Electroweak superpartners scrutinized at the LHC in events with multi-leptons

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Physics Letters B

www.elsevier.com/locate/physletb

Electroweak superpartners scrutinized at the LHC in events with multi-leptons

Iñaki Lara

^a,b,∗

, Daniel E. López-Fogliani

^c,d

, Carlos Muñoz

^a,b

aDepartamentodeFísicaTeórica,UniversidadAutónomadeMadrid(UAM),CampusdeCantoblanco,28049Madrid,Spain bInstitutodeFísicaTeórica(IFT)UAM-CSIC,CampusdeCantoblanco,28049Madrid,Spain

cInstitutodeFísicadeBuenosAiresUBA&CONICET,DepartamentodeFísica,FacultaddeCienciaExactasyNaturales,UniversidaddeBuenosAires, 1428 Buenos Aires,Argentina

dPontificiaUniversidadCatólicaArgentina,1107BuenosAires,Argentina

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received8November2018

Receivedinrevisedform8January2019 Accepted8January2019

Availableonline17January2019 Editor:J.Hisano

Keywords:

Supersymmetryphenomenology Supersymmetricstandardmodel LHCphenomenology

We analyzeamulti-leptonsignal plusmissing transverse energyfromneutrinosexpected atthe LHC for abino-likeneutralinoas thelightestsupersymmetricparticle(LSP),whentheleftsneutrinoisthe next-to-LSP and henceasuitable source of binos. The discussionis carried outinthe framework of theμνSSM,wherethepresenceofR-parityviolating(RPV)couplingsinvolvingright-handedneutrinos solvestheμproblemandcanreproducesimultaneouslytheneutrinodata.Leftsneutrinos/sleptonsare pair-produced at pp collisionsdecayingto binos,withthe latterdecayingviaRPVto Wor Zν.This signal canbecomparedwithLHCsearchesforelectroweaksuperpartnersthroughchargino–neutralino production. Thereducedcrosssectionofthesneutrino/sleptonproductionincomparisonwiththeone ofthelatterprocess,limits thesensitivityofthesearchestosmallsneutrino/sleptonmasses.Although theresultingcompressedspectrumtypicallyevadestheaforementionedsearches,weshowthatanalyses usingrecursivejigsawreconstructionaresensitivetothesescenarios.Asaby-product,wefindthatthe regionofbino masses110–120 GeV and sneutrinomasses120–140 GeVcan giverise toatri-lepton signalcompatiblewiththelocalexcessrecentlyreportedbyATLAS.

©^{2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Search forsupersymmetry (SUSY)ataccelerators hasbeen fo- cused mainly on signals with missing transverse energy (MET) inspiredin R-parityconserving(RPC)models,suchastheminimal supersymmetric standard model(MSSM) [1–3], where significant boundsonsparticle masseshavebeenobtained [4].Inparticular, strongly interacting sparticles have to have masses above about 1 TeV, whereas the bound for the weakly interacting sparticles is about100GeV, with theexception ofthe bino-like neutralino whichisbasicallynotconstrainedduetoitssmallpairproduction crosssection.Qualitativelysimilarresultshavealsobeenobtained intheanalysisofsimplifiedR-parityviolating(RPV)scenarioswith trilinearlepton- orbaryon-numberviolatingterms [5],assuminga single channel available for the decay of the lightest supersym- metric particle (LSP). However, such assumption is not possible in other RPV scenarios, such as the ‘

μ

from

ν

’ supersymmetric

*

Correspondingauthor.

E-mailaddresses:[email protected](I. Lara),[email protected] (D.E. López-Fogliani),[email protected](C. Muñoz).

standardmodel(

μν

SSM) [6,7],wheretheseveraldecaybranching ratios (BRs) ofthe LSP significantly decrease the signal. Thisim- plies that a naive extrapolationof the usual bounds onsparticle massestothe

μν

SSM is notapplicable.In addition,inRPVmod- els basically all sparticles are potential candidates for LSPs, and therefore analyses ofthe LHC phenomenology associated toeach candidatearecrucialtotestthem.

Theonlyrecentanalyses [8,9] ofsignalsattheLHCforLSPcan- didatesinthe

μν

SSM havebeendedicatedtotheleftsneutrino.¹ Thereitwasshownthatbecausetheleftsneutrinohasseveralrel- evant decay modes, the LEP lower bound onthe sneutrino mass of about 90 GeV [14–19] obtained under the assumption of BR onetoleptons,viatrilinearRPVcouplings,isnotapplicableinthe

μν

SSM. The same conclusion was obtained for the left slepton, giventhatsearchesforitsdirectdecayarenotrelevantbecauseit decaysthroughanoff-shellW andasneutrino.Thus,inRef. [8] the prospects fordetection ofsignals withdi-photon plus leptons or

1 The phenomenology of a neutralino LSP was analyzed in the past in Refs. [10–13].

https://doi.org/10.1016/j.physletb.2019.01.010

0370-2693/©^{2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

METfromneutrinos,andmulti-leptons, fromthepairproduction ofleftsneutrinos/sleptonsandtheirpromptdecayswereanalyzed.

Asignificantevidenceisexpectedonlyinthemassrangeofabout 100to300GeV.Themassrangeof45to100GeV(withthelower limitimposed not todisturb thedecaywidthofthe Z ) was cov- eredin Ref. [9], studying the displaced-vertex decays ofthe left sneutrino LSP producing signals with di-lepton pairs. Using the presentdata set ofthe ATLAS 8-TeV dileptonsearch [20], one is able to constrain the left sneutrino LSP only in some regions of theparameter space ofthe

μν

SSM,especially when theYukawa couplings andmass scale of neutrinos are rather small.In order toimprovethesensitivityofthissearch,itwasproposedin [9] an optimizationofthetriggerrequirementsexploitedinATLASbased onahighleveltriggerthatutilizesthetrackerinformation.

Allthisshowsthatthecommonloreonsparticlemassbounds mustbe carefullyre-analyzed inthe light ofdifferent theoretical models.Thiscrucialtaskgiventhecurrentexperimentalresultson SUSYsearches, hasjuststartedinthe caseofthe

μν

SSM,andit hasbeenconcentrated forthe momentontheelectroweaksector asdiscussedabove.Inthiscontext,wherebasicallythemassesare poorlyconstrainedornotatall,weconsidercrucialtotakeintoac- counttherecentsearchesattheLHCforeventswithmulti-leptons plusMET [21–24], sincethey can be comparedwith

μν

SSM sig- nals.Thisistheaimofthiswork.

Inthe

μν

SSM,when the bino-like neutralino is theLSP with theleftsneutrinothenext-to-LSP(NLSP),theRPCdecays

ν

˜_→

ν χ

˜₁⁰ and² ˜ →  ˜

χ

₁⁰ dominateover theRPVones, therebypair produc- tion of sneutrinos/sleptons at the LHC will be a source of bino pairs. Subsequently, binos will decay via RPV couplings to W or Z

ν

, giving rise to signals with multi-leptons plus MET from neutrinos. In addition, we will also obtain regions of bino and sneutrinomassesproducingatri-leptonsignalcompatiblewiththe localexcess reportedby ATLAS [24]. There,this signal was stud- ied inthe context ofsimplified RPC models, assuming wino-like chargino–neutralinoproductionwithabino-likeLSP.Thisscenario wasfurtherelaboratedinRefs. [25,26],includingalsodarkmatter constraintsandthemeasuredanomalousmagneticmomentofthe muon.

Thepaperisorganized asfollows.InSection 2,we willbriefly reviewthe

μν

SSM anditsrelevantparametersforouranalysisof the electroweak sector. In Section 3 we will introduce the phe- nomenology of the bino-like LSP with the left sneutrino as the NLSP,studyingtheirrelevantpairproductionattheLHC,aswellas thesignals.Ontheway,wewillanalyzethedecaywidths,BRsand decaylengthsof the bino. InSection 4, we will considerthe re- centATLASsearchesformulti-leptonsplusMET,anddiscusstheir significance on bino searches in the

μν

SSM. We will also show ourprescriptionforrecastingtheATLASresult[24] to thecaseof thesneutrino–bino scenario.We then willshow in Section 5the prospects for the searches at the LHC using an integrated lumi- nosityof100and300fb⁻¹.Ourconclusions andoutlookwill be presentedinSection6.

2. The

μν

SSM

The

μν

SSM [6,7], is a natural extension of the MSSM,where the

μ

problemissolvedand,simultaneously,theneutrinodatacan bereproduced [6,7,10,11,27,28].Thisisobtainedthroughthepres- enceoftrilineartermsinthesuperpotentialinvolvingright-handed

2 Inwhatfollows,thenotationslepton(lepton)willbeusedforachargedslepton (chargedlepton),andsneutrino(neutrino)foraneutralslepton(neutrallepton).The symbolwillbeusedforelectron,muonortau=^e,μ,τ,andchargeconjugation offermionsistobeunderstoodwhereappropriate.

neutrinosuperfields

ν

ˆ_i^c,whichrelate the originofthe

μ

-termto the originofneutrinomassesandmixing. The simplestsuperpo- tentialofthe

μν

SSM [6,7] isbuiltwithone

ν

ˆ^c:

W

= 

_ab

^

Ye_{i j}H

ˆ

^a_d

ˆ

L^b_ie

ˆ

^c_j

+

Y_{di j}H

ˆ

^a_dQ

ˆ

_i^b_d

ˆ

^c_j

+

Yu_{i j}H

ˆ

^b_uQ

ˆ

^au

ˆ

^c_j

 + 

_ab

^

Y_νiH

ˆ

^b_uL

ˆ

^a_i

ν ˆ

^c

_{− λ ˆ} ν

^cH

ˆ

^b_uH

ˆ

^a_d

 +

¹

3

κ ν ˆ

^c

ν ˆ

^c

ν ˆ

^c

,

(1) wherethe summationconvention is impliedon repeatedindices, witha,b=¹,2 SU(2)L indicesand i,j=¹,2,3 theusual family indicesofthestandardmodel.

The simultaneous presence of the last three terms in Eq. (1) makesitimpossibletoassign R-paritychargesconsistentlytothe right-handed neutrino

ν

R, thus producing explicitRPV (harmless for proton decay). Note nevertheless, that in the limit Yνi→^0,

ˆ

ν

^c can be identified in the superpotential as a pure singlet su- perfield without lepton number, similar to the next-to-MSSM (NMSSM) [29], andtherefore R parity is restored. Thus,the neu- trinoYukawacouplings Yνi aretheparameters whichcontrol the amount of RPV in the

μν

SSM,and asa consequencethis viola- tion is small. After the electroweak symmetry breaking induced by the soft SUSY-breaking terms of the order of TeV, and with the choice of CP conservation, the neutral Higgses develop the vacuumexpectationvalues(VEVs)^Hd,u= ^v√d,u₂^{,therightsneutri-} nos

ν

R=^√vR₂^{,andtheleftsneutrinos}

ν

i=^√vi₂^,wherevR∼ ^TeV whereasvi∼Yνivu^{10−4GeVbecauseofthesmall}contributions Yνi^{10−6whosesizeisdeterminedbythe}electroweak-scalesee- saw ofthe

μν

SSM [6,7]. Noteinthissense that the last termin Eq. (1) generates dynamically Majorana masses, m_M=²

κ

√^vR

2 ∼ TeV.Ontheotherhand,thefifthterminthesuperpotentialgener- atesthe

μ

-term,

μ

= λ^√vR₂∼^TeV.

The newcouplings and sneutrino VEVsin the

μν

SSM induce newmixingofstates.Theassociated massmatriceswerestudied indetailinRefs. [7,11,8].Summarizing,inthecaseofone

ν

ˆ^c there are six neutral scalars and five neutral pseudoscalars (Higgses- sneutrinos),sevenchargedscalars(chargedHiggses-sleptons), five charged fermions (charged leptons-charginos), and eight neutral fermions (neutrinos–neutralinos). In our analysis of the elec- troweaksectorbelow,wearemainlyinterestedinthescalars/pseu- doscalarsandneutralfermions.

Theneutralfermionshavetheflavorcomposition(

ν

i,B,W,H_d,

Hu,

ν

R).Thus,withthelow-energybinoandwinosoftmasses,M1 andM₂,oftheorderofTeV,andthesamefor

μ

andm_Masdis- cussedabove,thisgeneralizedseesawproducesthreelightneutral fermions dominated by the left-handedneutrino flavor composi- tion. One neutrinogets its mass attree level,whereas the other two atoneloop. Asdiscussed inRef. [9],thetree-levelmasscan be approximated as mν ≈

iv²_i/4M, with _M¹ ≡ ^g_M ²₁ + _M^g2₂^{. The} rest of neutral fermions get masses around the TeV scale. How- ever, if M₁ is small compared with the rest of the parameters, thefourthlightesteigenstateofthemassmatrix,whichweiden- tify asthe lightest neutralino

χ

˜₁⁰, is mainly binodominated and theLSP withmχ_˜1⁰≈^M1,sincethelargestoff-diagonalmassentry m_B˜H˜

u=^√1₂^gvu issmall.

The neutral scalars have the flavor composition (H_d^R,H^R_u ,



ν

^R_R ,

ν

_i^R), but the off-diagonal terms of the mass matrix mixing the left sneutrinos with Higgses and right sneutrinos are sup- pressedby Yν andviL,implyingthattheleftsneutrinostateswill bealmostpure.Thesamehappensforthepseudoscalarleftsneu- trino states

ν

_i^I, which have in addition degenerate masses with thescalarsm_ν^R_i ≈^m_νI

i ≡^mνi.Theirapproximatetree-levelvalueis m_²νi≈ ^Yν_2v^iv_i^uvR(−√

2Aνi−

κ

v_R+_tan^λvR_β),where Aνi arethetrilinear

parametersinthesoftLagrangian,andtanβ≡^vu/v_d.Asdiscussed inRef. [8],thereisenoughfreedominthe

μν

SSM totunethesoft parametersinordertoget lightsneutrinos.Besides,theleft slep- tonswillalsobelight,onlyalittleheavierthantheleftsneutrinos sincetheyareinthesame SU(2)doublet,withthemasssplitting mainlyduetotheusualsmallD-termcontribution,−m²_Wcos 2β. 3. Bino-likeLSPphenomenologyinthe

μν

SSM

The pair production cross section of bino-like neutralinos at large hadroncolliders isvery small, since thereis nodirect cou- plingbetweenthebinoflavorstateandthegaugebosons,andwe areassumingthattherestofthespectrumremainsdecoupled.Bi- nosareproducedmainlythroughvirtualZ bosonsintheschannel exploitingtheir smallHiggsinoflavorcomposition, orthroughthe t channel interchange ofvirtual first generation squarks,strongly suppressedby their large masses. Nevertheless,the bino-like LSP can be produced in the decayof other SUSY particles, which al- thoughheavier,haveahigherproductioncrosssectionattheLHC.

ThatisthecasewhentheleftsneutrinoistheNLSP.Afterproduc- tion,theleftsneutrinosdecaytothebinoLSP.

The dominant pair-production channels ofsleptons at hadron colliderswerestudiedinRefs. [30–35].Themainproductionchan- nels at the LHC are through a virtual Z boson in the s channel forthepairproduction ofscalarandpseudoscalarleft sneutrinos

˜

ν ν

˜,avirtual W boson fortheproduction ofaleft slepton anda (scalar or pseudoscalar) sneutrino ˜˜

ν

,and both virtual Z and

γ

forthepairproductionofleftsleptons ˜˜.Notethatalthoughthe leftsneutrinoislighter thanitscorresponding leftslepton asdis- cussedintheprevioussection,sincethemassseparationisalways smaller than mW, the phase spacesuppression makes the decay

˜ → ˜

χ

₁⁰_{+ }dominant.

InFig.1,we showtheproductionchannelsaswellastheRPC decaysof theleft sneutrino andleft slepton to producethe bino LSP,whichdominateovertheRPVonessincethesearesuppressed bythesmallnessofYν .Therightsleptonscanbealsoasourceof binoLSPattheLHC.Iftheir massesaresimilartotheonesofthe leftsleptons,anadditionaldiagramasthethirdone ofFig. 1will bepresent.However,theproductioncrosssectioncorrespondingto thisextradiagramissignificantlysmallerthanforthoseshownin Fig.1.Altogether,thenumberofbinosproducedafterthedecayof rightsleptonsisaroundatenthofthenumberproducedthrough leftsneutrinos/sleptons.

Ifthemass ofthebino-like neutralino liesbetweenthe Higgs and Z masses, thepossible twobody RPVdecaysare to W and Z

ν

,asshownalsoinFig. 1.There weonly depictedthedecayof each neutralinopair to W and Z ,andtheleptonic decaysofthe latter. Note nevertheless that both neutralinos can also decay to Z or W indistinctly, and that the hadronic decay of the W bo- son, as well asthe invisible decay of one of the Z ’s, contribute tothesignal ofleptonicsearches,inadditiontothediagramsdis- played. As we will discussin Section 5, the latterprocesses can also contribute to the signal we are interested in analyzing, but withsmalleryields.ThebinodecaysaremediatedthroughtheRPV mixingbetweenthebinoandneutrinos.Althoughthreebody de- caysinvolvingvirtual Higgsbosonorother virtualheavierscalars are possible,all ofthem sufferfromkinematicsuppression. Thus therelevant diagramswillbe the twobody decays,and approxi- mateformulasforthepartialdecaywidthsareasfollows:

( χ ˜

⁰

→

^W



i

) ≈

^g

2m_χ˜0

16

π



1

−

^m2W

m²_χ˜0



2



1

+

^m

2˜ χ⁰ 2m²_W



^UV_B˜ν

i

²

,

(2)

Fig. 1. Relevant diagrams ofthe benchmark μνSSM scenario ofRPC leftsneu- trino/sleptonpairproduction,followedbytheRPVdecayofthebino-likeLSP,χ˜₁⁰.

i

( χ ˜

⁰

_→

Z

ν

i

) ≈

^g

2m_χ˜0

16

π

cos²

θ

W



1

−

^m2Z

m²_χ˜0



2

×



1

+

^m

2˜ χ⁰ 2m²_Z



i

j

U^V_˜

BνjU_ν^V_i^∗_νj

2

,

(3)

whereU^V isthematrixthatdiagonalizesthemassmatrixforthe neutralfermions [7,8],andU^V_˜

Bνi canbeapproximatedas ^g_M^vi

1. Sinceweareinterestedinthenextsectionsinanalyzingsignals withelectrons ormuonsinthefinal states,wefocusnow onthe cases inourparameterspacewherethe decaywidthoftheneu- tralinototauis smallerthantothe twolight families ofleptons.

Thiscan beachievedbyadjusting thesneutrinoVEVs,whilepro- ducing an acceptable mass scale for the neutrinos. For example, in order to optimizethe signal we can use v1≈^v2>v3. Then, we can compare roughly the above decay widths summing over the two light families of leptons. Taking into account the kine- maticfactors,weobtainfortheratioanapproximateupperbound

≈^2cos2θW,implyingthatthedecaytoWwillalwaysbeatleast about a factor of 1.5 larger than the decay to Z

ν

. On the other hand,given thesmallvalue of M1,fromEqs. (2) and (3) we can alsoobtainanupperboundforthetotalwidth^{10−12GeV,cor-}

respondingto a proper decay length c

τ

⁰.2 mm. This isshort enoughtoexpectmostofthedecaystohappeninsidethefiducial region definedby the values ofthe transverse impact parameter (d₀^{P V}) andthelongitudinalimpactparameter(z₀^{P V})relativetothe primary vertex, considered in prompt ATLAS and CMS searches.

Subsequently,theW and Z bosonsdecaypromptlyproducinglep- tons,neutrinosorjets.Thustheneutralino couldbedetectablein eventsincludingleptons,jetsand/orMET.

Notethatifthe massoftheLSP dropsbelowthe massofthe W boson,itsdecayisstillpossibleandwillproceedthroughthree- bodydecays mediatedby off-shellgauge bosons andscalars. The totalwidthwillbe inthiscasesmaller,duetothereducedphase space, and will lead to leptons and/or quarks originated at dis- placedvertices.Thissignalcannotbetestedwiththeusualsparti- clessearches,butratherwithdedicatedanalysis.Thestudyofthis possibility,althoughinteresting,isbeyondthescopeofthiswork.

Ifthe mass ofthe bino-like neutralino is larger than the one oftheHiggsboson,thedecay

χ

˜⁰_→h

ν

isalsopossible,withthe dominantdiagram mediated by the sneutrino–Higgsmixing. The approximateformulaforthecorrespondingpartial decaywidthis givenby:

i

( χ ˜

⁰

_→

h

ν

i

) ≈

^g

2m_χ˜0

64

π   

₁

−



m_h m_χ˜0



2

i

j

Z_h^H_ν˜

jU_ν^V∗

iνj

2

,

(4) where Z^H isthematrixthatdiagonalizesthemassmatrixforthe neutralscalars [7,8].Ontheonehand,therelativesizeofthedecay ofneutralino toHiggscompared tothe decayto gaugebosons is suppressedbythe kinematicfactors. Ontheotherhand,thecon- tribution of the sneutrino–Higgs mixing is not necessarily small comparedtothebino–neutrinomixing. Moreover,asdiscussedin detail in Ref. [8], the former mixing can be enhanced when the massseparationbetweenmν and_˜ m_h0 issmall.Asaconsequence, fromtheperspectiveofthesearchesusingeventswithleptons,the openingofthischannelsoftensthesignal.

4. ElectroweaksearchesattheLHC

Asshownintheprevioussection,theproductionanddecayof thesneutrino (andslepton)NLSP when theneutralino isthe LSP can produce signalsincluding up to six leptons plus MET.These

μν

SSM signals can be compared with searches for electroweak SUSYpartnersattheLHC.

Theanalyses [21,22] and [23] use theproton–proton(pp)col- lision data delivered by the LHC at a center-of-mass energy of

√s=^{13 TeV, tosearch foreventswithtwoorthree electronsor} muonsandfourormore electrons,muons andtaus,respectively.

Theformeranalysistargetsdirectchargino/neutralinoandslepton pairproduction in simplified RPC models, whereas the latterin- cludesthestudyofsimplifiedRPVscenarioswithalepton-number violating term, targeting direct pair production of chargino/neu- tralino,leftslepton/sneutrino,andgluinos.

Inthecaseofleftsleptons/sneutrinos analyzedinRef. [23] us- ing an integratedluminosity of36.1 fb⁻¹,the resultextends the regionofSUSYparameterspacepreviouslyexcludedbyATLAS [36]

putting a lower bound of 1.06 TeV on their masses assuming a singleRPVchannel,λ12kˆL1Lˆ2eˆ^c_k,availableforthedecayoftheneu- tralinoLSP.This assumptionis not allowed inthe

μν

SSM where the neutralino LSP has always decay channels to W and Z as shown in the previous section, and, in addition, the BRs of the leptonicdecays ofthelatterare small, oforder0.1 and0.03,re- spectively.Taking all thisinto account, we havechecked that no

constraintontheleftsneutrino/sleptonmassisobtainedfromthis search.

Concerningthe searchesof Refs. [21] and [22] using35.9and 36.1 fb⁻¹, respectively, for chargino–neutralino pair production, they assume a wino-likeproductionmechanism anddecayswith BR one to a bino-like LSP anda leptonically decaying W and Z bosonsintofinalstateswiththreelightleptons(electronsormuons) orahadronicallydecayingW bosonandaleptonicallydecaying Z bosonintofinal stateswithtwolight leptonsandtwojets.Inthis way, CMS andATLAS obtainedexclusion limits inthe parameter spacemχ_˜1^±/χ˜₂⁰−^m_χ˜1^{0.For example,fora massless}

χ

˜₁⁰ neutralino,

˜

χ

₁^±/

χ

˜₂⁰ masses up to approximately600 GeV are excluded. This analysisusesa moderatetolarge amountofMETto discriminate againstbackgrounds,thusitisnotsensitivetoacompressedspec- trumwherethisamountisnotlarge.Productioncrosssectionsfor chargino/neutralinopairs attheLHC [37,38] aremuchlarger than theproductioncrosssectionsforsleptonpairs [39].Thus wehave obtainedthatthekinematicrequirementforamassseparationbe- tween sleptons and neutralinos to have enough MET, forces the sleptonsinthe

μν

SSM to havelargemasseswherethe expected number of pairs produced at the LCH is not enough to obtain bounds.

Anovel approachfortheidentificationof eventscomingfrom theproductionofsparticlesincompressedspectra,wherethede- cay products carry low momenta, is the recursive jigsaw recon- struction(RJR)technique [40,41].Thishasmadepossibletodesign competitivesearchesforchargino–neutralinopairseveninscenar- ios where the mass splitting is close to the mass of the gauge bosons [24]. As we willanalyze below,the sameanalysiscan be used to put constraints on the slepton/sneutrino NLSP pair pro- ductionwhentheneutralinoistheLSPinthe

μν

SSM.

TheATLAS chargino–neutralinosearchusingRJRinRef. [24] is basedonthe 13-TeVdatawith36.1fb⁻¹.Allthesearch channels analyzedrequiretwoorthreelightleptonsoriginatedfromthede- cayofthegaugebosonsplusMET.Thedifferentsignalregionsare optimizedtotargetspecificmasssplittingsbetweentheproduced chargino–neutralino and the neutralino LSP, for whichthe initial state radiation (ISR) signal regions are designedto maximize the sensitivetothecasewherem=^m_χ˜^±

1/χ˜₂⁰−^m_χ˜⁰

1 isintherangebe- tween100and160GeV.TheresultsextendtheregionofSUSYpa- rameterspacepreviouslyexcludedbyATLASsearchesinthehigh- andintermediate-massregions.Inthelow-massandISRsignalan excessofeventsabovethestandard modelpredictionisobserved andtheregionofparameterspacebelowmχ_˜1^±/χ˜₂⁰=^{200 GeV can-} not be excluded. In our case, since the production cross section of the left sneutrino/sleptonis much smaller than the chargino–

neutralino one, theISR signal regions have thelargest sensitivity tothemassrangewheretheproductioncrosssectionisnotnegli- gible,andmχ_˜1⁰^mZ.

In the ISR signal regions, the events haveto fit in the “com- presseddecaytree”describedinRef. [24].Asignalsparticlesystem SdecaystoasetofvisiblemomentaVandinvisiblemomentum I recoils from a jet-radiation system ISR. The preselection criteria require exactlytwo or three light leptons, and betweenone and threenonb-taggedjets.Thetransversemomentumoftheleptons mustfulfillp^_T^1/2>25 and p^_T³>20 GeV.Theselectioncriteriaap- pliedtotheeventsafterpreselectionaregiveninTable1.

Atfirstatleastonesame-flavoroppositesign(SFOS)pairisre- quired, and from the formed SFOS pairs the one with invariant massclosesttom_Z shouldbeintherange(75,105).Theremaining leptonisusedtoconstructthe W -bosontransversemass,m^W_T ,as follows:m^W_T =

2p^_TE^miss_T (1−^cosφ),whereφistheazimuthal opening anglebetween the lepton associated withthe W boson

Table 1

Selectioncriteriaforthe3_ISRand2_ISRsignalregions.ThevariablesaredefinedinRefs. [24] and [40].

Region m[GeV] m^W_T [GeV] φ^{C M}_{I S R,I} RI S R p^{C M}_{T I S R}[GeV] p^{C M}_{T I}[GeV] p^{C M}_T [GeV]

SR3_ISR ∈ (75,105) >100 >2.0 ∈ (0.55,1.0) >100 >80 <25

Region mZ[GeV] mJ [GeV] φ_{I S R}^{C M}_,I RI S R p^{C M}_{T I S R}[GeV] p^{C M}_{T I} [GeV] p^{C M}_T [GeV]

SR2_ISR ∈ (⁸⁰,100) ∈ (⁵⁰,110) >2.8 ∈ (⁰.4,0.75) >180 >100 <20

Table 2

ComparisonbetweentheATLAScutflowshownintheauxiliaryfiguresofRef. [24] andourimplementation.

Cut applied ATLAS yield Implemented yield Normalized yield

Trigger matching & Preselection 1829 1398 1829

m∈ (75,105)GeV & m^W_T >100 GeV 533 406 531

φ^{C M}_{I S R,I}>2.0 408 308 403

RI S R∈ (⁰.55,1.0) 157 179 234

p^{C M}_{T I S R}>100 GeV 115 132 173

p^{C M}_{T I}>80 GeV 114 115 150

p^{C M}_T <25 GeV 73 68 89

andthe missing transverse momentum. Afterthat, the following variablesareusedasdiscriminant:

• ^{pC M}T I S R:Themagnitudeofthevector-summedtransverse mo- mentaofthejetsassignedtotheISRsystem.

• ^{pC M}_{T I}^{: The magnitude of the} vector-summed transverse mo- mentaoftheinvisiblesystem.

• ^{pC M}_T ^{: The magnitude of the} vector-summed transverse mo- mentaoftheCMsystem.

• ^RI S R≡ ^{pC M}I · ˆ^{pC M}T S/p^{C M}_{T S}:Servesasanestimateofmχ_˜1⁰/mχ_˜2⁰/χ˜₁^±. Thiscorrespondstothefractionofthemomentumofthesys- temthatiscarriedby itsinvisible systemI,withmomentum 

p^{C M}_I intheCM frame.As p^{C M}_{T S} grows,itbecomesincreasingly hardforbackgroundstopossessalargevalueinthisratio,un- likecompressedsignalswherethisfeatureisexhibited [40].

• φ^{C M}I S R,I:TheazimuthalopeninganglebetweentheISRsystem andtheinvisiblesystemintheCMframe.

OuranalysisisimplementedusingtheMadanalysis v5.17 [42–44] package,andvalidatedwithsimulatedMonteCarlo(MC) events corresponding to the production of neutralino–chargino pairs in the context of the MSSM decaying to a neutralino LSP andleptonically decaying gauge bosons, with selected masses of mχ_˜1^±/χ˜₂⁰=^{200 andm}_χ˜⁰

1=^{100 GeV.Tenthousandeventsaregener-} atedusingMadGraph5_aMC@NLO v2.6.3.2[45] atleadingor- der(LO)ofperturbativeQCDsimulatingtheproductionofthede- scribedprocesswiththestandardmodelfilesfortheMSSM.Events are then passed for showering and hadronization to PYTHIA v8.201 [46] using the A14 tune [47], and then to DELPHES v3.3.3[48] fordetectorsimulation.Theresultsoftheeventsse- lectionarecomparedwiththecutflowtableprovidedbytheATLAS collaboration, as shown in Table 2. The first column reproduces the unweighted yields from the ATLAS analysis, the second one presentstheunweightedyields fromourimplementation,andthe lastone thesameyields butnormalizedto thenumberofevents inthe first column. As can be seen fromthe table, thenumbers agreewithina20% error,thus weusethisimplementationtoob- taintheefficiencymapoftheATLASsearchfordifferentmassesof sneutrinos/sleptonsandneutralinos.

The sneutrino/slepton pair production is simulated in a simi- larway,butwithmodelfilesgeneratedusingasuitable modified version of SARAH code [49–51], and the spectrum is generated using SPheno v3.3.6 code [52,53]. Cross sections are calculated at NLO+NLL using Resummino v2.01 [54–57,38]. For each se-

lected point, tenthousand MC events aregenerated asexplained andpassedthroughthedescribedselectioncriteria.Theresultsare thencomparedwiththeexpected(S⁹⁵_exp)andobserved(S⁹⁵_obs)upper limitsobtainedintheATLASsearch.

5. Results

We have already obtained that results [21,22] and [23] do not produce bounds on the bino-like neutralino and left sneu- trino/slepton masses in the

μν

SSM. By using now the method describedintheprevioussection,wecalculatethecurrentandpo- tentiallimits onthe two-dimensionalparameter spacemν_˜ −^m_χ˜⁰

1

fromthe36.1fb⁻¹ ATLASresult [24],anddiscusstheprospectsfor the100and300fb⁻¹ searches.

Thepointsanalyzedinthe

μν

SSM parameterspaceshow alla worseefficiencypassingtheselectionrequirementsofSR2_ISRin comparison withSR3_ISRin Table 1.Thus the results discussed here are derived from the limits corresponding to the SR3_ISR signal region. Notefirst that the preselection requirementof ex- actly three light leptons, implies that the separation of masses betweenslepton/sneutrinoandneutralinointheprocessesshown in Fig.1must besmall enoughto avoidtheleptons produced in thedecayofsleptonstocontributetothesignal.Otherwise,these processesarediscardedfromtheATLASsearches.Theprocessesin Fig.1showthehighestyieldofthepossiblecombinationsofneu- tralinodecays.Otherpossibilities,likeW decayinghadronicallyor bothneutralinosdecayingto Z bosons,withonlyoneofthemde- cayingleptonically, contributealsotothesignal, butwithsmaller yields. The possibility of both neutralinos decaying to Z bosons, withthelatterdecayingtoleptons,produceanegligiblecontribu- tioncausedbothbythesmallcorrespondingBRandtheexcessof predictedsignalleptons.

Ourresultinthe massregions consideredisthat nopoints of the

μν

SSM canbeexcludedfromcurrentdata.Concerningtheex- cessofeventsmentionedintheprevious section,letuspointout that theobservedlimitinthe3_ISRsignalregion(S⁹⁵_obs=¹⁵.3)is significantlylargerthan theexpectedlimit(S⁹⁵_exp=⁶.9⁺₋³₂^._.¹₂),dueto a 3.02sigmaexcess [24].Wehavecheckedthatpoints ofourpa- rameterspaceintheregionmχ_˜1⁰∈ (¹¹⁰,120)andmν_˜∈ (¹²⁰,140) can predict a number of events similar to the observed excess.

As anexample,Table3showsa benchmarkpoint(BP)inS3_ISR withM₁=^{127 GeV,and v√1,2}₂ =⁵.2×^{10−4GeV, √v3}₂=¹.07×¹⁰⁻⁴ GeV. These VEVs have typical values fulfilling the minimizations

Table 3

BenchmarkpointoftheμνSSM intheS3_ISRsignalregion.Inthethirdrowtheefficiencypassingtheselectionrequirementsisshown.

m_˜χ0 120 GeV m_˜ν 125 GeV m_˜ 145 GeV

BR( ˜i→ iχ˜⁰) 1 BR(ν˜i→νχ˜⁰) 1 BR(χ˜⁰→^{W e}/μ) 3.5×¹⁰⁻¹

BR(χ˜⁰→Wτ) 2.9×10⁻² BR(χ˜⁰→Zν) 2.4×10⁻¹ _˜χ0 1.28×10⁻¹²GeV

W_Z_ 0.0092 W_hZ_ 0.0021 Z_Z_ν 0.0215

σ(pp→ ˜νν˜) 143.75 fb σ(pp→ ˜ν˜) 276.32 fb σ(pp→ ˜ ˜) 80.94 fb

Events above background in S3_ISR: 5.1

Fig. 2. Regionsofthe μνSSM thatwillbeprobedbythesignalwiththreelight leptonsplusMETdiscussedinthetextintheparameterspacem_˜ν−m_˜χ0

1 withuni-

versalsneutrinomasses,forthe13-TeVsearchwithanintegratedluminosityof100 fb⁻¹(green)and300fb⁻¹(yellow).

conditions,andproducingtheheavierneutrinomassintheexperi- mentallyconstrainedrangemν∼^(0.05,0.23)eV [58,59],giventhe neutrinomass formuladiscussed in Section 2. In particular, this BPpredicts5.1eventsabovebackground.Otherparameters,whose effecton thebino-like neutralino decayproperties isless signifi- cant,ascanbe understoodfromformulasinSection 3, aresetto beλ=⁰.2,

κ

=⁰.3,tanβ=^{10, √vR}₂ =^{1350 GeV,andM}2=^{1 TeV,} throughoutthiscomputation. Inorder to optimize thesignal we haveassumedthatthemassesofthethreefamiliesofleftsneutri- nos/sleptonsaredegenerated,andthereforeallofthemcontribute tothesignal.GiventhesneutrinomassformulainSection2,there is enough freedom to tune the masses in that way allowing for non-universalityofthe parameters Yνi or Aνi.ForthisBPwe set thetypicalvalues Yν1,2=⁵×^10−7, Yν3=¹×^{10−7 anduniversal} Aν= −^{396 GeV.}

Iftheobservedlocalexcesswereduetoastatisticalfluctuation, andtheobservedupperlimitconvergedtotheexpectedlimit,we caneasilyinferthepotentialboundsontheparameterspaceofthe sneutrino–neutralinomassinthe

μν

SSM.For100and300fb⁻¹to bereachedattheendofRun2,wejusthavetorescalethelimits by√

100/36.1 and√

300/36.1,respectively.Theresultisshownin Fig.2.Inthisplotthe parametersforthe BPabove areused,but varyingM1 between95and215GeV, andAν between −470 and

−^{376 GeV in order to obtain the range of neutralino and sneu-} trinomassesshown. There, thesolid black lineshowsthepoints wherethe sneutrinoandneutralino aredegeneratedinmass.The greenareaenclosestheexcludedregionfor100fb⁻¹ ifnoexcess isobserved,andtheyellowarea showsthesamefor300fb⁻¹.As wecansee,theprospectsshow apotentialexclusionofsneutrino massesupto160and185GeVfor100and300fb⁻¹,respectively.

Thisregionextendsuptothesolidline,reflectingthefactthatthe searchwillbefullysensitivetothedegeneratedscenario.

Fig. 3. ThesameasinFig.2,butfornon-universalsneutrinomassesasdiscussedin thetext.

In Fig. 2, for a given sneutrino mass, smaller value of the neutralino mass does not give rise to a worse sensitivity until the kinematic functions in Eq. (3) make the product B R(

χ

˜⁰_→ Z

ν

)B R(

χ

˜⁰→^W) toosmallandthe search becomes ineffective.

On the other hand, for a given neutralino mass the larger the valueofthesneutrinomassthesmallertheproductioncrosssec- tionbecomes,limitingtheexclusionscope.Noticealsothatinthe lower-right cornerofthefigure,the limitsare weakerdueto the larger massseparationbetweensneutrinoandneutralino. Asdis- cussedabove,theincreasedenergyoftheleptonsfromthedecay ofsleptonsmakethemtocontributetothesignal givingrisetoa signaturewithmorethanthreelightleptons.

Todiscusshowgeneralisthisresultintheparameterspaceof the

μν

SSM,we canconsider a (non-optimized)signal withnon- degeneratesneutrino/sleptonmasses.Forthatwecanuseuniversal Yν1,2,3=⁵×^{10−7,producingm}ν˜3=².24mν_˜1,2.Then,onlytwofam- iliesofsneutrinos/sleptonscontributetothesignal,andtheresult isshown inFig.3 withmν=^mν_˜1,2. Obviously,thelimitsare less stringent, but still some regions of the parameter space can be bounded. The prospects show a potential exclusion of sneutrino massesupto145and170GeVfor100and300fb⁻¹,respectively.

Asimilarresultwouldbeobtainedassuming universalityofVEVs andmasses,sinceontheonehandthelatterassumptionincreases thesignalbutontheotherhandtheformerdecreasesit.

6. Conclusionsandoutlook

There is a lack of experimental bounds on the masses of the electroweak superpartners in the

μν

SSM from accelerator searches,apartfromveryspecificregions ofa sneutrinoLSPwith a mass between45 and100 GeV [9]. In order to fillthisgap in SUSY searches, it is crucial to analyzeall recentresults that can potentially leadto (even small)limitson sparticle massesinthis model. Following thisline of thought,we have discussed in this workhowstringentarefortheparameterspaceofthe

μν

SSM the