function for m0 at small values reflects the ex-tension to m0 = 0 of the 95% CL region in thetop right panel of Fig. 1. On the other hand, theχ2 function for m1/2 rises rapidly at small values,reflecting the close spacing of the 95 and 99.7%CL contours for m1/2 ∼ 1 TeV seen in the sameplane. The impact of the LHC13 constraints is

visible in the differences between the solid anddashed curves at small m0, in particular. The(g − 2)µ constraint has less impact, as shown bythe smaller differences between the green and bluecurves. We see that the χ2 function for m0 risesby & 1 at large mass values, whereas that form1/2 falls monotonically at large values. The χ2

function for m1/2 exhibits a local maximum atm1/2 ∼ 3 TeV, which corresponds to the separa-tion between the two 68% CL regions in the topright plane of Fig. 1. These are dominated bychargino coannihilation (larger m1/2, green shad-ing) and by rapid annihilation via A/H bosons(smaller m1/2, blue shading) and other mecha-nisms, respectively.

4.2. Squarks and gluinosThe various panels of Fig. 2 show the lim-

ited impact of the LHC 13-TeV constraints onthe possible masses of strongly-interacting spar-ticles in the sub-GUT model, comparing the solidand dashed curves. The upper left panel showsthat the 95% CL lower limit on mg ∼ 1.5 TeV,whether the LHC 13-TeV data and the (g − 2)µconstraint are included or not. However, the best-fit value of mg increases from ∼ 2 TeV to a verylarge value when (g − 2)µ is dropped, althoughthe ∆χ2 price for mg ∼ 2 TeV is ∼ 1. The up-per right panel shows similar features in the pro-file likelihood function for mqR (that for mqL issimilar), with a 95% CL lower limit of ∼ 2 TeV,which is again quite independent of the inclusionof (g − 2)µ and the 13-TeV data. The lower pan-els of Fig. 2 show the corresponding profile likeli-hood functions for mt1

(left panel) and mb1(right

panel). We see that these could both be consid-

10

0 1000 2000 3000 4000mg[GeV]

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0 1000 2000 3000 4000 5000 6000mqR[GeV]

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0 1000 2000 3000 4000mt1[GeV]

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0 1000 2000 3000 4000mb1

[GeV]

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2

sub-GUTLHC13, (g− 2)µ

LHC8, (g− 2)µ

LHC13, w/o (g− 2)µ

LHC8, w/o (g− 2)µ

Figure 2. One-dimensional profile likelihood functions for mg (upper left panel), mqR (upper right panel),mt1

(lower left panel) and mb1(lower right panel).

erably lighter than the gluino and the first- andsecond-generation squarks, with 95% CL lowerlimits mt1

∼ 900 GeV and mb1∼ 1.5 TeV, re-

spectively.

4.3. The lightest neutralino and lighterchargino

The top left panel of Fig. 3 shows the profilelikelihood function for mχ0

1, and the top right

panel shows that for mχ±1

. We see that in all the

cases considered (with and without the (g − 2)µand LHC13 constraints), the value of ∆χ2 cal-culated using the LHC constraints on strongly-interacting sparticles is larger than 4 for mχ0

1.

750 GeV and mχ±1

. 800 GeV. Therefore, the

LHC electroweakino searches [38] have no impacton the 95% CL regions in our 2-dimensional pro-jections of the sub-GUT parameter space, and wedo not include the results of [38] in our global fit.

We now examine the profile likelihood func-tions for the fractions of Bino, Wino and Higgsinoin the χ0

1 composition:

χ01 = N11B +N12W

3 +N13Hu +N14Hd , (7)

which are shown in Fig. 4. As usual, results froman analysis including the 13-TeV data are shownas solid lines and without them as dashed lines,with (g−2)µ as blue lines and without it as green

11

0 500 1000 1500 2000mχ0

1[GeV]

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0 1000 2000 3000 4000mχ±1 [GeV]

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10-1 100 101 102 103

mχ±1 −mχ01 [GeV]

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1000 2000 3000 4000MA[GeV]

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LHC8, (g− 2)µ

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LHC8, w/o (g− 2)µ

0 1000 2000 3000 4000

mχ±1 [GeV]

10-16

10-15

10-14

10-13

10-12

10-11

10-10

τ χ± 1 [

s]

sub-GUT MSSM: 1σ, 2σ, 3σ

Figure 3. One-dimensional profile likelihood functions for mχ01

(top left panel) and mχ±1

(top right panel),

mχ±1− mχ0

1(middle left panel) the χ±

1 lifetime (middle right panel) and MA (bottom left panel). The

bottom right panel shows the regions of the (mχ±1, τχ±

1) plane with τχ±

1≥ 10−15 s that are allowed in the

fit including the (g − 2)µ and LHC 13-TeV constraints at the 68 (95) (99.7)% CL in 2 dimensions, i.e.,∆χ2 < 2.30(5.99)(11.83), enclosed by the red (blue) (green) contour.

12

lines. The top left panel shows that in the LHC13-TeV case with (g−2)µ an almost pure B com-position of the χ0

1 is preferred, N11 → 1, thoughthe possibility that this component is almost ab-sent is only very slightly disfavoured. Conversely,before the LHC 13-TeV data there was a verymild preference for N11 → 0, and this is still thecase if (g−2)µ is dropped. The upper right panel

shows that a small W 3 component in the χ01 is

strongly preferred in all cases. Finally, the lowerpanel confirms that small Hu,d components arepreferred when the LHC 13-TeV and (g−2)µ con-

straints are applied, but large Hu,d componentsare preferred otherwise.

The χ01 compositions favoured at the 1-, 2- and

3-σ levels (blue, yellow and red) are displayed inFig. 5 for fits including LHC 13-TeV data with(without) the (g−2)µ constraint in the left (right)panel. We see that these regions are quite similarin the two panels, and correspond to small Winoadmixtures. On the other hand, the Bino fractionN2

11 and the Higgsino fraction N213 +N2

14 are rela-tively unconstrained at the 95% CL. The best-fitpoints are indicated by green stars, and the leftpanel shows again that in the fit with (g − 2)µthe LSP is an almost pure Bino, whereas an al-most pure Higsino composition is favoured in thefit without (g−2)µ, as also seen in Table 3. Thesetwo extremes have very similar χ2 values in eachof the fits displayed.

B W3 Hu Hd

With (g − 2)µWith 13-TeV 0.999 -0.010 0.041 -0.025

Without 13-TeV 0.007 -0.011 0.707 -0.707Without (g − 2)µ

With 13-TeV 0.006 -0.010 0.707 -0.707Without 13-TeV 0.007 -0.011 0.707 -0.707

Table 3Composition of the χ0

1 LSP at the best-fit pointswith and without (g − 2)µ and the LHC 13-TeVdata.

The global χ2 function is minimized for mχ01'

1.0 TeV, which is typical of scenarios with a

Higgsino-like LSP whose density is brought intothe Planck 2015 range by coannihilation with anearly-degenerate Higgsino-like chargino χ±

1 . In-deed, we see in the top right panel of Fig. 3that χ2 is minimized when also mχ±

1' mχ0

1'

1.0 TeV. Table 3 displays the LSP compositionof the sub-GUT model at the best-fit points withand without (g − 2)µand the LHC 13-TeV data.We see again that the χ0

1 LSP is mainly a Hig-gsino with almost equal Hu and Hd components,except in the fit with both LHC 13-TeV data and(g − 2)µ included, in which case it is an almostpure Bino.

Looking at the middle left panel of Fig. 3, wesee that the best-fit point has a chargino-LSPmass difference that may be O(1) GeV or ∼ 200to 300 GeV, with similar χ2 in all the cases con-sidered, namely with and without the (g−2)µ andLHC13 constraints. As seen in the middle rightpanel of Fig. 3, in the more degenerate case thepreferred chargino lifetime τχ±

1∼ 10−12 s. The

current LHC searches for long-lived charged par-ticles [39] therefore do not impact this charginocoannihilation region, and are also not includedin our global fit.

The top right panel of Fig. 3 displays an almost-degenerate local minimum of χ2 with mχ±

1∼

1.3 TeV, corresponding to a second, local mini-mum of χ2 where mχ±

1−mχ0

1∼ 200 to 300 GeV,

as seen in the middle left panel. In this regionthe relic density is brought into the Planck 2015range by rapid annihilation through A/H bosons,as can be inferred from the bottom left panel ofFig. 3, where we see that at this secondary min-imum MA ' 2 TeV ' 2mχ0

1. The χ±

1 lifetime inthis region is too short to appear in the middleand bottom right panels of Fig. 3, and too shortto have a separated vertex signature at the LHC.

Finally, the bottom right panel of Fig. 3 showsthe regions of the (mχ±

1, τχ±

1) plane with τχ±

1∈

(10−16, 10−10) s that are allowed in the fit includ-ing the (g − 2)µ and LHC 13-TeV constraints atthe 68 (95) (99.7) % CL in 2 dimensions, i.e.,∆χ2 < 2.30(5.99)(11.83). Since the charginowould decay into a very soft track and a neu-tralino, detecting a separated vertex in the regionaround the best-fit point would be very challeng-

13

0.0 0.2 0.4 0.6 0.8 1.0N 2

11

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0.0 0.2 0.4 0.6 0.8 1.0N 2

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0.0 0.2 0.4 0.6 0.8 1.0N 2

13 +N 214

0

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2

sub-GUTLHC13, (g− 2)µ

LHC8, (g− 2)µ

LHC13, w/o (g− 2)µ

LHC8, w/o (g− 2)µ

Figure 4. Plots of the one-dimensional profile likelihood for the B fraction in the LSP χ01 (upper left), for

the W 3 fraction (upper right) and for the Hu,d fraction (lower panel).

ing.

4.4. SleptonsThe upper left panel of Fig. 6 shows the profile

likelihood function for mµR(that for meR is indis-

tinguishable, the µL and eL are slightly heavier).We see that in the sub-GUT model small valuesof mµR

were already disfavoured by earlier LHCdata (dashed lines), and that this tendency hasbeen reinforced by the LHC 13-TeV data (com-pare the solid lines). The same is true whetherthe (g − 2)µ constraint is included or dropped(compare the blue and green curves).

The upper right panel Fig. 6 shows the cor-responding profile likelihood function for mτ1 ,

which shares many similar features. However,we note that the χ2 function for mτ1 is generallylower than that for mµR

∈ (1, 2) TeV, though the95% lower limits on mτ1 and mµR

are quite simi-lar, and both are ' 1 TeV when the LHC 13-TeVconstraints are included in the fit.

The lower left panel of Fig. 6 shows that verysmall values of mτ1 −mχ0

1in the stau coannihi-

lation region are allowed at the ∆χ2 ∼ 1 level inall the fits with the (g − 2)µ constraint, rising to∆χ2 & 2 for mτ1−mχ0

1& 20 GeV when the LHC

13-TeV data are included.The lower right panel of Fig. 6 shows the

(mτ1 , ττ1) plane, where we see that ττ1 ∈

14

0.0

1.0

1.0

0.0

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0.1

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Pure higgsino

Pur

ebi

no

Pure

wino

N213 +

N214

N2

11

N 212

sub-GUT with (g − 2)µ χ01 composition

0.0

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Pur

ebi

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wino

N213 +

N214

N2

11

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sub-GUT w/o (g − 2)µ χ01 composition

0.0

1.5

3.0

4.5

6.0

7.5

9.0

10.5

∆χ

2

Figure 5. Triangular presentations of the χ01 composition in the fit with LHC 13-TeV including (dropping)

the (g− 2)µ constraint in the left (right) panel. The 1-, 2- and 3-σ regions in the plots are coloured blue,yellow and red, and the best-fit points are indicated by green stars.

(10−7, 103) s is allowed at the 68% CL, for1600 GeV . mτ1 . 2000 GeV and at the 95%CL also for mτ1 ∼ 1100 GeV. This region of pa-rameter space is close to the tip of the stau coan-nihilation strip. Lower τ1 masses are strongly dis-favoured by the LHC constraints, particularly at13 TeV, as seen in the upper right panel of Fig. 6.The heavier τ1 masses with lower ∆χ2 seen theredo not lie in the stau coannihilation strip, andhave larger mτ1−mχ0

1and hence smaller lifetimes

that are not shown in the lower right panel ofFig. 6. Because of the lower limit on mτ1 seenin this panel, neither the LHC search for long-lived charged particles [39] nor the LHC searchfor (meta-)stable massive charged particles thatexit the detector [40] are relevant for our globalfit.

In view of this, and the fact that the searchfor long-lived particles [39] is also insensitive inthe chargino coannihilation region, as discussedabove, the results of [39, 40] are not included inthe calculation of the global likelihood function.

4.5. (g − 2)µWe see in the left panel of Fig. 7 that only a

small contribution to (g − 2)µ is possible in sub-GUT models, the profile likelihood functions with

and without the LHC 13-TeV data and (g − 2)µbeing all quite similar. This is because in thesub-GUT model with low Min the LHC searchesfor strongly-interacting sparticles constrain theµ mass more strongly than in the GUT-scaleCMSSM. The dotted line shows the ∆χ2 contri-bution due to our implementation of the (g− 2)µconstraint alone. We see that in all cases it con-tributes ∆χ2 & 9 to the global fit.

4.6. The (MA, tanβ) PlaneThe right panel of Fig. 7 shows the (MA, tanβ)

plane when the LHC 13-TeV data and the (g−2)µconstraint are included in the fit. We see thatMA & 1.3 TeV at the 95% CL and that, whereastanβ ∼ 5 is allowed at the 95% CL. Larger val-ues tanβ & 30 are favoured at the 68% CL, andthe best-fit point has tanβ ' 36. (This increasesto tanβ ∼ 45 if either the LHC 13-TeV and/or(g − 2)µ constraint is dropped.) As in the previ-ous two-dimensional projections of the sub-GUTparameter space, the 99.7% (3-σ) CL contour liesclose to that for the 95% CL.

4.7. B Decay ObservablesWe see in the left panel of Fig. 8 that values of

BR(Bs,d → µ+µ−) smaller than that in the SMare favoured. The sub-GUT models with µ > 0

15

0 1000 2000 3000 4000mµR[GeV]

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[GeV]

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10-3 10-2 10-1 100 101 102 103 104 105

mτ1−mχ0

1 [GeV]

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0 1000 2000 3000 4000

mτ1[GeV]

10-1210-1110-1010-910-810-710-610-510-410-310-210-1100101102103

τ τ1 [

s]

sub-GUT MSSM: 1σ, 2σ, 3σ

Figure 6. One-dimensional profile likelihood functions for mµR(upper left panel), mτ1 (upper right

panel) and mτ1 − mχ01

(lower left panel). The lower right panel shows the (mτ1 , ττ1) plane, colour-coded as indicated in the right-hand legend. The 68 (95) (99.7)% CL regions in 2 dimensions, i.e.,∆χ2 < 2.30(5.99)(11.83), are enclosed by the red (blue) (green) contours.

16

0.0 0.5 1.0 1.5 2.0

∆(g− 2

2

)1e 9

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0 1000 2000 3000 4000

MA[GeV]

10

20

30

40

50

60

tanβ

sub-GUT MSSM: best fit, 1σ, 2σ, 3σ

χ ±1 coann. A/H funnel t1 coann. + H/A funnel

Figure 7. Left panel: One-dimensional profile likelihood function for (g−2)µ, where the dotted line showsthe χ2 contribution due to the (g − 2)µ constraint alone. Right panel: Two-dimensional projection of thelikelihood function in the (MA, tanβ) plane.

flavour constraints

electroweak precision observables

(g− 2)µ

Higgs

DM

nuisance parameters

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

BRMSSM/SMBs, d→µ + µ −

0

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LHC8, w/o (g− 2)µ

4 6 8 10 12 14 16

Log Min[GeV]

0

10

20

30

40

50

60

χ2

Figure 8. Left panel: One-dimensional profile likelihood function for BR(Bs,d → µ+µ−), where the dottedline shows the χ2 contribution due to the BR(Bs,d → µ+µ−) constraint alone. Right panel: Breakdownof the contributions to the global χ2 as functions of Min. The shadings correspond to the different classesof observables, as indicated in the legend.

17

that we have studied can accommodate comfort-ably the preference seen in the data (dotted line)for such a small value of BR(Bs,d → µ+µ−) 6,which is not the case in models such as theCMSSM that impose universal boundary condi-tions on the soft supersymmetry-breaking param-eters at the GUT scale, if µ > 0. The rightpanel of Fig. 8 shows how the contributions ofthe flavour (blue shading) and other observablesto the global likelihood function depend on Min

for values between 104 and 1016 GeV. This vari-ation in the flavour contribution (which is domi-nated by BR(Bs,d → µ+µ−)) is largely responsi-ble for the sub-GUT preference for Min < MGUT

seen in the top left panel of Fig. 1. Values ofMin ∈ (105, 1012) GeV can accommodate verywell the experimental value of BR(Bs,d → µ+µ−).

This preference is made possible by the differ-ent RGE running in the sub-GUT model, whichcan change the sign of the product Atµ thatcontrols the relative signs of the SM and SUSYcontributions to the Bs,d → µ+µ− decay am-plitudes, permitting negative interference thatreduces BR(Bs,d → µ+µ−). As already dis-cussed, the reduction in BR(Bs,d → µ+µ−) andthe global χ2 function for 108 GeV . Min .1012 GeV is associated with the blue 68% CLregions with Min . 1012 GeV seen in the mid-dle panels of Fig. 1. On the other hand, we seein Fig. 9 that sub-GUT models favour values ofBR(b→ sγ) that are close to the SM value.

The contributions to the global χ2 function ofother classes of observables as functions of Min

are also exhibited in the right panel of Fig. 8. Inaddition to the aforementioned reduction in theflavour contribution when Min . 1012 GeV (blueshading), there is a coincident (but smaller) in-crease in the contribution of the electroweak pre-cision observables (orange shading) related to ten-sion in the electroweak symmetry-breaking con-ditions. The other contributions to the globalχ2 function, namely the nuisance parameters(red shading), Higgs mass (light green), (g − 2)µ(teal) and DM (red), vary smoothly for Min ∼1012 GeV.

6This is also the case for the smaller sub-GUT sample withµ < 0 that we have studied.

4.8. Higgs MassWe see in Fig. 10 that the profile likelihood

function for Mh lies within the contribution of thedirect experimental constraint convoluted withthe uncertainty in the FeynHiggs calculation ofMh (dotted line). We infer that there is no ten-sion between the direct experimental measure-ment of Mh and the other observables includedin our global fit. We have also calculated (notshown) the branching ratios for Higgs decays intoγγ, ZZ∗ and gg (used as a proxy for gg → hproduction), finding that they are expected to bevery similar to their values in the SM, with 2-σranges that lie well within the current experimen-tal uncertainties.

4.9. Searches for Dark Matter ScatteringThe left panel of Fig. 11 shows the nominal

predictions for the spin-independent DM scatter-ing cross-section σSI

p obtained using the SSARD

code [53]. We caution that there are considerableuncertainties in the calculation of σSI

p , which aretaken into account in our global fit. Thus pointswith nominal values of σSI

p above the experimen-tal limit may nevertheless lie within the 95% CLrange for the global fit. We see that sub-GUTmodels favour a range of σSI

p close to the presentlimit from the LUX, XENON1T and PandaX-IIexperiments 7. Moreover, at the 95% CL, thenominal sub-GUT predictions for σSI

p are withinthe projected reaches of the LZ and XENON1/nTexperiments. However, they are subject to theconsiderable uncertainty in the σSI

p matrix ele-ment, and might even fall below the neutrino‘floor’ shown as a dashed orange line in [69].

We see in the right panel of Fig. 11 that thesub-GUT predictions for the spin-dependent DMscattering cross-section σSD

p lie somewhat belowthe present upper limit from the PICO direct DMsearch experiment. Spin-dependent DM scatter-ing is also probed by indirect searches for neutri-nos produced by the annihilations of neutralinostrapped inside the Sun after scattering on protonsin its interior. If the neutralinos annihilate intoτ+τ−, the IceCube experiment sets the strongest

7We also show, for completeness, the CRESST-II [72],CDMSlite [73] and CDEX [74] constraints on σSI

p , whichdo not impact range of mχ0

1found in our analysis.

18

0.6 0.8 1.0 1.2 1.4

BREXP/SMBs→Xsγ

0

1

2

3

4

5

6

7

8

9∆χ

2sub-GUT

LHC13, (g− 2)µ

LHC8, (g− 2)µ

LHC13, w/o (g− 2)µ

LHC8, w/o (g− 2)µ

Figure 9. One-dimensional profile likelihood function for BR(b→ sγ), showing the experimental constraintas a dotted line.

120 122 124 126 128 130Mh[GeV]

0

1

2

3

4

5

6

7

8

9

∆χ

2

sub-GUTLHC13, (g− 2)µ

LHC8, (g− 2)µ

LHC13, w/o (g− 2)µ

LHC8, w/o (g− 2)µ

Figure 10. One-dimensional profile likelihood function for Mh, where the dotted line shows the χ2 contri-bution due to the (g − 2)µ constraint alone.

19

100 101 102 103 104

mχ01[GeV]

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

10-42

10-41

10-40

10-39

10-38

σSIp

[cm

2]

PANDAX-II

neutrino floor

XENONnT

LZ

XENON1T

XENON1T

LUX

CRESST-II

CDMSlite

CDEX-1

sub-GUT MSSM: best fit, 1σ, 2σ, 3σ

100 101 102 103 104

mχ01[GeV]

10-47

10-46

10-45

10-44

10-43

10-42

10-41

10-40

10-39

10-38

10-37

σSD

p[c

m2]

PICO-60

IC (2016) ττ

IC (2016) ττ floor

Super-K (2016) ττ

Super-K (2016) ττ floor

sub-GUT MSSM: best fit, 1σ, 2σ, 3σ

χ ±1 coann.

A/H funnel

t1 coann.

τ1 coann.

focus point

t1 coann. + H/A funnel

τ1 + t1 coann.

t1 + χ ±1 coann.

τ1 coann. + t1 coann. + H/A

Figure 11. Left panel: Two-dimensional profile likelihood function for the nominal value of σSIp calcu-

lated using the SSARD code [53] in the (mχ01, σSIp ) plane, displaying also the upper limits established by

the LUX [3], XENON1T [5] and PandaX-II Collaborations [6] shown as solid black, blue and greencontours, respectively. The projected future 90% CL sensitivities of the LUX-Zeplin (LZ) [67] andXENON1T/nT [68] experiments are shown as dashed magenta and blue lines, respectively, and theneutrino background ‘floor’ [69] is shown as a dashed orange line with yellow shading below. Rightpanel: Two-dimensional profile likelihood function for the nominal value of σSD

p calculated using the

SSARD code [53] in the (mχ01, σSDp ) plane, showing also the upper limit established by the PICO Collabora-

tion [4].We also show the indirect limits from the Icecube [56] and Super-Kamiokande [70] experiments,assuming χ0

1χ01 → τ+τ− dominates, as well as the ‘floor’ for σSD

p calculated in [71].

such indirect limit [56], and we also show the con-straint from Super-Kamiokande [70]. These con-straints are currently not sensitive enough to cutinto the range of the (mχ0

1, σSDp ) plane allowed in

our global fit. We also show the neutrino ‘floor’for σSD

p , taken from [71]: wee that values of σSDp

below this floor are quite possible in the sub-GUTmodel.

5. Impacts of the LHC 13-TeV and NewDirect Detection Constraints

We show in Fig. 12 some two-dimensional pro-jections of the regions of sub-GUT MSSM param-eters favoured at the 68% (red lines), 95% (bluelines) and 99.7% CL (green lines), comparing the

results of fits including the LHC 13-TeV dataand recent direct searches for spin-independentdark matter scattering (solid lines) and discardingthem (dashed lines). The upper left panel showsthe (mqR ,mg) plane, the upper right plane showsthe (mqR ,mχ0

1) plane, the lower left plane shows

the (mg,mχ01) plane, and the lower right panel

shows the (mχ01, σSIp ) plane. We see that in the up-

per panels that the new data restrict the favouredparameter space for mqR ∼ 2 TeV, the two leftpanels show a restriction for mg ∼ 1.3 TeV, andthe right and lower panels show that the newdata also restrict the range of mχ0

1to & 800 GeV.

However, the lower right panel does not show anynew restriction on the range of possible values ofσSIp .

20

0 1000 2000 3000 4000 5000 6000

mqR[GeV]

0

1000

2000

3000

4000

5000

6000

7000

8000

mg[G

eV

]

sub-GUT w/ LHC13: best fit, 1σ, 2σ, 3σsub-GUT w/o LHC13: best fit, 1σ, 2σ, 3σ

0 1000 2000 3000 4000 5000 6000

mqR[GeV]

0

500

1000

1500

2000

mχ

0 1[G

eV

]

sub-GUT w/ LHC13: best fit, 1σ, 2σ, 3σsub-GUT w/o LHC13: best fit, 1σ, 2σ, 3σ

0 1000 2000 3000 4000 5000 6000 7000 8000

mg[GeV]

0

500

1000

1500

2000

mχ

0 1[G

eV

]

sub-GUT w/ LHC13: best fit, 1σ, 2σ, 3σsub-GUT w/o LHC13: best fit, 1σ, 2σ, 3σ

100 101 102 103 104

mχ01[GeV]

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

10-42

10-41

10-40

10-39

10-38

σSIp

[cm

2]

PANDAX-II

neutrino floor

XENONnT

LZ

XENON1T

XENON1T

LUX

CRESST-II

CDMSlite

CDEX-1

sub-GUT w/ LHC13: best fit, 1σ, 2σ, 3σsub-GUT w/o LHC13: best fit, 1σ, 2σ, 3σ

Figure 12. Two-dimensional projections of the global likelihood function for the sub-GUT MSSM in the(mqR ,mg) plane (upper left panel), the (mqR ,mχ0

1) plane (upper right panel), the (mg,mχ0

1) plane (lower

left panel), and the (mχ01, σSIp ) plane (lower right panel). In each panel we compare the projections of the

sub-GUT parameter regions favoured at the 68% (red lines), 95% (blue lines) and 99.7% CL (green lines)in global fits with the LHC 13-TeV data and results from LUX, XENON1T, and PandaX-II [3,5,6] (solidlines), and without them (dashed lines).

21

6. Best-Fit Points, Spectra and DecayModes

The values of the input parameters at the best-fit points with and without the (g−2)µ and LHC13-TeV constraints have been shown in Table 2.The best fits have Min between 1.6 × 105 and4.1 × 108 GeV, and we note that the input pa-rameters are rather insensitive to the inclusionof the 13-TeV data when (g − 2)µ is dropped.Table 4 displays the mass spectra obtained asoutputs at the best-fit point including the 13-TeV data (quoted to 3 significant figures) and in-cluding (left column) or dropping (right column)the (g − 2)µ constraint. As could be expected,the sparticle masses are generally heavier when(g − 2)µ is dropped. However, the differences aresmall in the cases of the χ0

1, χ02 and χ±

1 , beinggenerally < 10 GeV. We also give in the next-to-last line of Table 4 the values of the globalχ2 function at these best-fit points, dropping theHiggsSignals contributions, as was done previ-ously [21,33] to avoid biasing the analysis.

The contributions of different observables tothe global likelihood function at the best-fitpoints including LHC13 data are shown inFig. 13. We compare the contributions when(g−2)µ is included (pink histograms) and without(g − 2)µ (blue histograms). We note, in particu-lar, that the contribution of BR(Bs,d → µ+µ−)is very small in both cases, which is a distinctivefeature of sub-GUT models.

The last line of Table 4 shows the p-values forthe best fits with and without (g − 2)µ, whichwere calculated as follows. In the case with (with-out) (g − 2)µ, setting aside HiggsSignals so asto avoid biasing the analysis [21, 33], the num-ber of constraints making non-zero contributionsto the global χ2 function (not including nuisanceparameters) is 29 (28), and the number of freeparameters is 5 in each case. Hence the numbersof degrees of freedom are 24 (23) in the two cases.The values of the total χ2 function at the best-fitpoints, dropping the HiggsSignals contribution,are 28.9 (18.0) and the corresponding p-values are23% (76%). The qualities of the global fits withand without (g−2)µ are therefore both good. andthe fit including (g − 2)µ is not poor enough to

With (g − 2)µ Without (g − 2)µ

MH,A,H+ 2060 2220

dL, uL, sL, cL 2510 5050

dR, uR, sR, cR 2450 4835

b1 1830 4100

b2 2190 4210t1 1130 3430t2 1850 4150

eL, νeL , µL, νµL2040 3740

eR, µR 1980 3510τ1 1380 2740τ2 1780 3390ντL 1770 3390g 2120 7240

mχ01

1040 1060

mχ02

1270 1060

mχ03

1740 6010

mχ04

1740 6300

mχ±1

1270 1060

mχ±2

1740 6310

χ2 withoutHiggsSignals 28.86 18.02

Number of d.o.f. 24 23

p-value 23% 76%

Table 4The spectra at the best-fit points including the

LHC 13-TeV data and including (left column) ordropping (right column) the (g − 2)µ constraint.The masses are quoted in GeV. The three bottomlines give the values of the χ2 function droppingHiggsSignals, the numbers of degrees of freedom(d.o.f.) and the corresponding p-values.

reject this fit hypothesis.The spectra for the best fits are displayed

graphically in Fig. 14, including the (g − 2)µconstraint (upper panel) and dropping it (lowerpanel). Also shown are the decay modes withbranching ratios > 5%, as dashed lines whose in-tensities increase with the branching ratios. Theheavy Higgs bosons decay predominantly to SMfinal states, hence no dashed lines are shown. Wesee that in both cases the squarks and gluino areprobably too heavy to be discovered at the LHC,and the sleptons are too heavy to be discoveredat any planned e+e− collider. The best prospectsfor sparticle discovery may be for χ±

1 and χ02 pro-

duction at CLIC running at ECM & 2 TeV [75].

22

0 2 4 6 8 10 12

mt

∆α(5)had(MZ)

σ0had

Rl

A lFB

Al(Pτ)

Rb

A bFB

A cFB

Ab

Ac

A eLR

sin2θeff

MW

(g− 2)µ

Mh

BREXP/SMB→Xsγ

BREXP/SMBs, d→µ + µ −

BREXP/SMB→τν

BREXP/SMB→Xsll

BREXP/SMK→πνν

∆MEXP/SMBs

∆MBs/SM

∆MBd

εK

ΩCDMh2

σSIp

∆χ2HiggsSignals

H/A→τ+τ−

with (g− 2)µ

without (g− 2)µ

68

∆χ2

Figure 13. Contributions to the global χ2 function at the best-fit points found in our sub-GUT analy-sis including LHC 13-TeV data, in the cases with and without the (g − 2)µ constraint (pink and bluehistograms, respectively).

23

0

400

800

1200

1600

2000

2400

2800

Mas

s/

GeV

h0

H0A0

H±

qR

qL

b1

t2

t1

˜R

νL˜L

τ1

ντ

τ2

g

χ01

χ02 χ±

1

χ03

χ04 χ±

2

b2

0

800

1600

2400

3200

4000

4800

5600

6400

7200

8000

Mas

s/

GeV

h0

H0A0

H±

qR

qL

b1

t2

b2

t1˜R

νL˜L

τ1

ντ

τ2

g

χ01

χ02 χ±

1

χ03

χ04 χ±

2

Figure 14. The spectra of Higgs bosons and sparticles at the best-fit points in the sub-GUT model includingLHC 13-TeV data, including the (g − 2)µ constraint (upper panel) and dropping it (lower panel), withdashed lines indicating the decay modes with branching ratios > 5%. These plots were made usingPySLHA [76].

24

The global likelihood function is quite flat atlarge sparticle masses, and very different spec-tra are consistent with the data, within the cur-rent uncertainties. The 68 and 95% CL rangesof Higgs and sparticle masses are displayed inFig. 15 as orange and yellow bands, respectively,with the best-fit values indicated by blue lines.The upper panel is for a fit including the (g−2)µconstraint, which is dropped in the lower panel.At the 68% CL there are possibilities for squarkand gluino discovery at the LHC and the τ1, µRand eR become potentially discoverable at CLICif it operates at ECM = 3 TeV [75].

7. Summary and Perspectives

We have performed in this paper a frequen-tist analysis of sub-GUT models in which softsupersymmetry-breaking parameters are assumedto be universal at some input scale Min < MGUT.The best-fit input parameters with and without(g − 2)µ and the LHC 13-TeV data are shownin Table 2. The physical sparticle masses includ-ing the LHC data, with and without (g−2)µ, areshown in Table 4 and in Fig. 14, where decay pat-terns are also indicated. As seen in the bottomline of Table 4, the p-values for the fits with andwithout (g−2)µ are ' 23% and 76%, respectively.

Compared to the best fits with Min = MGUT,we have found that the minimum value of theglobal χ2 function may be reduced by ∆χ2 ∼ 2in the sub-GUT model, with the exact amount de-pending whether the (g − 2)µ constraint and/orLHC13 data are included in the fit. Whetherthese observables are included, or not, the globalχ2 minimum occurs for Min ∼ 107 GeV, and isdue to the sub-GUT model’s ability to providea better fit to the measured value of BR(Bs,d →µ+µ−) than in the CMSSM. Although intriguing,this improvement in the fit quality is not very sig-nificant, but it will be interesting to monitor howthe experimental measurement of BR(Bs,d →µ+µ−) evolves.

In all the scenarios studied (with/without (g−2)µ and/or LHC13), the profile likelihood func-tion for mg (mq) varies by . 1 for mg &1.9 TeV (mq & 2.2 TeV). The correspondingslowly-varying ranges of χ2 for mt1

(mb1) start

at ∼ 1 TeV (∼ 1.6 TeV), respectively. On theother hand, we find a more marked preferencefor mχ0

1∼ 1 TeV, with the χ±

1 and χ02 being

slightly heavier and large mass values being dis-favoured at the ∆χ2 ∼ 3 level. The best-fit pointis in a region where rapid annihilation via H/Apoles is hybridized with stop coannihilation, withchargino coannihilation and stau coannihilationalso playing roles in both the 68 and 95% CL re-gions. Within the 95% CL region, the charginolifetime may exceed 10−12 s, and the stau life-time may be as long as one second, motivatingcontinued searches for long-lived sparticles at theLHC.

Taking the LHC13 constraints into account, wefind that the spin-independent DM cross-section,σSIp , may be just below the present upper lim-

its from the LUX, XENON1T and PandaX-II ex-periments, and within the reaches of the plannedXENONnT and LZ experiments. On the otherhand, the spin-dependent DM cross-section, σSD

p ,may be between some 2 and 5 orders of magni-tude below the current upper limit from the PICOexperiment.

Within the sub-GUT framework, therefore, wefind interesting perspectives for LHC searchesfor strongly-interacting sparticles via the con-ventional missing-energy signature. Future /ETsearches for electroweakly-interacting sparticlesand for long-lived massive charged particles mayalso have interesting prospects. The best-fit re-gion of parameter space accommodates the ob-served deviation of BR(Bs,d → µ+µ−) fromits value in the SM, and it will be interest-ing to see further improvement in the precisionof this measurement. A future e+e− colliderwith centre-of-mass energy above 2 TeV, suchas CLIC [75], would have interesting perspec-tives for discovering and measuring the proper-ties of electroweakly-interacting sparticles. Thereare also interesting perspectives for direct DMsearches via spin-independent scattering.

Acknowledgements

The work of E.B. and G.W. is supported in partby the Collaborative Research Center SFB676of the DFG, “Particles, Strings and the early

25

Mh 0MH 0MA 0MH± mχ01mχ0

2mχ0

3mχ0

4mχ±1 mχ±2 meL

meRmµL

mµR mτ1mτ2

mνemνµ mντ mdR

muRmt1 mt2 mb1

mb2mg

0

500

1000

1500

2000

2500

3000

3500

4000

Part

icle

Mass

es

[GeV

]

Mh 0MH 0MA 0MH± mχ01mχ0

2mχ0

3mχ0

4mχ±1 mχ±2 meL

meRmµL

mµR mτ1mτ2

mνemνµ mντ mdR

muRmt1 mt2 mb1

mb2mg

0

500

1000

1500

2000

2500

3000

3500

4000

Part

icle

Mass

es

[GeV

]

Figure 15. The spectra in the sub-GUT model including LHC 13-TeV data, with (upper panel) and without(lower panel) the (g − 2)µ constraint, displaying the best-fit values as blue lines, the 68% CL ranges asorange bands, and the 95% CL ranges as yellow bands.

26

Universe”. The work of M.B. and D.M.S. issupported by the European Research Council viaGrant BSMFLEET 639068. The work of J.C.C. issupported by CNPq (Brazil). The work of M.J.D.is supported in part by the Australia ResearchCouncil. The work of J.E. is supported in part bySTFC (UK) via the research grant ST/L000326/1and in part via the Estonian Research Council viaa Mobilitas Pluss grant, and the work of H.F. isalso supported in part by STFC (UK). The workof S.H. is supported in part by the MEINCOPSpain under contract FPA2016-78022-P, in partby the Spanish Agencia Estatal de Investigacion(AEI) and the EU Fondo Europeo de Desar-rollo Regional (FEDER) through the projectFPA2016-78645-P, in part by the AEI throughthe grant IFT Centro de Excelencia Severo OchoaSEV-2016-0597, and by the Spanish MICINNConsolider-Ingenio 2010 Program under GrantMultiDark CSD2009-00064. The work of M.L.and I.S.F. is supported by XuntaGal. The workof K.A.O. is supported in part by DOE grant de-sc0011842 at the University of Minnesota. K.S.thanks the TU Munich for hospitality duringthe final stages of this work and has been par-tially supported by the DFG cluster of excellenceEXC 153 “Origin and Structure of the Universe,by the Collaborative Research Center SFB1258.The work of K.S. is also partially supportedby the National Science Centre, Poland, un-der research grants DEC-2014/15/B/ST2/02157,DEC-2015/18/M/ST2/00054 and DEC-2015/19/D/ST2/03136. The work of G.W. isalso supported in part by the European Commis-sion through the “HiggsTools” Initial TrainingNetwork PITN-GA-2012-316704.

REFERENCES

1. For a compendium of CMSsearches for supersymmetry, seehttps://twiki.cern.ch/twiki/bin/view/

CMSPublic/PhysicsResultsSUS.2. For a compendium of ATLAS

searches for supersymmetry, seehttps://twiki.cern.ch/twiki/bin/view/

AtlasPublic/SupersymmetryPublicResults.3. D. S. Akerib et al. [LUX Collaboration],

Phys. Rev. Lett. 118 (2017) no.2, 021303[arXiv:1608.07648 [astro-ph.CO]].

4. C. Amole et al. [PICO Collaboration],arXiv:1702.07666 [astro-ph.CO].

5. E. Aprile et al. [XENON Collaboration],arXiv:1705.06655 [astro-ph.CO].

6. X. Cui et al. [PandaX-II Collaboration],arXiv:1708.06917 [hep-ex], which updatesA. Tan et al. [PandaX-II Collaboration],Phys. Rev. Lett. 117 (2016) no. 12, 121303[arXiv:1607.07400 [hep-ex]].

7. H. Goldberg, Phys. Rev. Lett. 50 (1983) 1419;J. Ellis, J. Hagelin, D. Nanopoulos, K. Oliveand M. Srednicki, Nucl. Phys. B 238 (1984)453.

8. O. Buchmueller et al., Eur. Phys. J.C 72 (2012) 1878 [arXiv:1110.3568 [hep-ph]]; Eur. Phys. J. C 72 (2012) 2243[arXiv:1207.7315]; Eur. Phys. J. C 74 (2014)2809 [arXiv:1312.5233 [hep-ph]].

9. O. Buchmueller et al., Eur. Phys. J. C 74(2014) 2922 [arXiv:1312.5250 [hep-ph]].

10. P. Bechtle et al., Eur. Phys. J. C 76 (2016)no.2, 96 [arXiv:1508.05951 [hep-ph]].

11. P. Athron et al. [GAMBIT Collaboration],arXiv:1705.07935 [hep-ph].

12. O. Buchmueller et al., Eur. Phys. J. C 74(2014) 12, 3212 [arXiv:1408.4060 [hep-ph]].

13. See, for example, C. F. Berger, J. S. Gainer,J. L. Hewett and T. G. Rizzo, JHEP0902, 023 (2009) [arXiv:0812.0980 [hep-ph]]; S. S. AbdusSalam, B. C. Allanach,F. Quevedo, F. Feroz and M. Hobson, Phys.Rev. D 81, 095012 (2010) [arXiv:0904.2548[hep-ph]]; J. A. Conley, J. S. Gainer,J. L. Hewett, M. P. Le and T. G. Rizzo, Eur.Phys. J. C 71, 1697 (2011) [arXiv:1009.2539[hep-ph]]; J. A. Conley, J. S. Gainer,J. L. Hewett, M. P. Le and T. G. Rizzo,[arXiv:1103.1697 [hep-ph]]; S. S. Abdus-Salam, et al., Eur. Phys. J. C 71 (2011)1835 [arXiv:1109.3859 [hep-ph]]; S. Sek-men, S. Kraml, J. Lykken, F. Moort-gat, S. Padhi, L. Pape, M. Pierini andH. B. Prosper et al., JHEP 1202 (2012)075 [arXiv:1109.5119 [hep-ph]]; A. Arbey,M. Battaglia and F. Mahmoudi, Eur. Phys.J. C 72 (2012) 1847 [arXiv:1110.3726 [hep-

27

ph]]; A. Arbey, M. Battaglia, A. Djouadiand F. Mahmoudi, Phys. Lett. B 720 (2013)153 [arXiv:1211.4004 [hep-ph]]; M. W. Cahill-Rowley, J. L. Hewett, A. Ismail andT. G. Rizzo, Phys. Rev. D 88 (2013) 3, 035002[arXiv:1211.1981 [hep-ph]].

14. K. J. de Vries et al., Eur. Phys. J. C 75 (2015)no.9, 422 [arXiv:1504.03260 [hep-ph]].

15. P. Athron et al. [GAMBIT Collaboration],arXiv:1705.07917 [hep-ph].

16. E. Bagnaschi et al., arXiv:1710.11091 [hep-ph].

17. J. Ellis, T. Falk, and K.A. Olive, Phys. Lett.B444 (1998) 367 [arXiv:hep-ph/9810360]; J.Ellis, T. Falk, K.A. Olive, and M. Srednicki,Astr. Part. Phys. 13 (2000) 181 [Erratum-ibid. 15 (2001) 413] [arXiv:hep-ph/9905481];R. Arnowitt, B. Dutta and Y. Santoso,Nucl. Phys. B 606 (2001) 59 [arXiv:hep-ph/0102181]; M. E. Gomez, G. Lazaridesand C. Pallis, Phys. Rev. D D61 (2000)123512 [arXiv:hep-ph/9907261]; Phys. Lett.B487 (2000) 313 [arXiv:hep-ph/0004028];Nucl. Phys. B B638 (2002) 165 [arXiv:hep-ph/0203131]; T. Nihei, L. Roszkowski andR. Ruiz de Austri, JHEP 0207 (2002) 024[arXiv:hep-ph/0206266].

18. M. Citron, J. Ellis, F. Luo, J. Marrouche,K. A. Olive and K. J. de Vries, Phys. Rev. D87 (2013) no.3, 036012 [arXiv:1212.2886 [hep-ph]].

19. C. Boehm, A. Djouadi and M. Drees,Phys. Rev. D 62, 035012 (2000) [arXiv:hep-ph/9911496]; J. R. Ellis, K. A. Oliveand Y. Santoso, Astropart. Phys. 18, 395(2003) [arXiv:hep-ph/0112113]; J. L. Diaz-Cruz, J. R. Ellis, K. A. Olive and Y. San-toso, JHEP 0705, 003 (2007) [arXiv:hep-ph/0701229]; I. Gogoladze, S. Raza andQ. Shafi, Phys. Lett. B 706, 345 (2012)[arXiv:1104.3566 [hep-ph]]; M. A. Ajaib, T. Liand Q. Shafi, Phys. Rev. D 85, 055021(2012) [arXiv:1111.4467 [hep-ph]]; J. Harz,B. Herrmann, M. Klasen, K. Kovarik andQ. L. Boulc’h, Phys. Rev. D 87 (2013) 5,054031 [arXiv:1212.5241]; J. Ellis, K. A. Oliveand J. Zheng, Eur. Phys. J. C 74 (2014) 2947[arXiv:1404.5571 [hep-ph]]; J. Harz, B. Her-

rmann, M. Klasen and K. Kovarik, Phys.Rev. D 91 (2015) 3, 034028 [arXiv:1409.2898[hep-ph]]; A. Ibarra, A. Pierce, N. R. Shahand S. Vogl, Phys. Rev. D 91, no. 9, 095018(2015) [arXiv:1501.03164 [hep-ph]]; A. Pierce,N. R. Shah and S. Vogl, arXiv:1706.01911[hep-ph].

20. S. Mizuta and M. Yamaguchi, Phys. Lett.B 298 (1993) 120 [arXiv:hep-ph/9208251];J. Edsjo and P. Gondolo, Phys. Rev. D56, 1879 (1997) [hep-ph/9704361]; H. Baer,C. Balazs and A. Belyaev, JHEP 0203, 042(2002) [hep-ph/0202076]; A. Birkedal-Hansenand E. h. Jeong, JHEP 0302, 047 (2003)[hep-ph/0210041]; J. Edsjo, M. Schelke, P. Ul-lio and P. Gondolo, JCAP 0304, 001 (2003)[hep-ph/0301106].

21. E. Bagnaschi et al., Eur. Phys. J. C 77 (2017)no.2, 104 [arXiv:1610.10084 [hep-ph]].

22. S. Profumo and C. E. Yaguna, Phys. Rev. D69, 115009 (2004) [hep-ph/0402208]; D. Feld-man, Z. Liu and P. Nath, Phys. Rev. D80, 015007 (2009) [arXiv:0905.1148 [hep-ph]];N. Chen, D. Feldman, Z. Liu, P. Nathand G. Peim, Phys. Rev. D 83, 035005(2011) [arXiv:1011.1246 [hep-ph]]; I. Gogo-ladze, R. Khalid and Q. Shafi, Phys.Rev. D 79, 115004 (2009) [arXiv:0903.5204[hep-ph]]; I. Gogoladze, R. Khalid andQ. Shafi, Phys. Rev. D 80, 095016 (2009)[arXiv:0908.0731 [hep-ph]]; M. Adeel Ajaib,T. Li, Q. Shafi and K. Wang, JHEP 1101, 028(2011) [arXiv:1011.5518 [hep-ph]]; K. Hari-gaya, M. Ibe and T. T. Yanagida, JHEP1312, 016 (2013) [arXiv:1310.0643 [hep-ph]]; K. Harigaya, K. Kaneta and S. Mat-sumoto, Phys. Rev. D 89, no. 11, 115021(2014) [arXiv:1403.0715 [hep-ph]]; S. Raza,Q. Shafi and C. S. Un, Phys. Rev. D 92, no.5, 055010 (2015) [arXiv:1412.7672 [hep-ph]];J. L. Evans and K. A. Olive, Phys. Rev. D90, no. 11, 115020 (2014) [arXiv:1408.5102[hep-ph]]; A. De Simone, G. F. Giudiceand A. Strumia, JHEP 1406, 081 (2014)[arXiv:1402.6287 [hep-ph]]; JHEP 1408, 161(2014) [arXiv:1404.0682 [hep-ph]].

23. J. Ellis, F. Luo and K. A. Olive, JHEP 1509(2015) 127 [arXiv:1503.07142 [hep-ph]]; J. El-

28

lis, J. L. Evans, F. Luo and K. A. Olive, JHEP1602 (2016) 071 [arXiv:1510.03498 [hep-ph]].

24. J. R. Ellis, K. A. Olive and P. Sandick, Phys.Lett. B 642 (2006) 389 [hep-ph/0607002],JHEP 0706 (2007) 079 [arXiv:0704.3446[hep-ph]] and JHEP 0808 (2008) 013[arXiv:0801.1651 [hep-ph]].

25. J. Ellis, F. Luo, K. A. Olive and P. Sandick,Eur. Phys. J. C 73, no. 4, 2403 (2013)[arXiv:1212.4476 [hep-ph]]; J. Ellis,J. L. Evans, F. Luo, N. Nagata, K. A. Oliveand P. Sandick, Eur. Phys. J. C 76, no. 1, 8(2016) [arXiv:1509.08838 [hep-ph]].

26. H. Itoh, N. Okada and T. Yamashita,arXiv:hep-ph/0606156.

27. C. Csaki, in M. Shifman et al. (eds.),From fields to strings, vol. 2, pp967-1060,[hep-ph/0404096]; K. Choi, A. Falkowski,H. P. Nilles and M. Olechowski, Nucl.Phys. B 718 (2005) 113 [arXiv:hep-th/0503216]; K. Choi, K. S. Jeong andK. i. Okumura, JHEP 0509 (2005) 039[arXiv:hep-ph/0504037]; M. Endo, M. Ya-maguchi and K. Yoshioka, Phys. Rev. D72 (2005) 015004 [arXiv:hep-ph/0504036];A. Falkowski, O. Lebedev and Y. Mam-brini, JHEP 0511 (2005) 034 [arXiv:hep-ph/0507110]; R. Kitano and Y. Nomura,Phys. Lett. B 631 (2005) 58 [arXiv:hep-ph/0509039]; R. Kitano and Y. Nomura,Phys. Rev. D 73 (2006) 095004 [arXiv:hep-ph/0602096]; A. Pierce and J. Thaler, JHEP0609 (2006) 017 [arXiv:hep-ph/0604192];K. Kawagoe and M. M. Nojiri, [arXiv:hep-ph/0606104]; H. Baer, E.-K. Park, X. Tataand T. T. Wang, JHEP 0608 (2006)041 [arXiv:hep-ph/0604253]; K. Choi,K. Y. Lee, Y. Shimizu, Y. G. Kim andK. i. Okumura, JCAP 0612 (2006) 017[arXiv:hep-ph/0609132]; O. Lebedev,V. Lowen, Y. Mambrini, H. P. Nillesand M. Ratz, JHEP 0702 (2007) 063[arXiv:hep-ph/0612035].

28. S. Kachru, R. Kallosh, A. D. Linde andS. P. Trivedi, Phys. Rev. D 68, 046005 (2003)[hep-th/0301240].

29. M. Dine and D. MacIntire, Phys. Rev. D46, 2594 (1992) [hep-ph/9205227]; L. Ran-

dall and R. Sundrum, Nucl. Phys. B 557,79 (1999) [arXiv:hep-th/9810155]; G. F. Giu-dice, M. A. Luty, H. Murayama and R. Rat-tazzi, JHEP 9812, 027 (1998) [arXiv:hep-ph/9810442]; A. Pomarol and R. Rattazzi,JHEP 9905, 013 (1999) [hep-ph/9903448];J. A. Bagger, T. Moroi and E. Poppitz, JHEP0004, 009 (2000) [arXiv:hep-th/9911029];P. Binetruy, M. K. Gaillard and B. D. Nel-son, Nucl. Phys. B 604, 32 (2001) [arXiv:hep-ph/0011081].

30. G. Bennett et al. [The Muon g-2 Collabo-ration], Phys. Rev. Lett. 92 (2004) 161802,[arXiv:hep-ex/0401008]; and Phys. Rev. D 73(2006) 072003 [arXiv:hep-ex/0602035].

31. D. Stockinger, J. Phys. G 34 (2007)R45 [arXiv:hep-ph/0609168]; J. Miller,E. de Rafael and B. Roberts, Rept. Prog.Phys. 70 (2007) 795 [arXiv:hep-ph/0703049];J. Prades, E. de Rafael and A. Vainshtein,arXiv:0901.0306 [hep-ph]; F. Jegerlehnerand A. Nyffeler, Phys. Rept. 477, 1 (2009)[arXiv:0902.3360 [hep-ph]]; M. Davier,A. Hoecker, B. Malaescu, C. Z. Yuan andZ. Zhang, Eur. Phys. J. C 66, 1 (2010)[arXiv:0908.4300 [hep-ph]]. J. Prades,Acta Phys. Polon. Supp. 3, 75 (2010)[arXiv:0909.2546 [hep-ph]]; T. Teubner,K. Hagiwara, R. Liao, A. D. Martin andD. Nomura, arXiv:1001.5401 [hep-ph];M. Davier, A. Hoecker, B. Malaescu andZ. Zhang, Eur. Phys. J. C 71 (2011) 1515[arXiv:1010.4180 [hep-ph]].

32. E. A. Bagnaschi et al., Eur. Phys. J. C 75(2015) 500 [arXiv:1508.01173 [hep-ph]].

33. E. Bagnaschi et al., Eur. Phys. J. C 77 (2017)no.4, 268 [arXiv:1612.05210 [hep-ph]].

34. K. J. de Vries, PhD thesis Global Fits ofSupersymmetric Models after LHC Run 1(2015), available on the MasterCode website:http://cern.ch/mastercode/.

35. For more information and updates, please seehttp://cern.ch/mastercode/.

36. A. M. Sirunyan et al. [CMS Collaboration],arXiv:1705.04650 [hep-ex].

37. A. M. Sirunyan et al. [CMS Collaboration],arXiv:1705.04673 [hep-ex].

38. A. M. Sirunyan et al. [CMS Collaboration],

29

arXiv:1709.05406 [hep-ex].39. V. Khachatryan et al. [CMS Collabora-

tion], Eur. Phys. J. C 75 (2015) no.7, 325[arXiv:1502.02522 [hep-ex]].

40. CMS Collaboration, CMS-PAS-EXO-16-036.41. V. Khachatryan et al. [CMS and LHCb

Collaborations], Nature 522 (2015) 68[arXiv:1411.4413 [hep-ex]]

42. M. Aaboud et al. [ATLAS Collaboration],Eur. Phys. J. C 76 (2016) no.9, 513[arXiv:1604.04263 [hep-ex]].

43. R. Aaij et al. [LHCb Collaboration], Phys.Rev. Lett. 118 (2017) no.19, 191801[arXiv:1703.05747 [hep-ex]].

44. D. S. Akerib et al. [LZ Collaboration],arXiv:1509.02910 [physics.ins-det].

45. E. Aprile et al. [XENON Collaboration],arXiv:1708.07051 [astro-ph.IM].

46. G. Aad et al. [ATLAS and CMS Collabora-tions], JHEP 1608 (2016) 045[arXiv:1606.02266 [hep-ex]].

47. P. Bechtle, S. Heinemeyer, O. Stal, T. Ste-faniak and G. Weiglein, Eur. Phys. J. C74 (2014) 2, 2711 [arXiv:1305.1933 [hep-ph]]; JHEP 1411 (2014) 039 [arXiv:1403.1582[hep-ph]].

48. P. Bechtle, O. Brein, S. Heinemeyer,G. Weiglein and K. E. Williams, Com-put. Phys. Commun. 181 (2010) 138[arXiv:0811.4169 [hep-ph]], Comput. Phys.Commun. 182 (2011) 2605 [arXiv:1102.1898[hep-ph]]; P. Bechtle et al., Eur. Phys. J. C74 (2014) 3, 2693 [arXiv:1311.0055 [hep-ph]];P. Bechtle, S. Heinemeyer, O. Stal, T. Ste-faniak and G. Weiglein, Eur. Phys. J. C 75(2015) no.9, 421 [arXiv:1507.06706 [hep-ph]].

49. ATLAS Collaboration,http://cds.cern.ch/record/2273866/

files/ATLAS-CONF-2017-050.pdf.50. P. A. R. Ade et al. [Planck Collabora-

tion], Astron. Astrophys. 594 (2016) A13[arXiv:1502.01589 [astro-ph.CO]].

51. G. Belanger, F. Boudjema, A. Pukhov andA. Semenov, Comput. Phys. Commun. 185(2014) 960 [arXiv:1305.0237 [hep-ph]], andreferences therein.

52. J. R. Ellis, A. Ferstl and K. A. Olive, Phys.Lett. B 481, 304 (2000) [hep-ph/0001005];

J. R. Ellis, K. A. Olive, Y. Santoso andV. C. Spanos, Phys. Rev. D 71, 095007 (2005)[hep-ph/0502001]; J. R. Ellis, K. A. Olive andC. Savage, Phys. Rev. D 77 (2008) 065026[arXiv:0801.3656 [hep-ph]].

53. Information about this code is available fromK. A. Olive: it contains important contribu-tions from J. Evans, T. Falk, A. Ferstl, G. Ga-nis, F. Luo, A. Mustafayev, J. McDonald, F.Luo, K. A. Olive, P. Sandick, Y. Santoso,C. Savage, V. Spanos and M. Srednicki.

54. X. Z. Ling, X. L. Ren and L. S. Geng,arXiv:1710.07164 [hep-ph].

55. J. M. Alarcon, J. Martin Camalich andJ. A. Oller, Phys. Rev. D 85 (2012) 051503[arXiv:1110.3797 [hep-ph]]; J. M. Alar-con, L. S. Geng, J. Martin Camalich andJ. A. Oller, Phys. Lett. B 730 (2014) 342[arXiv:1209.2870 [hep-ph]].

56. M. G. Aartsen et al. [IceCube Collabora-tion], Eur. Phys. J. C 77 (2017) no.3, 146[arXiv:1612.05949 [astro-ph.HE]].

57. M. Papucci, K. Sakurai, A. Weiler and L. Ze-une, Eur. Phys. J. C 74 (2014) no.11, 3163[arXiv:1402.0492 [hep-ph]].

58. B. C. Allanach, Comput. Phys. Commun. 143(2002) 305 [arXiv:hep-ph/0104145].

59. F. Feroz and M.P. Hobson,Mon. Not. Roy. Astron. Soc. 384(2008) 449 [arXiv:0704.3704 [astro-ph]].F. Feroz, M.P. Hobson and M. Bridges,Mon. Not. Roy. Astron. Soc. 398 (2009)1601-1614 [arXiv:0809.3437 [astro-ph]].F. Feroz, M.P. Hobson, E. Cameron andA.N. Pettitt, [arXiv:1306.2144 [astro-ph]].

60. P. Skands et al., JHEP 0407 (2004) 036[arXiv:hep-ph/0311123]; B. Allanach et al.,Comput. Phys. Commun. 180 (2009) 8[arXiv:0801.0045 [hep-ph]].

61. S. Heinemeyer et al., JHEP 0608 (2006)052 [arXiv:hep-ph/0604147]; S. Heinemeyer,W. Hollik, A. M. Weber and G. Weiglein,JHEP 0804 (2008) 039 [arXiv:0710.2972[hep-ph]].

62. G. Isidori and P. Paradisi, Phys. Lett.B 639 (2006) 499 [arXiv:hep-ph/0605012];G. Isidori, F. Mescia, P. Paradisi andD. Temes, Phys. Rev. D 75 (2007)

30

115019 [arXiv:hep-ph/0703035], and refer-ences therein.

63. F. Mahmoudi, Comput. Phys. Commun.178 (2008) 745 [arXiv:0710.2067 [hep-ph]];Comput. Phys. Commun. 180 (2009) 1579[arXiv:0808.3144 [hep-ph]]; D. Eriksson,F. Mahmoudi and O. Stal, JHEP 0811 (2008)035 [arXiv:0808.3551 [hep-ph]].

64. S. Heinemeyer, W. Hollik and G. Wei-glein, Comput. Phys. Commun. 124 (2000)76 [arXiv:hep-ph/9812320]; S. Heinemeyer,W. Hollik and G. Weiglein, Eur. Phys.J. C 9 (1999) 343 [arXiv:hep-ph/9812472];G. Degrassi, S. Heinemeyer, W. Hollik,P. Slavich and G. Weiglein, Eur. Phys. J.C 28 (2003) 133 [arXiv:hep-ph/0212020];M. Frank et al., JHEP 0702 (2007) 047[arXiv:hep-ph/0611326]; T. Hahn, S. Heine-meyer, W. Hollik, H. Rzehak and G. Weiglein,Comput. Phys. Commun. 180 (2009) 1426;T. Hahn, S. Heinemeyer, W. Hollik, H. Rze-hak and G. Weiglein, Phys. Rev. Lett. 112(2014) 14, 141801 [arXiv:1312.4937 [hep-ph]];H. Bahl and W. Hollik, Eur. Phys. J. C 76(2016) 499 [arXiv:1608.01880 [hep-ph]]. Seehttp://www.feynhiggs.de .

65. M. Muhlleitner, A. Djouadi and Y. Mambrini,Comput. Phys. Commun. 168 (2005) 46 [hep-ph/0311167].

66. J. D. Hunter, Computing In Science & Engi-neering, 9.3 (2007), pp90-95.

67. B. J. Mount et al., arXiv:1703.09144[physics.ins-det].

68. E. Aprile et al. [XENON Collabora-tion], JCAP 1604 (2016) no.04, 027doi:10.1088/1475-7516/2016/04/027[arXiv:1512.07501 [physics.ins-det]].

69. J. Billard, L. Strigari and E. Figueroa-Feliciano, Phys. Rev. D 89, no. 2, 023524(2014) [arXiv:1307.5458 [hep-ph]]; P. Cush-man, C. Galbiati, D. N. McKinsey, H. Robert-son, T. M. P. Tait, D. Bauer, A. Borgland andB. Cabrera et al., Snowmass Working GroupReport: WIMP Dark Matter Direct Detec-tion, arXiv:1310.8327 [hep-ex].

70. K. Choi et al. [Super-Kamiokande Collabo-ration], Phys. Rev. Lett. 114 (2015) no.14,141301 doi:10.1103/PhysRevLett.114.141301

[arXiv:1503.04858 [hep-ex]].71. K. C. Y. Ng, J. F. Beacom, A. H. G. Peter

and C. Rott, arXiv:1703.10280 [astro-ph.HE].72. G. Angloher et al. [CRESST Collabora-

tion], Eur. Phys. J. C 76 (2016) no.1,25 doi:10.1140/epjc/s10052-016-3877-3[arXiv:1509.01515 [astro-ph.CO]].

73. R. Agnese et al. [SuperCDMS Collabora-tion], Phys. Rev. Lett. 116 (2016) no.7,071301 doi:10.1103/PhysRevLett.116.071301[arXiv:1509.02448 [astro-ph.CO]].

74. L. T. Yang et al. [CDEX Collaboration],arXiv:1710.06650 [hep-ex].

75. M. J. Boland et al. [CLIC and CLICdp Col-laborations], arXiv:1608.07537 [physics.acc-ph].

76. A. Buckley, Eur. Phys. J. C 75, no. 10, 467(2015) [arXiv:1305.4194 [hep-ph]].