Closing in on t-channel simplified dark matter models

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Closing

in

on

t-channel

simplified

dark

matter

models

Chiara Arina

a

,

Benjamin Fuks

b

,

c

,

Luca Mantani

a

,

Hanna Mies

d

,

Luca Panizzi

e

,

f

,

∗

,

Jakub Salko

e

a_{CentreforCosmology,ParticlePhysicsandPhenomenology(CP3),UniversitécatholiquedeLouvain,B-1348Louvain-la-Neuve,Belgium} b_{SorbonneUniversité,CNRS,LaboratoiredePhysiqueThéoriqueetHautesÉnergies,LPTHE,F-75005Paris,France}

c_{InstitutUniversitairedeFrance,103boulevardSaint-Michel,F-75005Paris,France}

d_{InstituteforTheoreticalParticlePhysicsandCosmology,RWTHAachenUniversity,D-52056Aachen,Germany} e_{DepartmentofPhysicsandAstronomy,UppsalaUniversity,Box516,SE-75120Uppsala,Sweden}

f_{SchoolofPhysicsandAstronomy,UniversityofSouthampton,Highfield,SouthamptonSO17 1BJ,UK}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received19October2020

Receivedinrevisedform30November2020 Accepted16December2020

Availableonline19December2020 Editor: G.F.Giudice

Keywords:

Darkmattersimplifiedmodels Collidersearches

Cosmologicalbounds

A comprehensive analysis of cosmological and collider constraints is presented for three simplified models characterised bya darkmatter candidate (realscalar,Majorana fermion and realvector) and acoloured mediator (fermion, scalar and fermion respectively) interacting with the right-handed up quark of the Standard Model. Constraints from dark matter direct and indirect detection and relic densityare combined with bounds originating fromthe re-interpretation of afull LHC run 2 ATLAS searchtargetingfinalstateswithmultiplejetsand missingtransverseenergy.Projectionsforthe high-luminosityphaseoftheLHCarealsoprovidedtoassessfutureexclusionand discoveryreaches,which showthatanalogousfuturesearchstrategieswillnotallowforasignificantimprovementcomparedwith thepresent status.Fromthe cosmologicalpoint ofview,wedemonstratethat thermaldark matteris largelyprobed(anddisfavoured)byconstraintsfromcurrentdirectandindirectdetectionexperiments. Theseboundsandtheirfutureprojectionshavemoreoverthepotentialofprobingthewholeparameter spacewhencombinedwiththeexpectationofthehigh-luminosityphaseoftheLHC.

©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

The nature of dark matter and the way it is connected to the Standard Model (SM) is one of the most puzzling issues in particle physics today. Dark matter searches consequently hold a centralplaceinthepresentastroparticleandparticlephysics pro-gram.However,despiteofconvincingindirectevidenceforits exis-tence [1],darkmatterstillevadesanydirectdetectionprobes. Ex-perimentalsearchesatcolliders,inundergroundnuclearrecoil ex-periments andwithgamma-ray telescopesthereforeput stronger andstrongerconstraintsontheviabilityofanydarkmattermodel. Those bounds are very often explored, in a model-independent approach, as limits on a set of simplified models for dark mat-ter phenomenology. In those simplified models, the dark matter is considered as a massive particle whose interactions with the SM arise through a mediator particle. In so-called s-channel se-tups [2–4],themediator isa coloursingletandcouplesto apair

*

Correspondingauthor.

E-mailaddresses:chiara.arina@uclouvain.be(C. Arina),fuks@lpthe.jussieu.fr (B. Fuks),luca.mantani@uclouvain.be(L. Mantani),hannamies@gmx.de(H. Mies), luca.panizzi@physics.uu.se(L. Panizzi),kubo.salko@gmail.com(J. Salko).

of either dark matter or SM particles. On the contrary, in a

t-channelconfiguration,themediatorinteractsinsteadwithoneSM stateandthedarkmatter [5].

Inthiswork, weconsiderthreesimplifiedt-channel scenarios, thatwecoin

F3S_uR

,

S3M_uR

and

F3V_uR

,andthataredefined inref. [5].Theircommonfeaturesarethefollowing.First,thedark matter candidate is a real particle, singlet under the SM gauge group,sothatitsstabilitycanbeensuredthrougha

Z

2 symmetry.

This contrasts with other t-channel models including a complex darkmatterfield andthusexhibitinginsteadacontinuous unbro-kenglobalU

(

1

)

symmetry. Second,themediatorcouplesthedark matter candidateto the right-handed up-quark field, so that the mediatorisitselfan SU

(

2

)

L weaksinglet.Other choicesare how-everpossible, as darkmatter could interactwith different quark flavoursandchiralities.TheuR choiceisonlyoneofthenumerous possibilities, justifiedby its simplicity(it only involvesweak sin-glets)andbytheenhancement oftherelevantcollideranddirect detection processes due to valence quarks. We will nevertheless highlight,inthefollowing,whereverothermediatorchoicescould make a difference. The defining features of the three scenarios thenconsist inthespinsofthedarkmatter andofthe mediator, which affect the kinematics of any signal and therefore current https://doi.org/10.1016/j.physletb.2020.136038

0370-2693/©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

C. Arina, B. Fuks, L. Mantani et al. Physics Letters B 813 (2021) 136038

bounds andprojections for future searches. We comprehensively derive updated constraintson thethree modelparameter spaces, consideringbothcosmologicalandcolliderobservations.Moreover, weadditionallyprovideprojectionsforthefuturehigh-luminosity phaseoftheLHC(HL-LHC).

Therestofthepaperisorganisedasfollows.Inthenextsection we briefly define the

DMSimpt

general framework fort-channel

darkmattermodels,whilein section3wedescribeouranalysisof thecolliderconstraintsandprovideresultswithcurrentexclusion bounds. In section 4 we study the astrophysical and cosmologi-cal constraints on thesesimplified models under the assumption of thermal relic dark matter. In section 5 we combine these re-sults andinclude futureexperiment expectations, illustrating the impact of the collider/cosmology combination on representative projectionsofthemodelparameterspace.Wesummariseourmain findingsanddiscussfuturedevelopmentsin section6.

2. The t-channel

simplified models

Thethreesimplifiedmodelsunderstudyaredefinedwithinthe

DMSimpt

framework [5],whichprovidesagenerict-channeldark matter simplified model.Inthe latter,the SM isextended by six realorcomplexdarkmatterfields,collectivelydenoted by X and

all singletsunderthe SM gaugegroup SU

(

3

)

c

×

SU

(

2

)

L

×

U

(

1

)

Y, plusthecorresponding mediatorparticles,collectivelydenotedby

Y ,alllyinginthefundamentalrepresentationof SU

(

3

)

c and cou-plingthe X particlestotheSMquarks.

Thescenariosconsideredinthepresentanalysisarerestrictions of thegeneral

DMSimpt

framework to setupsin whichthe dark matterparticleX isrealandsolelycouplestotheright-handed up-quark. Thereishenceauniquemediator particleY ,singletunder

SU

(

2

)

L.ThecorrespondinginteractionLagrangiansforthe

F3S_uR

(realscalardarkmatter

˜

S withafermionicmediator

ψ

),

S3M_uR

(Majorana darkmatter

χ

˜

witha scalarmediator

ϕ

)and

F3V_uR

(realvectordarkmatter V μ with

˜

afermionicmediator

ψ

) models respectivelyread

L

F3S_uR

=



ˆλ

ψ

¯ψ

uRS

˜

+

h.c.



,

L

S3M_uR

=



λ

ϕ

χ

˜

uR

ϕ

†

+

h.c.



,

L

F3V_uR

=



ˆλ

ψ

¯ψ /˜

V uR

+

h.c.



.

(1)

In those expressions,

ˆλ

ψ

,

λ

ϕ and

ˆλ

ψ stand for real coupling strengths, that together withthe dark matter (MS

,

Mχ and MV) andmediator(Mψ

,

Mϕ andMψ)massesleadtothreefree param-eters for each of the considered models. We collectively denote thissetoffreeparametersby

{

mX

,

mY

,

λ

}

.

In this work, we allow the two masses mX andmY to vary in the

[

1

,

104

_]

_{GeV range and consider}

_λ

_{coupling values in}

the

[

10−4

,

4

π

]

range (couplings larger than 4

π

are shown in our results, but the 4

π

contour is always highlighted when rel-evant). We use the corresponding next-to-leading-order (NLO) UFO [6] model files with five massless quarks for collider stud-ies with MG5_aMC [7], andboth theleading-order (LO) UFOand CalcHep [8] model fileswith six massive quarks forsimulations with MadDM [9] and MicrOMEGAs [10] respectively. All those modelfileshavebeenobtainedwith FeynRules [11] andare avail-ablefromhttps://feynrules.irmp.ucl.ac.be/wiki/DMsimpt.

3. Collider bounds

Three typesofprocesses areconsidered forthe determination ofthecolliderconstraintsonthemodels.Theyconsistinthe pro-duction of a pair of dark matter particles (pp

→

X X ), of a pair

of mediators(pp

→

Y Y ) andthe associate production of a dark matter and a mediator (pp

→

X Y ). Mediator pair-production is itself composed of three components, namely a QCD contribu-tion,adark-matter-inducedcontribution(withthepropagationof thedark matter particlein the t-channel)andtheir interference. Whenthemediatorisproduced,itsubsequentlydecaysintoadark mattercandidateandaright-handedup-quark(Y

→

X uR),the de-cayprocessbeingalways factorisedfromtheproductionone.This howeverassumesthatthedecaywidthofthemediator



Y issmall relatively toits mass, such that the narrow-widthapproximation (NWA)holds.1 _{Therelativecontributionsofthedifferentchannels} dependontheexactdetailsofthemodel,andinparticularonthe

λ

coupling value. In particular, the relevance ofthe X X channel

originates from the emission of jets by the initial state and the internalmediator,that arebothconsideredatthematrix-element andparton-showerlevelinourNLOsimulationsmatchedwith par-ton showers. In terms of the kinematics, the channels with the largestcrosssectionare,however,notnecessarilytherelevantones intermsofprobingthemodelparameterspaceandsettinglimits, asalreadyillustratedinref. [5].

All simulations are performed with MG5_aMC and followthe procedure described in ref. [5], the NLO matrix elements be-ing convoluted with the NNPDF 3.0 set of parton densities [13] throughthe LHAPDF6_{library [14].Moreover, toensurethe} valid-ityoftheNWA andthefactorisationoftheproductionanddecay processes,allsimulations havebeenperformedatafixed



Y

/

mY ratio of 1%, assuming that the final-state kinematics is not im-pactedby slightlylargervaluesofthisratio.Inthe following,we reweighthosegeneratedeventssothatthecrosssectionevaluation makesuseofa

λ

valueyielding



Y

/

mY

=

5%.Thischoicerequires amoreimportantcouplingandleadstoweakercosmological con-straints,whichthusallowsforalargercosmologically-viableregion of the parameter space to be probed by LHC searches (see sec-tion 4 and section 5). Different choices of the



Y

/

mY ratio can impacttheresults,aslower



Y

/

mY valuesimplylowercouplings. Besidesan expectedstrengtheningofthe relicdensityconstraints yieldedbyasmallerannihilationcrosssection,itwouldreducethe relativeweightsoftheX X , X Y andnon-QCD Y Y colliderchannels withrespectto QCD Y Y production whosecross section is inde-pendent of

λ

. On the other hand, larger width-over-mass ratios wouldmakethecollideranalysislessaccurate,asforlargewidths theNWA-motivatedfactorisationoftheproductionanddecay pro-cesses would not accurately describe the kinematics of the final state.

Weobtain constraintsonthemodels throughthe recastof an ATLASsearch targetingfinal stateswithmultiplejetsandmissing transverse energy [15] by means of the MadAnalysis 5 frame-work [16,17].Thissearch iswell suitedto probescenarioswhere dark matter interacts withlight quark flavours,as considered in thiswork.Whilemonojetsearchescouldberelevanttoo,they con-siststrictly speaking inmultijet plusmissing energysearches, as a subleading jet activity is allowed. They are thus only different fromthe consideredsearch bythedetails oftherequirementson theeventhadronicactivity.AsnoATLASandCMSmonojetsearch hasbeenupdatedasafullrun 2analysisyet,monojetprobeswill be ignored. Other searches could nevertheless be better in other contexts. For instance, for setups involving interactions with top quarks,searchesinvolvingfinal-statetopquarksandmissing trans-verseenergycouldprobablygiveaslightlybetterreach,asalready foundout forinstanceforscalar [18] orMajorana [19] dark mat-ter. The significance of the signal is derived for each of the ten

1 _{Inprinciple, theNWAapproximationisvalidonlyifthemassdifference} be-tween the decayingparticle and the decay productsis large [12].We however assumethatcorrectionsarisingfromsmallmasssplittingsarenotsignificantin thecorrespondingregionsoftheparameterspace.

Fig. 1. Toprow: Individual95%CLboundsarisingfromthethreedifferentchannelsX X (red),X Y (green)andY Y (blue)fortheF3S_uR(left),S3M_uR(centre)andF3V_uR

(right)scenarios,presentedinthe(mY,mX)planeforafixedmediatorwidth-to-massratio. Bottomrow: Combined95%CLbounds,withthesignalregionexhibitingthe bestsensitivitydepictedbythebackgroundcolour.Inallpanels,theblackdashedlinescorrespondtothevalueofthecouplingswhichisrequiredtoobtainawidthover massratioof5%,the4πvaluebeinghighlightedtoroughlyidentifytheperturbativeregime.Thecoloureddashedlinesidentifytheareaforwhichthenumberofsimulated MonteCarloeventspopulatingthebestregionislargerthan100(allowingforaPoissonuncertaintysmallerthan10%).

signal regions (SRs) of the search through the CLsmethod [20], and we include in our predictions signal systematics stemming from scalevariations andthe partondensityfits [21].The yields ofthe backgroundsforeach SR, withtheir uncertainties, andthe numberofobservedevents,areprovided bytheATLASsearch.As observationsarecompatiblewiththebackgroundwithin1

σ

forall signal regionsofrelevance,observedandexpectedboundsdonot significantly differ.We showtheformer inourresults.Obviously, forhigh-luminosityprojections(seesection5),expectedlimitsare usedfortheextrapolations.

Due to the different dependenceof the cross sections on the

λ

coupling andon the massesof the new particles, the relative weightsoftheX X , X Y andY Y contributionsinthedetermination oftheconstraintschangealongtheparameterspace, asshownin the top row of Fig. 1. The combination of the various contribu-tions tothe Y Y processconstrains themajorityofthe parameter space for all the considered scenarios. In contrast, the X X

pro-cessonly becomescompetitive inthe compressedregion andfor largemediatormasses,whiletheX Y oneprovidesinsteadstronger constraints for scenarios featuring a large mass gap and a large mediator mass. The region withsmalldark matter andmediator massesislikelytobe excludedtoo,butthenumberofinitialMC eventsrequiredtotesttheregionwithenoughstatisticsistoo de-mandingintermsofcomputingresources.

The combination of the bounds forany given scenario is ob-tainedintwosteps.Wefirstsumthenumberofeventspopulating each signal region asobtained from the individual X X , X Y and Y Y contributions, and then compute the corresponding signifi-cance.Wedisplaytheresultsinthebottomrowof Fig.1,inwhich weadditionallyhighlightthebestsignalregiondrivingthebound. ThedominanceoftheY Y componentinthedeterminationofthe

boundsisreflectedinthesimilaritiesoftheresultsforthe

F3S_uR

and

F3V_uR

modelsthatsharethesamemediatorparticle.Forthe

S3M_uR

classofscenarios,theboundsare sizeablyweaker, given thesmallercrosssectionforthepairproductionofascalar medi-atorthatfeatures asmallernumberofdegreesoffreedom thana fermion.

Thecombinedsignalkinematicsforanygivenscenariodepends onthesubprocessthatdominates,whichisreflectedinthe varia-tionsinthebestSRsdrivingtheboundsalongtheparameterspace. Regionsrequiringtwo veryhard jetsare moresuitable whenthe

Y Y channeldominatesandeachmediatordecayleadstoa signif-icantlyhardjet.Incontrast,SRsdedicatedtofinalstatesfeaturing fourjetsgive a betteroutcome inthe compressedregime. While theseregions selecteventsexhibitingalargernumberofjets,the associatedtransversemomentumrequirementsaremilderthanin thetwo-jetcase, andthusmoreefficientinmorecompressed se-tupsinwhichdecayandradiationjetsaresofter.

4. Cosmological bounds

Forall threemodels,we samplethethree-dimensional param-eter space with MicrOMEGAs and require that the dark matter candidate makes up 100% of the measured dark matter abun-dance,

h2_Planck

=

0

.

12 [22]. The thermally averaged dark matter annihilationcross section



σ

v



(v being therelative velocity be-tween two dark matter particles) is d-wave-suppressed for the realscalarcase [28–32] and p-wave-suppressedforMajoranadark matter [30,33]. NLO correctionsin the relic density computation might therefore be relevant [31,18]. To account for these cor-rections, we include the loop-induced X X

→

gg and X X

→

γ γ

C. Arina, B. Fuks, L. Mantani et al. Physics Letters B 813 (2021) 136038

processes,2 _{andthe three-body X X}

_→

_u

Ru

¯

Rg and X X

→

uRu

¯

R

γ

annihilationsthatcouldbepotentiallyenhancedbyvirtualinternal bremsstrahlung(VIB).Forourpredictions,weusetheanalytic ex-pressionsprovidedinrefs. [29,30,34] thatwe havevalidatedwith MadDM. While different choices of dark matter interactions (in termsoftheflavourandchiralityoftheinvolvedSMquarks)would leadtoadifferentinterplaybetweenthesubprocessescontributing tothe relicdensity,itwillalways bepossibleto findviable solu-tionsforthe

λ

parameter.

Through our scans ofthe model parameter spaces, we single out regionswheretheelastic darkmatter scatteringcrosssection offprotonsiscompatiblewithboththespin-independent(SI)and spin-dependent (SD)exclusionlimitsat90%confidencelevel (CL) from the XENON1T [23] and PICO [26] experiments, our predic-tionsrelyingonNLOcrosssections [35] toproperlymodelthe im-pactofQCDradiation.Inprinciple,runningcouplingeffectshould also be included [36]. The latter wouldlead to tighter exclusion limits, slightlyaugmenting their sensitivityfor large darkmatter masses. We have howeveromittedthem fromour computations, althoughwehaveverifiedthattheydonotimpactourconclusions. Wedonotexpecttheobtaineddirectdetectionboundstosensibly changefordifferentchoicesofdarkmatterinteractionswith right-handed valence quarks.For other scenarios involving sea quarks, wehoweverexpectthoseboundstobeweakened.Finally,we im-pose inour scanning procedure that predictedindirect detection signalsarecompatiblewiththecurrent(model-dependent) exclu-sion limitsat95% CL. Thistime, differentchoices ofdarkmatter interactions wouldresult ina different weighting of the subpro-cesses contributing to the gamma-ray signals, and therefore of differentresults.

Inthe caseofthe

F3S_uR

and

S3M_uR

models, spectral fea-tures in the gamma ray spectrum bring one of the strongest bounds as tree-level X X

→

uRu

¯

R annihilations are velocity sup-pressed. We therefore derive constraints by considering a com-bination of direct annihilations into photons and into a uRu

¯

R

γ

system,thelatterbeingpotentiallyenhancedbyVIBcontributions. Thetotalannihilationcrosssection



σ

v



tot

= 

σ

v



uRu¯Rγ

+

2



σ

v



γ γ

is then confronted with the most recent Fermi-LAT [24] and HESS [25] data from the Galactic Centre.3 We assume that the gamma-ray spectrumrelatedto the uRu

¯

R

γ

contributionpresents a sharp feature close to the dark matter mass, even though the exactpositionofthisfeaturedependsonr

≡

mY

/

mX [38].The ob-tainedconstraintsareintheworstcaseconservative,althoughfor mostscannedoverscenariostheyconsistinagoodapproximation. The three-body signal indeeddominates over the di-photonone, atleast atsmallr values,so that thepeak is oftenvery closeto the darkmatter mass.The derivationof moreprecise constraints wouldrequirearecastoftheexperimental results,whichlies be-yondthescopeofthisstudy.

Other relevant bounds can be obtained by investigating dark matter annihilations into gluons, as this could be constrained by the Fermi-LAT analysis of dwarf spheroidal galaxies (dSphs) data [27].Similarlytothegamma-raycase,we evaluate



σ

v



tot

=



σ

v



uRu¯Rg

+ 

σ

v



gg and compare our predictions with

Fermi-LAT dSph resultsfor the gg annihilation channel [9]. These con-straintsbeingcomparablewiththosearisingfromgamma-rayline searches, they are omitted from the discussion. Finally for the

F3V_uR

model,X X

→

uRu

¯

R annihilationsoccurinans-wave

con-2 _{X X→γZ annihilationsshouldbeincludedaswell,astheassociatedmatrix} el-ementisofthesameperturbativeorderastheX X→γ γ one.However,wehave foundoutthatthedi-photoncontributiontoσvissubdominanttotheX X→gg

oneintheentireparameterspace.Wehavethereforenotaccountedfor annihila-tionsintoaγZ system,thatisitselfsubleadingwithrespecttoX X→γ γ.

3 _{WederiveexclusionlimitsbyconsideringanEinastodarkmatterdensity} pro-file [37].

figuration.The moststringent indirectdetection boundsare thus givenbyFermi-LATdSphsearches,thistimeintheuu final

¯

state.

Ourresults are shown in Fig. 2. The grey shaded region rep-resents scenarios that can account for the correct relic density whenassumingastandardfreeze-outmechanism.Forthe

F3S_uR

model,NLOcorrectionsdrasticallymodify thecontours ofthe vi-ableparameterspaceregionatlarge r,selecting

λ

valuessmaller thanfortheLOcase.Thisstemsfromthe X X

→

gg contributions,

that are driven by the strong couplingconstant

α

s andthat en-hancetheannihilationcrosssection.Onthecontrary,NLO correc-tionsfortheMajoranadarkmattercasedonotimpacttheresults much.Inthelarger regime,weobtaindeviationsinthe

λ

valueof atmost15%withrespecttotheLOcase,whilstscenariosfeaturing asmallr valueareunaffected,theannihilationcrosssectionbeing dominatedby

α

s-dependent co-annihilations.Following thesame reasoning,itturnsoutthattheactualvalueof

λ

isirrelevantwhen co-annihilationsofthemediatorviaQCD processesdrivetherelic density.

The

F3V_uR

modelistheonethatfeaturesthelargest param-eterspaceforwhichtherelic densityasmeasuredby thePlanck collaborationcanbeaccommodated.Foranygiven

(

mX

,

mY

)

mass configuration, the

λ

value that is needed to obtain

h2

Planck is

smaller than in the scalar and Majorana dark matter cases. The annihilationstrengthofvectordarkmatterisindeedlarger,except intheco-annihilationregimewherethemodelisindistinguishable fromthe

F3S_uR

setupthatalsofeaturesafermionicmediator.

Ourfindings showanicecomplementaritybetweendirectand indirect dark matter searches in the case of the

F3S_uR

and

F3V_uR

models.Gamma-raysearches (green hatchedregion)are abletoprobeanddisfavourat95%CLdarkmattercandidateswith massesrangingdownto1 GeV,exceptforcompressedspectrawith

r

−

1



0

.

3 and very small couplings belowabout 10−2 (bottom rowofFig.2). Thisunexplored regionconsistsinone ofthe two co-annihilation-dominatedregionswhicharestillopen andmight giverisetointerestingLHCsignaturesthroughlonglivedparticles (LLPs) [39].Forthe

S3M_uR

model,indirectdetectionplays a mi-nor role, excluding a limited part of the parameter spacewhere dark matter is light. The two separated excluded regions corre-spondtoFermi-LATlimitsarising fromX X

→

γ γ

(larger values)

and X X

→

uRu

¯

R

γ

(small r values)annihilations respectively. Fi-nally,

F3S_uR

scenarios can be proved by the HESS experiment, asdepicted by the disfavoured island in the parameter spaceat

mX

>

300 GeV.

Direct and indirect detection bounds both exclude the inter-mediatemassrange,althoughdirectdetectionboundsadditionally contribute to cut down the parameter space. This is particularly trueforlarge darkmattermasses, closeto 1 TeVorevenhigher, whereonefindsasecondviableco-annihilationregimeandwhere theXENON1Tbounds(yellowhatchedregion)starttoplayarole. In addition, very light dark matter scenarios are excluded due toPICO constraints(cyanhatched region). Remarkably, thesetwo direct detectionexperiments are also able to probe the co-anni-hilation regime. The whole freeze out parameter space is hence disfavouredat90%CLfordarkmattermassesbetween4 GeVand 1000(500)GeVforthe

F3S_uR

(

F3V_uR

)model.

Spin-dependent direction detection exclusion bounds are the moststringentconstraintsonthe

S3M_uR

modelparameterspace, even though spin-independent experiments start to be sensitive to dark matter masseslarger than 4 TeV. Majorana dark matter isstrongly disfavoured formassesbetween8 and300GeV, even fortheco-annihilation regime thatcould give riseto LLPcollider signatures.Thelatterregime isevenfurtherconstrained, fordark mattermassesrangingupto10 TeV, bytheXENON1T SIbounds, theseconstraintsbeingduetothescalarnatureofthemediator.

Fig. 2. Toprow:Parameterspaceregionscompatiblewiththestandardfreeze-outmechanismandtheobservedrelicdensity [22],showninthe(mY,mX)planeforthe

F3S_uR(left),S3M_uR(centre)andF3V_uR(right)models.Thegrey shadingindicatestheλvalueneededtosatisfytherelicdensityconstraint.Theyellowhatchedregion isexcludedbytheSIXENON1Tbounds [23] (DDSI),thegreenhatchedonebygamma-raylinesearchesfromFermi-LAT [24] andHESS [25] (ID),andthecyanhatchedone bytheSDPICObounds [26] (DDSD).Moreover,fortheF3V_uRmodel,indirectdetectionboundsareextractedfromFermi-LATindSphssearches [27] (ID),whenonerelies ondarkmatterannihilationsintheuu final¯ state [9]. Bottomrow:Sameasforthetoprowbutinthe(r−1,mX)planewherer≡mY/mX.Thisallowsustohighlightbetter theco-annihilationregime.

5. Combining dark matter searches

We illustrate in Fig.3 the complementarity of theconsidered cosmological and collider constraints on the models, after map-pingthecosmologicalboundsofsection4ontoan

(

mX

,

mY

)

plane forafixed



Y

/

mY ratioof5%.4 However,contrarytotheprevious section, we allow for under-abundant dark matter and therefore only considertherelic densityconstraintasan upperbound. We henceimplicitlyassume the existenceof someother dark matter component,withdifferentpropertiesandinteractions.

Under theseassumptions, we obtain allowed parameter space regions for all scenarios. These regions feature mediator masses greater than 1.5 TeV (scalar mediator) and 2 TeV (fermion me-diator), and a neither toocompressed nor too split newphysics spectrum. The mediator mass is mostly constrained by collider searches,whilethedarkmattermassisrestrictedbythe combina-tionoftherelicdensity(lowerbound)andtheinterplaybetween theSDandSIdirectdetection(upperbound)constraints.Theonly exception concerns the smallmass gapregime in whichthe col-lider constraints tend to be competitive (despite of potentially non-perturbative couplings). For all scenarios, indirect detection constraintsaretooweaktoplayanyrole.Gamma-rayfluxesare

in-4 _{Representingtheresultsforafixedmediatorwidth-over-massratioisonlyone} ofthepossibilities.Wecouldinsteadenforceafixedλvalue.Inthiscase,Y/mY increasesforlargemediatorandsmalldarkmattermasses.TheNWAcanthusbreak down,dependingonthevalueofthecouplingandonthemodel,andsimulations relyingon thefactorisation ofthemediator production anddecay processes, as traditionallyperformed,wouldleadtoanincorrectdescriptionofthesignal kine-matics.

deedreducedbya

(

h2

model

/

h2Planck

)

2 factorforunder-abundant

darkmatter, contrarilytothedirectdetectionpredictionsthatare onlylinearlyrescaled.5

Thiscollider-cosmologycomplementarityofconstraintsis com-patible with the nature of the considered experimental probes. Collider bounds are largely dominated by the impact of the Y Y

channel. On the contrary, direct detection experiments are more sensitivetoscenariosfeaturinglargecouplingsand/orasmallX /Y

mass splitting, asthe direct detection cross section scales as

λ

4

andexhibitsapolynomialinr initsdenominator.Moreover,when allowingforunder-abundantdarkmatter,therelicdensityfavours largecouplingsaswellandopensthedoortoamuchwidersetof viablesolutions.

In the same Fig. 3, we provide projections for future experi-ments.Weshowprojected2

σ

exclusionand5

σ

discoveryreaches for the HL-LHC, which corresponds to a luminosity of 3 ab−1. Weextrapolate the currentreach undertwo assumptions forthe mannerthesystematicuncertaintiesonthebackground



systbgk could

evolve. In a first case, we consider that it is the same asin the initially considered 139 fb−1 ATLAS search, while in the second case, we assume that it reaches a floor of 5% for each SR. The resultsshowthatconsideringtherecastcut-and-countATLAS anal-ysis, the boundswill not improve significantly even withan op-timistic assumption on the systematics. Equivalently, this shows

5 _{Withoutsucharescaling (aswhenanon-thermalmechanismisinvoked to} reproducethedarkmatterdensity [40]),thecombinationofcurrentdirectand in-directdetectionboundsdisfavourstheparameterspaceregionswhichtheHL-LHC issensitiveto.Wedonotconsidersuchapossibilityinthiswork.

C. Arina, B. Fuks, L. Mantani et al. Physics Letters B 813 (2021) 136038

Fig. 3. Toprow: Boundsarisingfromcosmologicalobservations,representedinthe(mX,mY)planeforafixedmediatorwidthovermassratioof5%,ontheF3S_uR(left),

S3M_uR(centre)andF3V_uR(right)modelparameterspace.Weallowforunder-abundantdarkmatter,thebandwhichreproducestherelicdensityasmeasuredbythe Planckcollaborationlyingbetweenthe(almostindistinguishable)thinandthickmagentalines.Futureprojectionsoftheconstraintsareprovidedasdashedlines. Bottom

row: Combinationofcosmologicalandcolliderboundsandtheirprojections.ThecolliderprojectionscorrespondtoexclusionanddiscoveryreachesforaLHCluminosityof 3000 fb−1_{(i.e. theHL-LHCphase)andassumealevelofsystematicsonthebackgroundeitherequaltotheconsideredATLASsearchatcurrentluminosityorfixedto5%.} thatthediscoveryreachisveryclosetothecurrentexclusion

lim-its. Different, more complex, analysis strategies should therefore be considered tobetter assessthe potential offuturesearches in probing awider region ofthe parameterspace. For example,the ATLAS search that we have used in our analysis also includes a supersymmetry-inspired signal region relying on a boosted deci-sion tree, which we did not consider in our model-independent approach.

On the other hand, the projected cosmological bounds have a much larger potential. We present the expected sensitivity of futureSI(LZ [41])andSD(LZ,PICO-500 [42] andCOSINUS [43]) di-rectdetectionexperiments,thelatterbeingextractedfromref. [44] forthe

O4

operator(i.e. forstandardSDinteractions).Theinterplay of theprojected SD boundsandthe relic densityconstraints can completelyexcludethe

S3M_uR

scenario,whiletheimprovement oftheSIboundswoulddrasticallylimittheoptionsallowedbythe HL-LHCexpectationforthe

F3S_uR

model.Similarly,high-energy gamma-rayexperiments,such asCTA [45,46] andSWGO [47],and theLSST

+

Fermi-LATdSphssurvey [48] willbeabletoexplorethe modelparameterspacewellabovetheTeVregime,inaregionthat isout ofreachofLHCsearches.Inparticular,projectionsfor indi-rect detection have the largest impact on the

F3V_uR

scenario, beingthedominantconstraintforlargemediator masses.It how-everstillleavesalargewindowtestableattheHL-LHC.

6. Conclusions

We have performeda comprehensiveanalysis ofcosmological and collider bounds for three sets of t-channel simplified dark matter models inwhich thedark matter isa realfield. We have investigated the complementarity betweenthe different types of

boundsandmadeprojectionsforfuturecolliderandcosmological experiments.Ourfindingsshowthatmostparameterspacesare al-readystronglyconstrainedbycurrentbounds,andthatfuturedark matter directand indirectdetection probehave a large potential tocover the still allowed regions ofthe parameter space. In this way, conclusive statements on the phenomenological viability of the considered class oft-channel models will be in order inthe nextdecades.

One should however keep in mind that the models consid-eredin this analysis are simplified andmodel-independent con-structions. While being representative of different theoretical-ly-motivated new physics scenarios, they necessarily lack non-minimalfeatures,suchasthepresenceofmoremediators,a multi-componentdarkmatterspectrum,orawiderrangeofinteractions betweenthe newparticlesandtheSM. Suchfeatures canchange thepicturebyintroducing,forexample,interferencecontributions whichcanweakentheconstraintsoreffectsduetolargemediator widthswhichmodifythefinal-statekinematicsatcolliders.

Finally,wedidnot investigatefreeze-indarkmatter scenarios, which we leave for a separate work. This scenario is viable for tiny

λ

valuesoftheorderof10−6 _{orsmallerandmightopen up}

additionalwindows,asforinstancerelatedto LLPsearchesatthe LHC.

Declaration of competing interest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

We acknowledge J. Heisig, M. Kraemer and K. Mawatari for stimulating discussions during this study, and L. Lopez Honorez andM.Tytgatfortheir helpinthevalidationprocedure. LPwork issupported bythe KnutandAlice WallenbergFoundation under theSHIFTproject,grantKAW2017.0100.LPacknowledgestheuse oftheIRIDIS4HPCFacilityattheUniversityofSouthampton.CAis supportedbytheInnovirisATTRACT2018104BECAP2agreement. HMissupportedbytheGermanResearchFoundationDFGthrough the RTG 2497 and the CRC/Transregio 257. LM is supported by fundingfromtheEuropeanUnion’sHorizon2020researchand in-novationprogramme aspartoftheMarieSklodowska-Curie Inno-vativeTrainingNetworkMCnetITN3(grantagreementno.722104). References

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