Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Search
for
light
pseudoscalar
boson
pairs
produced
from
decays
of
the
125 GeV
Higgs
boson
in
final
states
with
two
muons
and
two
nearby
tracks
in
pp
collisions
at
√
s
=
13 TeV
.
The
CMS
Collaboration
CERN,Switzerland
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received16July2019
Receivedinrevisedform12October2019 Accepted4November2019
Availableonline8November2019 Editor: M.Doser Keywords: CMS Physics Higgsboson NMSSM 2HD+1S
A search is presented for pairs of light pseudoscalarbosons, in the mass range from 4 to 15 GeV, producedfromdecaysofthe125 GeVHiggsboson.Thedecaymodesconsideredarefinalstatesthatarise whenoneofthepseudoscalarsdecaystoapairoftauleptons,andtheotheroneeitherintoapairoftau leptonsormuons.Thesearchisbasedonproton-protoncollisionscollectedbytheCMSexperimentin 2016atacenter-of-massenergyof13 TeVthatcorrespondtoanintegratedluminosityof35.9 fb−1.The 2
μ
2τ
and4τ
channelsareusedincombinationtoconstraintheproductoftheHiggsbosonproduction cross sectionand the branchingfraction into 4τ
finalstate,σ
B,exploitingthe lineardependence of the fermioniccouplingstrengthofpseudoscalarbosonsonthe fermionmass. Nosignificantexcessis observedbeyondtheexpectationfromthestandardmodel.Theobservedandexpectedupperlimitsat 95% confidencelevel onσ
B,relativetothe standardmodel Higgsbosonproductioncrosssection,are setrespectivelybetween0.022and0.23andbetween0.027and0.19inthemassrangeprobedbythe analysis.©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
After the discovery of the 125GeV Higgs boson (H) [1,2], searches for additional Higgs bosons, based on predictions be-yond the standard model (SM), constitute an important part of the scientific program at the CERN Large Hadron Collider (LHC). Thepresentanalysisexaminestheoreticalmodelsthatcontaintwo Higgsdoubletsandanadditionalcomplex singletHiggsfield (de-noted hereafter as 2HD+1S), that does not couple at tree level to fermions or gauge bosons and interacts only with itself and the Higgs doublets [3–10]. In CP conserving models, which are considered in this Letter, the Higgs sector features seven physi-cal states, namely three CP-even, two CP-odd, and two charged bosons,whereoneoftheCP-evenstatescorrespondstotheH.This kindof Higgs sector is realized, forexample, in next-to-minimal supersymmetricmodelsthatsolvetheso-called
μ
problemofthe minimalsupersymmetricextension ofthe SM [11].Alarge setof the2HD+1S models is allowed by measurements andconstraints set by searches for additional Higgs bosons andsupersymmetric particles [12–17].E-mailaddress:cms-publication-committee-chair@cern.ch.
This Letter addresses specific 2HD+1S models in which the lightestpseudoscalarboson(a1) withmass2ma1
<
125GeV hasa large singletcomponent, andthereforeits couplings toSM parti-clesaresignificantlyreduced.Forthisreason,analysesusingdirect production modes of a1, such as gluon-gluon fusion (ggF) or bquarkassociatedproduction,havelimitedsensitivity.Thea1 boson
isnonetheless potentially accessibleinthe H decay totwo pseu-doscalarbosons.Thea1statescanbeidentifiedviatheirdecayinto
apairoffermions [18–25].ConstraintsontheH couplingsallowa branching fractionforH decays intonon-SMparticles aslarge as 34% [26],whichcanpotentiallyaccommodatetheH
→
a1a1 decayataratesufficientlyhighfordetectionattheLHC.
Several searches for H
→
a1a1 decays have been performedin the ATLAS andCMS experiments in Run1 (8TeV)and Run 2 (13TeV) ofLHC,exploitingvarious decaymodesofthe a1 boson,
andprobing different ranges ofits mass [27–40]. These searches found no significant deviation from the expectation of the SM backgroundandupperlimitswereset ontheproductofthe pro-ductioncrosssection andthe branchingfractionforsignal result-inginconstraintsonparametersofthe2HD+1Smodels.
Thisanalysispresentsasearchforlight a1 bosonsinthedecay
channels H
→
a1a1→
4τ
/
2μ
2τ
, using data corresponding to anintegratedluminosityof35
.
9fb−1,collectedwiththeCMSdetectorhttps://doi.org/10.1016/j.physletb.2019.135087
0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
Fig. 1. Illustrationofthesignaltopology,inwhichtheH decaysintotwoa1bosons,
whereonea1bosondecaysintoapairoftauleptons,whiletheotheronedecays
intoapairofmuonsorapairoftauleptons.Theanalyzedfinalstateconsistsof onemuonandanoppositelychargedtrackineacha1decay.
in2016atacenter-of-massenergyof13TeV.Theanalysiscovers themass rangefrom 4to 15GeV andemploys a special analysis strategytoselectandidentifyhighlyLorentz-boostedmuonortau leptonpairswithoverlappingdecayproducts.Thestudyupdatesa similaroneperformedbytheCMSCollaborationinRun1 [28],and complementsother recentCMSsearches forthe H
→
a1a1 decayperformedinRun2datainthe2
μ
2τ
[30],2τ
2b [31],2μ
2b [38] and4μ
[39] finalstates,coveringrespectivemassrangesof0.
25<
ma1
<
3.
40GeV forthe 4μ
final state and15.
0<
ma1<
62.
5GeV forthe2μ
2τ
,
2τ
2b,and2μ
2b finalstates.Thebranching fractiona1
→
τ τ
dependson thedetailsofthemodel,namelytheparametertan
β
,the ratioofvacuum expecta-tionvaluesofthetwoHiggsdoublets,andonwhichHiggsdoublet couples to either charged leptons, up-type quarks or down-type quarks [41]. InType-II 2HD+1S models,whereone Higgsdoublet couplestoup-typefermionswhiletheothercouplestodown-type fermions, the a1→
τ τ
decay rate gets enhanced atlarge valuesoftan
β
.Thebranchingfractionofthisdecayreachesvaluesabove 90% attanβ >
3 for 2mτ<
ma1<
2mb,wheremτ is themass ofthetauleptonandmb isthemassofthebottomquark.Forhigher
valuesofma1 thebranching fractiondecreases to 5–6% sincethe decayintoapairofbottomquarksbecomeskinematicallypossible andoverwhelmsthedecayintoapairoftauleptons.However, in someofthe2HD+1Smodelsthea1
→
τ τ
decaymaybedominantevenabovethe a1
→
bb decay¯
threshold.Thisisrealized,e.g.,fortan
β >
1 intheType-III2HD+1Smodels,whereoneHiggsdoublet couplestochargedleptons, whereas theother doubletcouplesto quarks [41].The signal topology targeted by the present analysis is illus-trated in Fig. 1. Each a1 boson is identified by the presence of
a muon and only one additional charged particle, the objective of this approach being the decay channels a1
→
μμ
and a1→
τ
μτ
one-prong. Theτ
μ denotes the muonic tau lepton decay, andτ
one-prong standsforitsleptonic orone-pronghadronicdecay.Thethree-prong modes are not used because of the very high QCD multijetbackgroundandlowerreconstructionsignalefficiency.
Giventhe large differencein massbetween thea1 andtheH
states,thea1 bosonswillbeproducedhighlyLorentz-boosted,and
their decay products are highly collimated. This will result in a signature with two muons, each of which is accompanied by a nearby particle of opposite charge. The search focuses primarily on the dominant ggF process, in which the H state is produced withrelativelysmall transversemomentum pT,andthe a1
pseu-doscalarsareemitted nearlyback-to-backinthetransverseplane, witha largeseparation inazimuth
φ
betweenthe particles orig-inating fromone of the a1 decaysand those of the other a1. IntheggF process,theHcanbealsoproducedwitharelativelyhigh Lorentzboostwhenahardgluonisradiatedfromtheinitial-state
gluonsorfromtheheavy-quarkloop.Inthiscase,theseparationin
φ
isreduced, buttheseparationinpseudorapidityη
canbelarge. The analysisthereforesearches forasignal ina sample of same-charge (SC)dimuoneventswithlargeangularseparationbetween the muons,where eachmuon isaccompaniedby one nearby op-positely chargedparticleoriginatingfromthe samea1 decay.Therequirement ofhaving SC muons in theevent largely suppresses background fromthe top-quark-pair,Drell–Yan, anddiboson pro-duction.Thisrequirementalsofacilitatesthe implementationofa dedicatedSCdimuontriggerwithrelativelylowthresholdsand ac-ceptableratesasdescribedinSection4.
2. CMSdetector
The central feature of the CMS detectoris a superconducting solenoid of 6m internal diameter, providing a magnetic field of 3
.
8T. Within the solenoid volume are a silicon pixel and strip tracker,aleadtungstatecrystalelectromagneticcalorimeter,anda brass andscintillatorhadroncalorimeter,eachcomposedofa bar-rel and two endcap sections.Forward calorimeters extend theη
coverage providedby thebarrelandendcapdetectors.Muonsare detected ingas-ionization chambers embedded in the steel flux-returnyokeoutsidethesolenoid.
Events ofinterest are selected using a two-tiered trigger sys-tem [42].Thefirstlevel,composedofcustomhardwareprocessors, usesinformationfromthecalorimetersandmuondetectorsto se-lect eventsat arateof around 100kHz within atime interval of less than 4μs. The second level, known asthe high-level trigger, consistsofafarmofprocessorsrunningaversionofthefullevent reconstructionsoftwareoptimizedforfastprocessing,andreduces theeventratebelow1kHz beforedatastorage.
AmoredetaileddescriptionoftheCMSdetector,togetherwith a definitionofthecoordinatesystemusedandtherelevant kine-maticvariables,canbefoundinRef. [43].
3. Simulatedsamples
For the simulation of the dominant ggF production process, the MonteCarlo (MC)event generators pythia (v.8.212) [44] and MadGraph5_amc@nlo (v.2.2.2) [45] are used in order to model the H
→
a1a1→
4τ
and H→
a1a1→
2μ
2τ
signal events,re-spectively. For both decay modes the pT distribution of the H
emerging fromggF isreweighted withnext-to-next-to-leading or-der (NNLO) K factors obtained by the program HqT (v2.0) [46,
47] withNNLONNPDF3.0partondistributionfunctions(PDF) [48], hereby takingintoaccount the moreprecise spectrum calculated to NNLO withresummationtonext-to-next-to-leading-logarithms order.Subdominantcontributionsfromother productionmodesof H, namely vector boson fusion process (VBF),vector boson asso-ciated production(VH) andtop quark pairassociated production (t
¯
tH)areestimatedusingthe pythia (v.8.212)generator.The backgroundsfromdibosonproductionandquantum chro-modynamics production ofmultijet (QCD multijet) are simulated with the pythia (v.8.212) generator. Inclusive Z and W boson production processes are generated with MadGraph5_amc@nlo (v.2.2.2).The single-topand t
¯
t production are generatedat Next-to-LO(NLO)withthe powheg (v.2.0)generator[49–53].Thesetof PDFusedisNLONNPDF3.0forNLOsamples,andLONNPDF3.0for LOsamples [48].Showering and hadronization are carried out by the pythia (v.8.212)generatorwiththeCUETP8M1underlyingeventtune [54], while a detailedsimulation of the CMSdetectoris based on the Geant4[55] package.
4. Eventselection
EventsareselectedusingaSC dimuontriggerwith pT
thresh-oldsof17
(
8)
GeV fortheleading (subleading)muon.Topassthe high-leveltrigger,thetracksofthetwomuonsareadditionally re-quiredtohavepoints ofclosestapproachtothebeamaxiswithin 2mm ofeachotheralongthelongitudinaldirection.Events are reconstructed with the particle-flow (PF) algo-rithm [56] whichaims toidentifyandreconstructindividual par-ticlesasphotons, chargedhadrons, neutralhadrons, electrons, or muons(PFobjects).Theproton-proton(pp)interactionverticesare reconstructedusingaKalmanfilteringtechnique [57,58].Typically morethanonesuchvertexisreconstructedbecauseofmultiplepp collisions within the sameor neighbouring bunch crossings. The meannumberof such interactions per bunch crossingwas 23in 2016.
The reconstructed vertex with the largest value of summed physics-object p2
T is taken to be the primary interaction vertex
(PV). The physics objects are the jets, clustered using the jet-findingalgorithm [59,60] withthetracksassignedtothevertexas inputs,andtheassociatedmissingtransversemomentum,takenas thenegative vectorsumofthe pT ofthosejets.Events must
con-tain atleasttwo SC muonsreconstructed withthe PFalgorithm, whichhavetofulfilthefollowingrequirements.
•
Thepseudorapidityoftheleading(higherpT)andthesublead-ing(lower pT)muonsmustbe
|
η
|
<
2.
4.•
The pT of the leading (subleading) muon must exceed 18(
10)
GeV.•
The transverse (longitudinal) impact parameters of muons with respectto thePVare required tobe|
d0|
<
0.
05(
|
dz|
<
0
.
1)
cm.•
Theangular separation between the muons is
R
=
(φ)
2+ (
η
2) >
2.IfmorethanoneSCmuonpairisfoundintheeventtosatisfy theserequirements,thepairwiththelargestscalarsumofmuon
pTischosen.
Inthenextstep,theanalysisemploysinformationabouttracks associatedwiththereconstructedchargedPFobjects,excludingthe pairofSCmuons.Selectedmuonsandtracksareusedtobuildand isolate candidates for the a1
→
τ
μτ
one-prong or a1→
μμ
decays(referredtoasa1candidatesthroughouttheLetter).Threetypesof
tracksareconsideredintheanalysis.
•
“Isolation”tracksareusedtodefineisolationrequirements im-posedon a1 candidatesandhavetofulfilthefollowingcrite-ria: pT
>
1GeV,|
η
|
<
2.
4,|
d0|
<
1cm,|
dz|
<
1cm.•
“Signal” tracks are selectedamong “isolation”tracks to build a1candidates.ThesetracksmusthavepT>
2.
5GeV,|
η
|
<
2.
4,|
d0|
<
0.
02cm,|
dz|
<
0.
04cm.•
“Soft” tracks are also a subset of “isolation” tracks.They are utilized to define one of the sideband regions, used for the construction of the background model, as described in Sec-tion 5.2. “Soft” tracks must satisfy the requirements: 1.
0<
pT
<
2.
5GeV,|
η
|
<
2.
4,|
d0|
<
1cm,|
dz|
<
1cm.Atrackisregardedasbeingnearbyamuoniftheangular sep-aration
R betweenthem issmaller than 0.5.Each muon ofthe SCpairisrequiredtohaveonenearby“signal”trackwithacharge opposite toits charge. This muon-tracksystemis acceptedas an a1candidateifnoadditional“isolation”tracksarefoundinthe
R
coneof 0.5around themuon momentum direction. The eventis selectedinthe final sample ifitcontains two a1 candidates.The
Table 1
Thesignalacceptanceandthenumberofexpectedsignaleventsafterselectionin theSR.Thenumberofexpectedsignaleventsiscomputedforabenchmarkvalue ofbranchingfraction,B(H→a1a1)B2(a1→τ τ)=0.2 andassumingthatthe H
productioncrosssectionistheonepredictedintheSM.Thequoteduncertainties forpredictionsfromsimulationincludeonlystatisticalones.
ma1[GeV] Acceptance×10 4 Number of events 4τ 2μ2τ 4τ 2μ2τ 4 3.29±0.16 89.3±1.4 129.9±6.2 54.7±0.9 7 2.50±0.14 69.0±1.4 98.8±5.5 22.5±0.5 10 1.46±0.11 47.1±1.2 57.8±4.2 14.2±0.4 15 0.21±0.04 3.5±0.3 8.5±1.1 1.0±0.1
setofselectionrequirementsoutlinedabovedefinesthesignal re-gion(SR).
Theexpectedsignalacceptanceandsignalyieldforafew rep-resentativevaluesofma1 arereportedinTable1.Thesignalyields are computed for a benchmark value of the branching fraction,
B(
H→
a1a1)B
2(
a1→
τ τ
)
=
0.
2 and assumingthattheHproduc-tion cross section is the one predicted in the SM. Contributions from the ggF, VBF, VH and t
¯
tH processes are summed up. The yield ofthe 2μ
2τ
signal is estimatedunderthe assumptionthat thepartialwidthsofthea1→
μμ
anda1→
τ τ
decayssatisfytherelation [23]
(
a1→
μμ
)
(
a1→
τ τ
)
=
m2μ m2 τ 1−
2mτ/
ma1 2.
(1)The ratioofbranchingfractionsofthe a1a1
→
2μ
2τ
anda1a1→
4
τ
decays is computed through the ratio of the partial widths(
a1→
μμ
)
and(
a1→
τ τ
)
asB
(
a1a1→
2μ
2τ
)
B
(
a1a1→
4τ
)
=
2B
(
a1→
μμ
)
B
(
a1→
τ τ
)
=
2(
a1→
μμ
)
(
a1→
τ τ
)
.
(2)The factor of 2 in Eq. (2) arises from two possible decays, a1(1)a(12)
→
2μ
2τ
anda1(1)a(12)→
2τ
2μ
,thatproducethefinalstate withtwo muonsandtwo tauleptons. TheratioinEq. (2) ranges fromabout0.0073atma1=
15GeV to0.0155atma1=
4GeV.The contributionfromtheH
→
a1a1→
4μ
decayisestimatedtakinginto account Eq. (1). It ranges between0.4 and2% of the totalsignalyieldinthe2
μ
2τ
and4τ
finalstates,dependingonthe probed massofthea1 boson.Thiscontributionis notconsideredinthepresentanalysis.
The number of observed events selected in the SR amounts to 2035. A simulation-based study shows that the QCD multijet eventsdominatethesampleofeventsselectedintheSR. Contribu-tionfromotherbackgroundsourcesconstitutesabout1% ofevents selectedintheSR.
The two-dimensional(2D) distributionoftheinvariant masses ofthe muon-tracksystems,constituting a1 candidates, isusedto
discriminatebetweensignalandthedominantQCDmultijet back-groundin the signal extractionprocedure. The 2D distribution is filledwithapairofthemuon-trackinvariantmasses(m1
,
m2),or-deredbytheirvalue,m2
>
m1.Thebinning ofthe2D distributionadopted inthe analysisis illustrated in Fig. 2. As m2 is required
to exceedm1, only
(
i,
j)
bins with j≥
i arefilled inthe 2Ddis-tribution,yielding intotal6
(
6+
1)/
2=
21 independentbins.Bins(
i,
6)
withi=
1,
5 containall eventswithm2>
6GeV.Bin(
6,
6)
containsalleventswithm1,2
>
6GeV.5. Modelingbackground
Asimulation-based studyrevealsthat thesample ofSC muon pairsselectedasdescribedinSection4,butwithoutrequiringthe
Table 2
Controlregionsusedtoconstructandvalidatethebackgroundmodel.ThesymbolsNsig,NisoandNsoftdenote
thenumberof“signal”,“isolation”(whichareasubsetof“signal”tracks)and“soft”tracks,respectively,withina coneofR=0.5 aroundthemuonmomentumdirection.ThelastrowdefinestheSR.
Control region Firstμ Secondμ Purpose Observed events
N23 Niso=1, Nsig=1 Niso=2,3 Determination of f1D(i) 62 438
Niso,2=1 Niso>1, Nsig≥1 Niso=1, Nsig=1 Validation of f1D(i) 472 570
Niso,2=2,3 Niso>1, Nsig≥1 Niso=2,3 Validation of f1D(i) 17 667 900
N45 Niso=1, Nsig=1 Niso=4,5 Assessment of
systematics in f1D(i) 52 437
Both muons
Loose-Iso Nsig=1, Nsoft=1,2 Determination of C(i,j) 35 824
Signal region Nsig=1, Niso=1 Signal extraction 2 035
Fig. 2. Binning of the 2D (m1,m2) distribution.
presence of a1 candidates, is dominatedby QCD multijet events,
whereabout85% ofall selectedevents containbottom quarksin thefinalstate.TheSCmuonpairsintheseeventsoriginatemainly fromthefollowingsources:
•
muonicdecayofabottomhadroninonebottomquarkjetand cascadedecayofabottom hadron intoa charmhadron with asubsequentmuonicdecayofthecharmhadronintheother bottomquarkjet;•
muonicdecayofabottomhadroninonebottomquarkjetand decayofaquarkoniumstateintoapairofmuonsintheother jet;•
muonicdecayofabottomhadroninonebottomquarkjetand muonicdecay ofa B0 mesonin the other bottom quark jet.TheSCmuonpairinthiscasemayappearasaresultofB0–B0 oscillations.
The normalized 2D (m1
,
m2) distribution for the muon-trackpairs with m2
>
m1 is represented in the sample of backgroundeventsbyabinned templateconstructedusingthefollowing rela-tion f2D
(
i,
j)
=
C(
i,
j)(
f1D(
i)
f1D(
j))
sym,
(
f1D(
i)
f1D(
i))
sym=
f1D(
i)
f1D(
i),
(
f1D(
i)
f1D(
j))
sym=
f1D(
i)
f1D(
j)
+
f1D(
j)
f1D(
i)
=
2 f1D(
i)
f1D(
j),
if j>
i,
(3) where•
f2D(
i,
j)
isthecontent ofthebin(
i,
j)
inthenormalized2D(m1
,
m2)distribution;•
f1D(
i)
is the content of bin i in the normalizedone-dimen-sional(1D)distributionofthemuon-trackinvariantmass;
•
C(
i,
j)
isasymmetricmatrix,accountingforpossiblecorrela-tion betweenm1 andm2, the elements of thematrix C
(
i,
j)
arereferredtoas“correlationfactors”inthefollowing. The condition C
(
i,
j)
=
1 for all bins(
i,
j)
would indicate an absenceofcorrelation betweenm1 andm2.Wesumthecontentsof the nondiagonal bins
(
i,
j)
and(
j,
i)
in the Cartesian productf1D
(
i)
f1D(
j)
toaccountforthefactthateachevententersthe2D(m1
,
m2) distribution with ordered values of the muon-trackin-variantmasses.
Byconstructionthebackgroundmodelestimatesthedominant QCDmultijetproductionaswellassmallcontributionsfromother processes.
Multiplecontrolregions(CRs)areintroducedinordertoderive and validate the modeling of f1D
(
i)
and C(
i,
j)
. The CRs arede-finedonthebasisofamodifiedisolationcriteriaappliedtooneor both muon-track pairs.The isolation criteriaare specified by the multiplicity of“isolation” tracks inthe cone of
R
=
0.
5 around the muon momentumdirection. The summary ofall CRsused to derive andvalidate themodelingofbackgroundshapeisgivenin Table2.5.1. Modelingof f1D
(
i)
The f1D
(
i)
distribution is modeled using the N23 CR. Eventsin thisCRpass theSC dimuonselection andcontainonly one a1
candidatecomposedoftheisolated“signal”trackandmuon(first muon). Theinvariant massofthefirstmuonandassociatedtrack entersthe f1D
(
i)
distribution.Anothermuon(secondmuon)isre-quiredtobeaccompaniedbyeithertwoorthreenearby“isolation” tracks. The simulation shows that more than 95% of events se-lectedintheCRN23areQCDmultijetevents,whiletheremaining
5% is comingfrom t
¯
t, Drell-Yanand other electroweakprocesses. The modeling ofthe f1D(
i)
template is based on the hypothesisthat thekinematic distributionsforthe muon-tracksystem, mak-ing up an a1 candidate(the first muonandassociatedtrack), are
weaklyaffectedbytheisolation requirementimposed onthe sec-ond muon; therefore the f1D
(
i)
distribution of the muon-tracksystem forming an a1 candidate is expectedto be similar in the
SRandtheN23CR.
Thishypothesisisverifiedincontrolregionslabelled Niso,2
=
1and Niso,2
=
2,
3. Events are selected in these CR if one of themuons(firstmuon)hasmorethanone“isolation”track(Niso
>
1).At least one of these“isolation” tracks should also fulfil the cri-teria imposed on the “signal” track. As more than one of these tracks can pass the criteria imposed on “signal”tracks, two sce-narios havebeen investigated,namely usingeither thelowest or thehighestpT “signal”tracks(“softest”and“hardest”)tocalculate
themuon-trackinvariantmass.Ifonlyone“signal”trackisfound nearby tothe firstmuon, thetrackis usedboth asthe“hardest”
Fig. 3. Theobservedinvariantmassdistribution,normalizedtounity,ofthefirst muonandthesoftest(upper)orhardest(lower)accompanying“signal”trackfor differentisolationrequirementsimposedonthesecondmuon:whenthe second muonhasonlyoneaccompanying“isolation”track(Niso,2=1;circles);orwhenit
hastwoorthreeaccompanying“isolation”tracks(Niso,2=2,3;squares).
andthe“softest”signaltrack.Forthesecondmuon,two isolation requirementsare considered: whenthe muon isaccompanied by onlyone“signal”trackandthemuon-tracksystemisisolatedasin theSR(CRNiso,2
=
1),orwhenitisaccompaniedby twoorthree“isolation”tracks as inthe CR N23 (CR Niso,2
=
2,
3). Theinvari-antmassdistributionsofthefirstmuonandthesoftestorhardest accompanyingtrackarethencomparedforthetwodifferent isola-tionrequirementsonthesecondmuon,Niso,2
=
1 andNiso,2=
2,
3.The results of this studyare illustrated in Fig. 3. In both cases, theinvariantmassdistributionsdifferineachbinbylessthan6%. This observation indicates that the invariant mass of the muon-tracksystem, makingup an a1 candidate,weaklydependsonthe
isolationrequirementimposedonthesecondmuon,thus support-ingtheassumptionthatthe f1D
(
i)
distributioncanbedeterminedfromtheN23CR.
Fig. 4. Theobservedinvariantmassdistribution,normalizedtounity,ofthe muon-trackinvariantmassincontrolregionsN23(circles)andN45(squares).
The potential dependence of the muon-track invariant mass distribution onthe isolation requirement imposed onthe second muon isverifiedalsoby comparingshapesinthecontrol regions
N23 and N45.The latter CR isdefined by requiring the presence
of4or5“isolation”tracksnearbytothesecondmuon, whilethe firstmuon-trackpairpassesselectioncriteriaforthea1 candidate.
TheresultsareillustratedinFig.4.Aslightdifferenceisobserved between distributions in these two CRs. This difference is taken asashapeuncertaintyinthenormalizedtemplate f1D
(
j)
enteringEq. (3).
Fig.5presentsthenormalizedinvariantmassdistributionofthe muon-tracksystem fordata selectedin theSR andforthe back-groundmodelderivedfromtheN23 CR.Thedataandbackground
distributions are compared to the signal distributions, obtained fromsimulation,forfourrepresentativemasshypotheses,ma1=4, 7, 10,and 15GeV.The invariant mass ofthe muon-track system is found to havehigher discrimination power betweenthe back-groundandthesignalathigherma1.Forlowermasses,thesignal shape becomes morebackgroundlike, resultingina reduction of discriminationpower.
5.2. ModelingofC
(
i,
j)
In order to determine the correlation factors C
(
i,
j)
, an addi-tional CR (labelled Loose-Iso) is used. It consists of events that containtwoSCmuonspassingtheidentificationandkinematic se-lectioncriteriaoutlinedinSection4.Eachmuonisrequiredtohave twoorthreenearbytracks.Oneofthemshouldbelongtothe cate-goryof“signal”tracks,whereasremainingtracksshouldbelongto thecategoryof“soft”tracks.About36kdataeventsareselectedin thisCR.ThesimulationpredictsthattheQCDmultijetevents dom-inatethisCR,comprisingmorethan99%ofselectedevents.Itwas alsofoundthattheoverallbackground-to-signalratioisenhanced comparedtotheSRbyafactorof30to40,dependingonthemass hypothesis,ma1. Theeventsample inthisregion isused tobuild thenormalizeddistribution f2D(
i,
j)
.Finally,thecorrelationfactorsC
(
i,
j)
areobtainedaccordingtoEq. (3) asC
(
i,
j)
=
f2D(
i,
j)
(
f1D(
i)
f1D(
j))
symFig. 5. Normalizedinvariantmassdistributionofthemuon-tracksystemforevents passingthesignalselection.Observednumbersofeventsarerepresentedbydata pointswith errorbars.TheQCDmultijetbackgroundmodelisderivedfromthe controlregionN23.Alsoshownarethenormalizeddistributionsfromsignal
sim-ulationsforfourmasshypotheses,ma1=4,7,10,and15GeV (dashedhistograms),
whereasforhighermassesthe analysishasnosensitivity.Eacheventinthe ob-servedandexpectedsignaldistributionscontributestwoentries,correspondingto thetwomuon-tracksystemsineacheventpassingtheselection.Thesignal distri-butionsinclude2μ2τand4τcontributions.Thelowerpanelshowstheratioofthe observedtoexpectednumberofbackgroundeventsineachbinofthedistribution. Thegreyshadedarearepresentsthebackgroundmodeluncertainty.
Fig. 6. The(m1,m2)correlationfactorsC(i,j)withtheirstatisticaluncertainties,
derivedfromdataintheCRLoose-Iso.
where f1D
(
i)
is the 1D normalized distribution withtwo entriesperevent(m1andm2).ThecorrelationfactorsC
(
i,
j)
derivedfromdataintheLoose-IsoCRarepresentedinFig.6.Toobtainestimates of C
(
i,
j)
in the signal region, the correlation factors derived in theLoose-IsoCRhavetobe correctedforthedifference inC(
i,
j)
betweenthesignal regionandLoose-IsoCR. Thisdifferenceis as-sessedbycomparingsamplesofsimulatedbackgroundevents.The correlationfactors estimatedfromsimulationinthesignal region andtheLoose-IsoCRarepresentedinFig.7.Fig. 7. The(m1,m2)correlationfactorsC(i,j)alongwith theirMCstatistical
un-certainties,derived fromsimulated samplesinthe (upper:signalregion, lower: Loose-IsoCR).
The correlationfactorsinthe signalregionare thencomputed as C
(
i,
j)
SRdata=
C(
i,
j)
CRdataC(
i,
j)
SR MC C(
i,
j)
CRMC,
(5) where•
C(
i,
j)
dataCR are correlation factorsderived fortheLoose-IsoCR indata(Fig.6);•
C(
i,
j)
SRMC arecorrelationfactorsderivedfortheSRinthe sim-ulatedQCDmultijetsample(Fig.7,upper);•
C(
i,
j)
MCCR are correlation factors derived for the Loose-IsoCR inthesimulatedQCDmultijetsample(Fig.7,lower).Table 3
SystematicuncertaintiesandtheireffectontheestimatesoftheQCDmultijetbackgroundandsignal.
Source Value Affected sample Type Effect on the total yield Stat. unc. in C(i,j) 3–60% bkg. bin-by-bin –
Extrapolation unc. in C(i,j) – bkg. shape –
Unc. in f1D(i) – bkg. shape –
Integrated luminosity 2.5% signal norm. 2.5% Muon id. and trigger efficiency 2% per muon signal norm. 4% Track id. efficiency 4–12% per track signal shape 10–18% MC stat. unc. in signal yields 8–100% signal bin-by-bin 5–20% Theoretical uncertainties in the signal acceptance
μRandμFvariations signal norm. 0.8–2%
PDF signal norm. 1–2%
Theoretical uncertainties in the signal cross sections
μR,Fvariations (ggF) 5–7% signal norm. 5–7%
μR,Fvariations (other processes) 0.4–9% signal norm. <0.5%
PDF (ggF) 3.1% signal norm. 3.1%
PDF (other processes) 2.1–3.6% signal norm. <0.5%
Fig. 8. Thedistributionofthesignaltemplates f2D(i,j)inonerowformass
hy-pothesisma1=4GeV (upper)and 10GeV (lower).TheH→a1a1→2μ2τ (blue
histogram)andH→a1a1→4τ(redhistogram)contributionsareshown.The
nota-tionofthebinsfollowsthatofFig.2.
The difference incorrelation factors derived in the SR(Fig. 7, upper)andintheLoose-IsoCR(Fig.7,lower)usingtheQCD mul-tijetsampleistakenintoaccountasanuncertaintyinC
(
i,
j)
.6. Modelingsignal
The signal templates are derived fromthe simulated samples oftheH
→
a1a1→
4τ
andH→
a1a1→
2μ
2τ
decays.The studyprobes the signal strength modifier, defined as the ratio of the product of the measured signal cross section andthe branching
fraction into the 4
τ
final stateB(
H→
a1a1)B
2(
a1→
τ τ
)
to theinclusive cross section of the H production predictedin the SM. The relative contributions from different production modesof H are defined by the corresponding cross sectionspredicted in the SM.ThecontributionoftheH
→
a1a1→
2μ
2τ
decay,iscomputedassumingthatthepartialwidthsofa1
→
τ τ
anda1→
μμ
decayssatisfyEq. (1).
The invariant mass distribution of the muon-track system in the a1
→
μμ
decay channel peaks at the nominal value of thea1 boson mass, while the reconstructed mass of the muon-track
system in the a1
→
τ τ
decay is typically lower, because of themissingneutrinos.ThisiswhytheH
→
a1a1→
2μ
2τ
signalsam-ples have a largely different shape of the (m1
,
m2) distributioncompared totheH
→
a1a1→
4τ
signal samples.Fig.8comparesthe (m1
,
m2) distributions unrolled in a one row between theH
→
a1a1→
4τ
and H→
a1a1→
2μ
2τ
signal samplesfor masshypothesesma14GeV and10GeV.Thesignaldistributionsare nor-malized assuming the SM H production rate withthe branching fraction
B(
H→
a1a1)B
2(
a1→
τ τ
)
equalto0.2.7. Systematicuncertainties
Table3liststhesystematicuncertaintiesconsideredinthe anal-ysisforbothsignalandbackground.
7.1. Uncertaintiesrelatedtothebackground
TheestimationoftheQCDmultijetbackgroundisbasedon ob-served data, therefore it is not affected by imperfections in the simulation,reconstruction,ordetectorresponse.
The shape of the background in the (m1
,
m2) distribution ismodeledaccordingtoEq. (3),whileitsuncertaintyisdominatedby uncertaintiesrelatedtothecorrelationfactorsC
(
i,
j)
(asdescribed inSection5.2).Additionally,itisalsoaffectedbytheshape uncer-taintyinthe1Dtemplate f1D(
m)
(asdiscussedinSection5.1).Thebin-by-binuncertaintiesinmasscorrelationfactorsC
(
i,
j)
,derived fromEq. (5), are composed of the statisticaluncertainties in ob-serveddataandsimulatedsamples,aspresentedinFigs. 6and7, andrangefrom3to60%.Theseuncertaintiesareaccountedforin thesignalextractionprocedurebyonenuisanceparameterperbin inthe (m1,
m2)distribution [61].The systematicuncertaintiesre-latedtotheextrapolationofC
(
i,
j)
fromtheLoose-IsoCRtotheSR are derivedfromthe dedicatedMC studyoutlinedinSection 5.2. Therelatedshapeuncertaintyisdeterminedbycomparing correla-tionfactors derivedinthesimulatedsamples,betweenthesignal regionandtheLoose-IsoCR.In the case when
B(
H→
a1a1)
B
2(
a1→
τ τ
)
=
0.
34,branching fraction of the H decay into non-SM particles from Ref. [26],theimpactofpossiblesignalcontaminationinthe Loose-IsoCRisestimatedonabin-by-binbasis,anditisatmost2.8%in thebin(6
,
6) whichwas foundto haveanegligible effectonthe finalresults.ForallotherCRs,thesignalcontaminationwasfound tobewellbelow1%.7.2. Uncertaintiesrelatedtosignal
Anuncertaintyof2.5%isassignedtotheintegratedluminosity estimate [62].
The uncertainty in the muon identification and trigger effi-ciencyisestimatedtobe2%foreachselectedmuonobtainedwith thetag-and-probe technique [63].The trackselection and muon-trackisolationefficiencyisassessedwitha studyperformedona sampleofZ bosonsdecayingintoa pairoftauleptons.Inthe se-lected Z
→
τ τ
events,one taulepton isidentified viaits muonic decay,while the other is identified asan isolated trackresulting froma one-prongdecay. The trackisrequired topass the nomi-nal selection criteria usedin the main analysis. From this study, the uncertainty in the track selection and isolation efficiency is evaluated. Therelated uncertaintyaffects theshape ofthe signal estimate, while changingthe overall signal yield by 10–18%. The muon and trackmomentum scale uncertainties are smaller than 0.3%andhaveanegligibleeffectontheanalysis.Thebin-by-binstatisticaluncertaintiesinthesignal acceptance rangefrom8to100%,whiletheimpactontheoverallsignal nor-malizationvariesbetween5and20%.
Theoretical uncertainties have an impact on the differential kinematic distributions of the produced H, in particular its pT
spectrum,therebyaffectingsignalacceptance.Theuncertaintydue tomissinghigher-ordercorrectionstotheggF processisestimated with the HqT programby varying the renormalization (
μ
R) andfactorization(
μ
F)scales.TheH pT-dependentK factorsarerecom-puted accordingtothese variations andappliedto thesimulated signalsamples.Theresultingeffectonthesignalacceptanceis esti-matedtovarybetween1.2and1.5%,dependingonma1.Inasimilar way,theuncertaintyinthesignal acceptanceiscomputedforthe VBF, VHandt
¯
tH productionprocesses.The impacton the accep-tanceisestimatedtovarybetween0.8and2.0%,dependingonthe processandprobedmassofthea1 boson.The HqT program is also used to evaluate the effect of the PDF uncertainties. The nominal K factors for the H pT spectrum
are computedwiththe NNPDF3.0PDF set [48]. Variations ofthe NNPDF3.0PDFswithintheiruncertaintieschangethesignal accep-tancebyabout1%,whilstusingtheCTEQ6L1PDFset [64] changes the signal acceptance by about 0.7%. The impact of the PDF un-certaintiesonthe acceptancefortheVBF,VHandt
¯
tH production processes is estimatedin the same wayand a 2% uncertaintyis consideredtoaccountforthese.Systematicuncertaintiesintheoreticalpredictionsforthesignal crosssectionsaredrivenbyvariationsofthe
μ
Randμ
FscalesandPDF uncertainties. Uncertainties related to scale variations range from0.4to9%, dependingon theproductionmode.Uncertainties relatedtoPDFvarybetween2.1and3.6%.
8. Results
The signal is extractedwitha binned maximum-likelihoodfit appliedtothe (m1
,
m2) distribution.Foreach probedmassofthea1 boson,the(m1
,
m2)distribution isfittedwiththe sumoftwotemplates,corresponding to expectationsforthesignal and back-ground,dominatedbyQCDmultijetevents.
The normalizationof both signal andbackground are allowed to float freely in the fit. The systematic uncertainties affecting
Fig. 9. The (m1,m2)inonerowdistributionusedtoextractthesignal.Observed
numbersofeventsarerepresentedbydatapointswitherrorbars.Thebackground withitsuncertaintyisshownasthebluehistogramwiththeshadederrorband. Theshapeandthenormalizationofthebackgrounddistributionareobtainedby applyingafittotheobserveddataunderthebackground-onlyhypothesis.Signal expectationsforthe4τand2μ2τ finalstatesareshownasdottedhistogramsfor themasshypothesesma1=4,7,10and15GeV.Therelativenormalizationofthe4τ
and2μ2τfinalstatesaregivenbyEq. (1) asexplainedinSection6.Thesignal nor-malizationiscomputedassumingthattheH bosonisproducedinpp collisionswith aratepredictedbytheSM,anddecaysintoa1a1→4τfinalstatewiththe
branch-ingfractionof20%.Thelowerplotshowstheratiooftheobserveddataeventsto theexpectedbackgroundyieldineachbinofthe(m1,m2)distribution.
the normalizationofthesignal templates areincorporatedin the fit via nuisance parameters with a log-normal prior probability density function. The shape-altering systematic uncertainties are represented by nuisance parameters whose variations cause con-tinuousmorphingofthesignalorbackgroundtemplateshape,and are assigned a Gaussian prior probability density functions. The bin-by-binstatisticaluncertaintiesareassignedgammaprior prob-abilitydensityfunctions.
Fig.9showsthedistributionof(m1
,
m2),wherethenotationforthebinsfollowsthatofFig.2.Theshapeandthenormalizationof the backgrounddistributionare obtainedby applyinga fitto the observeddataunderthebackground-onlyhypothesis.Alsoshown are the expectations for thesignal atma1=4, 7, 10,and 15GeV. ThesignalnormalizationiscomputedassumingthattheH is pro-ducedinpp collisionswitharatepredictedbythestandardmodel, anddecaysintoa1a1
→
4τ
finalstatewithabranchingfractionof20%.Nosignificantdeviationsfromthebackgroundexpectationare observedinthe(m1
,
m2)distribution.Results of the analysis are used to set upper limits at 95% CL on the product of the cross section and branching fraction,
σ
(
pp→
H+
X)B(
H→
a1a1)B
2(
a1→
τ τ
)
, relative to theinclu-sive SM cross section of H production. The modified frequentist CLs criterion [65,66], and the asymptotic formulae are used for
the test statistic [67], implemented inthe RooStats package [68]. Fig. 10showsthe observed andexpectedupperlimitsat 95% CL onthesignalcrosssectiontimesthebranchingfraction,relativeto the totalcross sectionof theH bosonproductionaspredictedin theSM. Theobservedlimit iscompatiblewiththe expectedlimit within one standard deviationinthe entirerangeof ma1 consid-ered,andrangesfrom0.022atma1
=
9GeV to0.23atma1=
4GeV andreaches0.16atma1=
15GeV.Theexpectedupperlimitranges from 0.027 at ma1=
9GeV to 0.16 at ma1=
4GeV and reaches 0.19 atma1=
15GeV.The degradation ofthe analysis sensitivity towardslowervaluesofma1 iscausedbytheincreaseofthe back-groundyield atlow invariant massesofthe muon-tracksystems, asillustratedinFigs.5and9.Withincreasingma1,theaveragean-Fig. 10. Theobservedandexpectedupperlimitsat95%confidencelevelsonthe productofsignalcrosssectionandthebranchingfractionσ(pp→H+X)B(H→ a1a1)B2(a1→τ τ),relativetotheinclusiveHiggsbosonproductioncrosssection
σSMpredictedintheSM.Thegreenandyellowbandsindicatetheregionsthat
con-tain68%and95%ofthedistributionoflimitsexpectedunderthebackground-only hypothesis.Theshadedareainblueindicatestheexcludedregionof>34%forthe branchingfractionoftheH decayintonon-SMparticlesat95%CL fromRef. [26].
gular separation between the decay products of the a1 boson is
increasing.Asaconsequence,theefficiencyofthesignalselection drops down, aswe require the muon and the track, originating fromthea1
→
τ
μτ
one-prongora1→
μμ
decay,tobewithinaconeof
R
=
0.
5.Thisexplainsthedeteriorationofthesearch sensitiv-ityathighervaluesofma1.The shadedarea inblueindicatesthe excludedregionof>
34%forthebranchingfractionoftheH decay intonon-SMparticlesat95%CL [26].The new limits improve significantly over the previous 8TeV limits [28] by30%(forlowmasses)andupto80%(for intermedi-atemassesof8GeV),while thenewanalysisfurther extendsthe coverageofma1 upto15GeV.
9. Summary
A search is presented for light pseudoscalar a1 bosons,
pro-ducedfromdecaysofthe 125GeV Higgsboson (H) ina dataset correspondingto anintegratedluminosity of35
.
9fb−1 of proton-protoncollisionsatacenter-of-massenergyof13TeV.Theanalysis isbasedontheH inclusiveproductionandtargetstheH→
a1a1→
4
τ
/
2μ
2τ
decaychannels. Both channelsareusedincombination to constrain the product of the inclusive signal production cross sectionandthebranchingfractionintothe4τ
finalstate, exploit-ingthelineardependenceofthefermioniccouplingstrengthofa1onthefermionmass.Withnoevidenceforasignal,theobserved 95% confidencelevel upper limit onthe product of the inclusive signalcrosssectionandthebranchingfraction,relative totheSM H productioncross section, ranges from0.022 atma1
=
9GeV to 0.23 at ma1=
4GeV and reaches 0.16 at ma1=
15GeV. The ex-pected upper limit ranges from0.027 at ma1=
9GeV to 0.16atma1
=
4GeV andreaches0.19atma1=
15GeV.Acknowledgements
WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technicalandadministrativestaffs atCERN andatother CMS in-stitutes for their contributions to the success of the CMS effort. Inaddition,wegratefullyacknowledgethecomputingcentersand
personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructureessential to ouranalyses. Finally, we acknowledge the enduring support for the construc-tionandoperation oftheLHC andtheCMSdetectorprovidedby thefollowing fundingagencies:BMBWF andFWF(Austria); FNRS and FWO(Belgium); CNPq,CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIENCIAS (Colombia); MSES andCSF (Croatia); RPF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, PUT and ERDF (Estonia); AcademyofFinland,MEC,andHIP(Finland);CEAandCNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NK-FIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN(Italy);MSIPandNRF(RepublicofKorea);MES(Latvia);LAS (Lithuania);MOEandUM(Malaysia);BUAP,CINVESTAV,CONACYT, LNS,SEP,andUASLP-FAI(Mexico);MOS(Montenegro);MBIE(New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portu-gal);JINR(Dubna); MON,ROSATOM,RAS, RFBR,andNRCKI (Rus-sia);MESTD(Serbia);SEIDI,CPAN,PCTI,andFEDER(Spain);MoSTR (Sri Lanka); Swiss Funding Agencies(Switzerland); MST (Taipei); ThEPCenter,IPST,STAR,andNSTDA(Thailand);TUBITAKandTAEK (Turkey);NASUandSFFR(Ukraine); STFC(United Kingdom);DOE andNSF(USA).
Individuals have received support from the Marie-Curie pro-gramandtheEuropeanResearchCouncilandHorizon2020Grant, contract Nos. 675440, 752730, and 765710 (European Union); the Leventis Foundation; the A.P. Sloan Foundation; the Alexan-der von Humboldt Foundation; the Belgian Federal Science Pol-icy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRSand FWO(Belgium) underthe “Excellence of Sci-ence – EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z181100004218003; the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Lendület (“Momentum”) Program and the János Bolyai Research Scholarship of the Hungarian Academy of Sci-ences, the New National Excellence Program ÚNKP, the NKFIA researchgrants123842,123959,124845,124850,125105,128713, 128786, and 129058 (Hungary); the Council of Science and In-dustrial Research,India;theHOMING PLUSprogramofthe Foun-dation for Polish Science, cofinanced from European Union, Re-gional Development Fund, the Mobility Plus program of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/ 02861,Sonata-bis2012/07/E/ST2/01406;theNationalPriorities Re-search Programby QatarNationalResearchFund;the Ministryof Science and Education, grant no. 3.2989.2017 (Russia); the Pro-gramaEstatalde Fomento delaInvestigación CientíficayTécnica de Excelencia María de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa del Principado de Asturias; the Thalis andAristeiaprogramscofinancedbyEU-ESF andtheGreek NSRF; theRachadapisekSompotFundforPostdoctoralFellowship, Chula-longkornUniversityandtheChulalongkornAcademic intoIts2nd CenturyProjectAdvancementProject(Thailand);TheWelch Foun-dation,contractC-1845;andtheWestonHavensFoundation(USA).
References
[1] ATLASCollaboration,Observationofanewparticleinthesearchforthe stan-dardmodelHiggsbosonwiththeATLASdetectorattheLHC,Phys.Lett.B716 (2012)1,https://doi.org/10.1016/j.physletb.2012.08.020,arXiv:1207.7214. [2] CMSCollaboration,Observationofanewbosonatamassof125GeVwith
theCMSexperimentattheLHC,Phys.Lett.B716(2012)30,https://doi.org/10. 1016/j.physletb.2012.08.021,arXiv:1207.7235.
[3] P.Fayet,SupergaugeinvariantextensionoftheHiggsmechanismandamodel fortheelectronanditsneutrino,Nucl.Phys.B90(1975)104,https://doi.org/ 10.1016/0550-3213(75)90636-7.
[4] R.K.Kaul,P.Majumdar,Cancellationofquadraticallydivergentmasscorrections ingloballysupersymmetricspontaneouslybrokengaugetheories,Nucl.Phys.B 199(1982)36,https://doi.org/10.1016/0550-3213(82)90565-X.
[5] R.Barbieri,S.Ferrara,C.A.Savoy,Gaugemodelswithspontaneouslybroken lo-calsupersymmetry,Phys.Lett.B119(1982)343,https://doi.org/10.1016/0370 -2693(82)90685-2.
[6] H.P.Nilles,M.Srednicki,D.Wyler,Weakinteractionbreakdowninducedby su-pergravity,Phys.Lett.B120(1983)346,https://doi.org/10.1016/0370-2693(83) 90460-4.
[7] J.-M.Frere,D.R.T.Jones,S.Raby,Fermionmassesandinductionoftheweak scale bysupergravity,Nucl. Phys. B 222(1983) 11, https://doi.org/10.1016/ 0550-3213(83)90606-5.
[8] J.-P.Derendinger,C.A.Savoy,QuantumeffectsandSU(2)×U(1)breakingin su-pergravity gaugetheories, Nucl. Phys. B 237(1984) 307,https://doi.org/10. 1016/0550-3213(84)90162-7.
[9] U.Ellwanger, C. Hugonie,A.M. Teixeira,The next-to-minimal supersymmet-ricstandardmodel,Phys.Rep.496(2010)1,https://doi.org/10.1016/j.physrep. 2010.07.001,arXiv:0910.1785.
[10] M.Maniatis,Thenext-to-minimalsupersymmetricextensionofthestandard modelreviewed,Int.J.Mod.Phys.A25(2010)3505,https://doi.org/10.1142/ S0217751X10049827,arXiv:0906.0777.
[11] J.E.Kim,H.P.Nilles,Theμ-problemandthestrongCP-problem,Phys.Lett.B 138(1984)150,https://doi.org/10.1016/0370-2693(84)91890-2.
[12] G.Belanger,U.Ellwanger,J.F.Gunion,Y. Jiang,S. Kraml,J.H.Schwarz,Higgs bosonsat98and125GeVatLEPandtheLHC,J.HighEnergyPhys.01(2013) 069,https://doi.org/10.1007/JHEP01(2013)069,arXiv:1210.1976.
[13]G.Belanger,U.Ellwanger,J.F.Gunion,Y.Jiang,S.Kraml,TwoHiggsbosonsat theTevatronandtheLHC?,arXiv:1208.4952,2012.
[14] J.F. Gunion, Y. Jiang, S. Kraml,Diagnosing degenerateHiggsbosons at 125 GeV,Phys. Rev.Lett.110(2013)051801, https://doi.org/10.1103/PhysRevLett. 110.051801,arXiv:1208.1817.
[15] J.F.Gunion,Y.Jiang,S.Kraml,CouldtwoNMSSMHiggsbosonsbepresentnear 125GeV?,Phys.Rev.D86(2012)071702,https://doi.org/10.1103/PhysRevD.86. 071702,arXiv:1207.1545.
[16] S.F.King, M.Mühlleitner,R. Nevzorov,NMSSMHiggsbenchmarksnear125 GeV,Nucl.Phys.B860(2012)207,https://doi.org/10.1016/j.nuclphysb.2012.02. 010,arXiv:1201.2671.
[17] S.F.King,M.Mühlleitner,R.Nevzorov,K.Walz,NaturalNMSSMHiggsbosons, Nucl.Phys.B870(2013)323,https://doi.org/10.1016/j.nuclphysb.2013.01.020, arXiv:1211.5074.
[18] U.Ellwanger,J.F.Gunion,C.Hugonie,DifficultscenariosforNMSSMHiggs dis-coveryattheLHC,J.HighEnergyPhys.07(2005)041,https://doi.org/10.1088/ 1126-6708/2005/07/041,arXiv:hep-ph/0503203.
[19]U.Ellwanger,J.F.Gunion,C.Hugonie,S.Moretti,Towardsano-losetheoremfor NMSSMHiggsdiscoveryattheLHC,in:PhysicsatTeVColliders,lesHouches Workshop,2003,arXiv:hep-ph/0305109.
[20]U.Ellwanger,J.F.Gunion,C.Hugonie,S.Moretti,NMSSMHiggsdiscoveryatthe LHC,in:PhysicsatTeVColliders,lesHouchesWorkshop,2003,arXiv:hep-ph/ 0401228.
[21]A. Belyaev,S. Hesselbach, S. Lehti, S.Moretti, A.Nikitenko, C.H. Shepherd-Themistocleous,Thescopeofthe4tauchannelinHiggs-strahlungandvector bosonfusionfor theNMSSMno-Lose TheoremattheLHC,arXiv:0805.3505, 2008.
[22] A.Belyaev,J.Pivarski,A.Safonov,S.Senkin,A.Tatarinov,LHCdiscovery po-tentialofthelightestNMSSMHiggsbosonintheh1→a1a1→4μchannel,
Phys. Rev. D81 (2010) 075021, https://doi.org/10.1103/PhysRevD.81.075021, arXiv:1002.1956.
[23] M.Lisanti,J.G.Wacker,DiscoveringtheHiggsbosonwithlowmassmuonpairs, Phys. Rev.D79 (2010) 115006,https://doi.org/10.1103/PhysRevD.79.115006, arXiv:0903.1377.
[24]M.M.Almarashi,S.Moretti,ScopeofHiggsproductioninassociationwitha bottomquarkpairinprobingtheHiggssectoroftheNMSSMattheLHC,arXiv: 1205.1683,2012.
[25] M.M.Almarashi,S.Moretti,LHCsignalsofaheavyCP-evenHiggsbosoninthe NMSSMviadecaysintoa Z andalightCP-oddHiggsstate,Phys.Rev.D85 (2012)017701,https://doi.org/10.1103/PhysRevD.85.017701,arXiv:1109.1735. [26] ATLASand CMSCollaborations, Measurements ofthe Higgs boson
produc-tionanddecay ratesandconstraintsonitscouplingsfromacombined AT-LAS and CMSanalysisofthe LHCpp collisiondata at √s=7 and8TeV, J.HighEnergyPhys.08(2016)045,https://doi.org/10.1007/JHEP08(2016)045, arXiv:1606.02266.
[27] CMSCollaboration,Searchfor lightbosonsindecaysofthe125GeVHiggs bosoninproton-protoncollisionsat√s=8 TeV,J.HighEnergyPhys.10(2017) 076,https://doi.org/10.1007/JHEP10(2017)076,arXiv:1701.02032.
[28] CMSCollaboration,SearchforaverylightNMSSMHiggsbosonproducedin decaysofthe125GeVscalarbosonanddecayingintoτleptonsinppcollisions
at√s=8 TeV,J.HighEnergy Phys.01(2016) 079,https://doi.org/10.1007/ JHEP01(2016)079,arXiv:1510.06534.
[29] CMSCollaboration,A searchforpairproductionofnewlight bosons decay-ingintomuons,Phys.Lett.B752(2016)146,https://doi.org/10.1016/j.physletb. 2015.10.067,arXiv:1506.00424.
[30] CMSCollaboration, SearchforanexoticdecayoftheHiggsbosontoapair oflightpseudoscalarsinthefinalstateoftwomuonsandtwoτ leptonsin proton-protoncollisionsat√s=13 TeV,J.HighEnergyPhys.11(2018)018, https://doi.org/10.1007/JHEP11(2018)018,arXiv:1805.04865.
[31] CMSCollaboration,SearchforanexoticdecayoftheHiggsbosontoapairof lightpseudoscalarsinthefinalstatewithtwobquarksandtwoτleptonsin proton-protoncollisionsat√s=13TeV,Phys.Lett.B785(2018)462,https:// doi.org/10.1016/j.physletb.2018.08.057,arXiv:1805.10191.
[32] ATLASCollaboration,SearchfortheHiggsbosonproducedinassociationwith aWbosonand decayingtofourb-quarksviatwospin-zero particlesinpp collisionsat13TeVwiththeATLAS detector,Eur.Phys. J.C76(2016)605, https://doi.org/10.1140/epjc/s10052-016-4418-9,arXiv:1606.08391.
[33] ATLASCollaboration,Searchfor newlightgaugebosonsinHiggsboson de-caystofour-leptonfinalstatesinppcollisionsat√s=8 TeVwiththeATLAS detectoratthe LHC,Phys.Rev.D92(2015)092001,https://doi.org/10.1103/ PhysRevD.92.092001,arXiv:1505.07645.
[34] ATLASCollaboration,Searchfornewphenomenaineventswithatleastthree photonscollectedinpp collisionsat √s=8 TeVwith the ATLAS detector, Eur.Phys.J.C76(2016)210,https://doi.org/10.1140/epjc/s10052-016-4034-8, arXiv:1509.05051.
[35] ATLASCollaboration,SearchforHiggsbosonsdecayingtoaa intheμμτ τfinal stateinpp collisionsat√s=8 TeV withtheATLASexperiment,Phys.Rev.D92 (2015)052002,https://doi.org/10.1103/PhysRevD.92.052002,arXiv:1505.01609. [36] ATLAS Collaboration, Search for Higgs boson decays into pairs of light (pseudo)scalarparticlesintheγ γj j finalstateinpp collisionsat√s=13 TeVwiththeATLASdetector,Phys.Lett.B782(2018)750,https://doi.org/10. 1016/j.physletb.2018.06.011,arXiv:1803.11145.
[37] ATLASCollaboration,SearchforHiggsbosondecaysto beyond-the-standard-modellightbosonsinfour-leptoneventswiththeATLASdetectorat√s=13 TeV,J.HighEnergyPhys.06(2018)166,https://doi.org/10.1007/JHEP06(2018) 166,arXiv:1802.03388.
[38] CMSCollaboration,SearchforanexoticdecayoftheHiggsbosontoapairof lightpseudoscalarsinthefinalstatewithtwomuonsandtwobquarksin ppcollisionsat13TeV,Phys.Lett.B795(2019)398,https://doi.org/10.1016/j. physletb.2019.06.021,arXiv:1812.06359.
[39] CMSCollaboration,Asearchforpairproductionofnewlightbosonsdecaying intomuonsinppcollisionsat13TeV,Phys.Lett.B796(2019)131,https:// doi.org/10.1016/j.physletb.2019.07.013,arXiv:1812.00380.
[40] ATLASCollaboration,SearchforHiggsbosondecaysintoapairoflightbosons inthebbμμfinalstateinppcollisionat√s=13TeVwiththeATLASdetector, Phys.Lett.B790(2019)1,https://doi.org/10.1016/j.physletb.2018.10.073,arXiv: 1807.00539.
[41] D.Curtin,R.Essig,S.Gori,P.Jaiswal,A.Katz,T.Liu,Z.Liu,D.McKeen,J.Shelton, M.Strassler,Z.Surujon,B.Tweedie,Y.-M.Zhong,Exoticdecaysofthe125GeV Higgsboson,Phys.Rev.D90(2014)075004,https://doi.org/10.1103/PhysRevD. 90.075004,arXiv:1312.4992.
[42] CMS Collaboration, The CMStrigger system,J. Instrum. 12 (2017) P01020, https://doi.org/10.1088/1748-0221/12/01/P01020,arXiv:1609.02366. [43] CMSCollaboration,TheCMSexperimentattheCERNLHC,J.Instrum.3(2008)
S08004,https://doi.org/10.1088/1748-0221/3/08/S08004.
[44] T. Sjöstrand,S.Ask,J.R. Christiansen,R.Corke,N.Desai,P.Ilten,S. Mrenna, S.Prestel,C.O.Rasmussen,P.Z.Skands,AnintroductiontoPYTHIA8.2, Com-put.Phys.Commun.191(2015)159,https://doi.org/10.1016/j.cpc.2015.01.024, arXiv:1410.3012.
[45] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H.S. Shao, T. Stelzer, P. Torrielli,M. Zaro,The automated computation of tree-levelandnext-to-leadingorderdifferentialcrosssections,andtheirmatching toparton showersimulations,J. HighEnergy Phys. 07(2014) 079,https:// doi.org/10.1007/JHEP07(2014)079,arXiv:1405.0301.
[46] G.Bozzi,S.Catani,D.deFlorian,M.Grazzini,Transverse-momentum resumma-tionandthespectrumoftheHiggsbosonattheLHC,Nucl.Phys.B737(2006) 73,https://doi.org/10.1016/j.nuclphysb.2005.12.022,arXiv:hep-ph/0508068. [47] D. deFlorian,G.Ferrera, M.Grazzini,D.Tommasini,Transverse-momentum
resummation:Higgsbosonproductionat theTevatronand theLHC,J.High EnergyPhys. 11(2011)064,https://doi.org/10.1007/JHEP11(2011)064,arXiv: 1109.2109.
[48] R.D. Ball, et al., NNPDF, Parton distributions for the LHC Run II, J. High EnergyPhys. 04(2015)040,https://doi.org/10.1007/JHEP04(2015)040, arXiv: 1410.8849.
[49] P.Nason, Anewmethodfor combiningNLOQCDwithshowerMonteCarlo algorithms,J.HighEnergyPhys.11(2004)040,https://doi.org/10.1088/1126 -6708/2004/11/040,arXiv:hep-ph/0409146.
[50] S.Frixione,P.Nason,C.Oleari,MatchingNLOQCDcomputationswithParton Showersimulations:thePOWHEGmethod,J.HighEnergyPhys.11(2007)070, https://doi.org/10.1088/1126-6708/2007/11/070,arXiv:0709.2092.
[51] S.Alioli, P.Nason, C. Oleari,E.Re, Ageneral framework for implementing NLOcalculationsinshowerMonteCarloprograms:thePOWHEGBOX,J.High Energy Phys.06(2010)043,https://doi.org/10.1007/JHEP06(2010)043, arXiv: 1002.2581.
[52] E.Re,Single-topWt-channelproductionmatchedwithpartonshowersusing thePOWHEGmethod,Eur.Phys.J.C71(2011)1547,https://doi.org/10.1140/ epjc/s10052-011-1547-z,arXiv:1009.2450.
[53] S.Alioli,P.Nason,C.Oleari,E.Re,NLOsingle-topproduction matchedwith showerinPOWHEG:s- andt-channelcontributions,J.HighEnergyPhys.09 (2009) 111,https://doi.org/10.1088/1126-6708/2009/09/111, arXiv:0907.4076, Erratum:https://doi.org/10.1007/JHEP02(2010)011.
[54] CMSCollaboration,Eventgeneratortunesobtainedfromunderlyingeventand multipartonscatteringmeasurements,Eur.Phys.J.C76(2016)155,https:// doi.org/10.1140/epjc/s10052-016-3988-x,arXiv:1512.00815.
[55] S.Agostinelli,etal.,GEANT4,GEANT4—asimulationtoolkit,Nucl.Instrum. MethodsA506(2003)250,https://doi.org/10.1016/S0168-9002(03)01368-8. [56] CMSCollaboration,Particle-flow reconstructionandglobalevent description
withtheCMSdetector,J.Instrum.12(2017)P10003,https://doi.org/10.1088/ 1748-0221/12/10/P10003,arXiv:1706.04965.
[57] CMSCollaboration,TrackReconstructionintheCMSTracker,TechnicalReport CMS-NOTE-2006-041,2006,https://cds.cern.ch/record/934067.
[58] CMSCollaboration,Descriptionandperformanceoftrackandprimary-vertex reconstructionwiththeCMStracker,J.Instrum.9(2014)P10009,https://doi. org/10.1088/1748-0221/9/10/P10009,arXiv:1405.6569.
[59] M.Cacciari,G.P.Salam,G.Soyez,Theanti-kTjetclusteringalgorithm,J.High
Energy Phys.04(2008) 063,https://doi.org/10.1088/1126-6708/2008/04/063, arXiv:0802.1189.
[60] M.Cacciari,G.P.Salam,G.Soyez,FastJetusermanual,Eur.Phys.J.C72(2012) 1896,https://doi.org/10.1140/epjc/s10052-012-1896-2,arXiv:1111.6097.
[61] J.S.Conway,Incorporatingnuisanceparametersinlikelihoodsformultisource spectra,in:ProceedingsofPHYSTAT2011WorkshoponStatisticalIssues Re-latedtoDiscoveryClaimsinSearchExperimentsandUnfolding,2011,p. 115, CERN-2011-006,http://cdsweb.cern.ch/record/1306523.
[62] CMSCollaboration, CMSluminosity measurementsforthe 2016datataking period,CMSphysicsanalysissummaryCMS-PAS-LUM-17-001,https://cds.cern. ch/record/2257069,2017.
[63] CMSCollaboration,MeasurementoftheinclusiveW and Z productioncross sectionsinpp collisionsat√s=7 TeV,J.HighEnergyPhys.10(2011)132, https://doi.org/10.1007/JHEP10(2011)132,arXiv:1107.4789.
[64] J.Pumplin,D.R.Stump,J.Huston,H.L.Lai,P.M.Nadolsky,W.K.Tung,New gen-erationofpartondistributionswithuncertaintiesfromglobalQCDanalysis,J. HighEnergyPhys.07(2002)012,https://doi.org/10.1088/1126-6708/2002/07/ 012,arXiv:hep-ph/0201195.
[65] A.L.Read,Presentationofsearchresults:theCLstechnique,J.Phys.G28(2002)
2693,https://doi.org/10.1088/0954-3899/28/10/313.
[66] T.Junk,Confidencelevelcomputationforcombiningsearcheswithsmall statis-tics,Nucl.Instrum.MethodsA434(1999)435,https://doi.org/10.1016/S0168 -9002(99)00498-2,arXiv:hep-ex/9902006.
[67] G.Cowan,K.Cranmer,E.Gross,O.Vitells,Asymptoticformulaefor likelihood-basedtestsofnewphysics,Eur.Phys.J.C71(2011)1554,https://doi.org/10. 1140/epjc/s10052-011-1554-0, arXiv:1007.1727, Erratum: https://doi.org/10. 1140/epjc/s10052-013-2501-z.
[68] L.Moneta,K.Belasco,K.S.Cranmer,A.Lazzaro,D.Piparo,G.Schott,W. Verk-erke,M.Wolf,TheRooStatsproject,in:13thInternationalWorkshopon Ad-vancedComputingandAnalysisTechniquesinPhysicsResearch(ACAT2010), SISSA,2010,http://pos.sissa.it/archive/conferences/093/057/ACAT2010_057.pdf, arXiv:1009.1003.
TheCMSCollaboration
A.M. Sirunyan,
A. Tumasyan
YerevanPhysicsInstitute,Yerevan,Armenia
W. Adam,
F. Ambrogi,
E. Asilar,
T. Bergauer,
J. Brandstetter,
M. Dragicevic,
J. Erö,
A. Escalante Del Valle,
M. Flechl,
R. Frühwirth
1,
V.M. Ghete,
J. Hrubec,
M. Jeitler
1,
N. Krammer,
I. Krätschmer,
D. Liko,
T. Madlener,
I. Mikulec,
N. Rad,
H. Rohringer,
J. Schieck
1,
R. Schöfbeck,
M. Spanring,
D. Spitzbart,
W. Waltenberger,
J. Wittmann,
C.-E. Wulz
1,
M. Zarucki
InstitutfürHochenergiephysik,Wien,Austria
V. Chekhovsky,
V. Mossolov,
J. Suarez Gonzalez
InstituteforNuclearProblems,Minsk,Belarus
E.A. De Wolf,
D. Di Croce,
X. Janssen,
J. Lauwers,
A. Lelek,
M. Pieters,
H. Van Haevermaet,
P. Van Mechelen,
N. Van Remortel
UniversiteitAntwerpen,Antwerpen,Belgium
F. Blekman,
J. D’Hondt,
J. De Clercq,
K. Deroover,
G. Flouris,
D. Lontkovskyi,
S. Lowette,
I. Marchesini,
S. Moortgat,
L. Moreels,
Q. Python,
K. Skovpen,
S. Tavernier,
W. Van Doninck,
P. Van Mulders,
I. Van Parijs
VrijeUniversiteitBrussel,Brussel,Belgium
D. Beghin,
B. Bilin,
H. Brun,
B. Clerbaux,
G. De Lentdecker,
H. Delannoy,
B. Dorney,
G. Fasanella,
L. Favart,
A. Grebenyuk,
A.K. Kalsi,
J. Luetic,
A. Popov
2,
N. Postiau,
E. Starling,
L. Thomas,
C. Vander Velde,
P. Vanlaer,
D. Vannerom,
Q. Wang
UniversitéLibredeBruxelles,Bruxelles,Belgium
T. Cornelis,
D. Dobur,
A. Fagot,
M. Gul,
I. Khvastunov
3,
C. Roskas,
D. Trocino,
M. Tytgat,
W. Verbeke,
B. Vermassen,
M. Vit,
N. Zaganidis
GhentUniversity,Ghent,Belgium
O. Bondu,
G. Bruno,
C. Caputo,
P. David,
C. Delaere,
M. Delcourt,
A. Giammanco,
G. Krintiras,
V. Lemaitre,
A. Magitteri,
K. Piotrzkowski,
A. Saggio,
M. Vidal Marono,
P. Vischia,
J. Zobec
UniversitéCatholiquedeLouvain,Louvain-la-Neuve,Belgium
F.L. Alves,
G.A. Alves,
G. Correia Silva,
C. Hensel,
A. Moraes,
M.E. Pol,
P. Rebello Teles
CentroBrasileirodePesquisasFisicas,RiodeJaneiro,Brazil
E. Belchior Batista Das Chagas,
W. Carvalho,
J. Chinellato
4,
E. Coelho,
E.M. Da Costa,
G.G. Da Silveira
5,
D. De Jesus Damiao,
C. De Oliveira Martins,
S. Fonseca De Souza,
L.M. Huertas Guativa,
H. Malbouisson,
D. Matos Figueiredo,
M. Melo De Almeida,
C. Mora Herrera,
L. Mundim,
H. Nogima,
W.L. Prado Da Silva,
L.J. Sanchez Rosas,
A. Santoro,
A. Sznajder,
M. Thiel,
E.J. Tonelli Manganote
4,
F. Torres Da Silva De Araujo,
A. Vilela Pereira
UniversidadedoEstadodoRiodeJaneiro,RiodeJaneiro,Brazil
S. Ahuja
a,
C.A. Bernardes
a,
L. Calligaris
a,
T.R. Fernandez Perez Tomei
a,
E.M. Gregores
b,
P.G. Mercadante
b,
S.F. Novaes
a,
Sandra
S. Padula
aaUniversidadeEstadualPaulista,SãoPaulo,Brazil bUniversidadeFederaldoABC,SãoPaulo,Brazil
A. Aleksandrov,
R. Hadjiiska,
P. Iaydjiev,
A. Marinov,
M. Misheva,
M. Rodozov,
M. Shopova,
G. Sultanov
InstituteforNuclearResearchandNuclearEnergy,BulgarianAcademyofSciences,Sofia,Bulgaria
A. Dimitrov,
L. Litov,
B. Pavlov,
P. Petkov
UniversityofSofia,Sofia,Bulgaria
W. Fang
6,
X. Gao
6,
L. Yuan
BeihangUniversity,Beijing,China
M. Ahmad,
J.G. Bian,
G.M. Chen,
H.S. Chen,
M. Chen,
Y. Chen,
C.H. Jiang,
D. Leggat,
H. Liao,
Z. Liu,
S.M. Shaheen
7,
A. Spiezia,
J. Tao,
E. Yazgan,
H. Zhang,
S. Zhang
7,
J. Zhao
InstituteofHighEnergyPhysics,Beijing,China
Y. Ban,
G. Chen,
A. Levin,
J. Li,
L. Li,
Q. Li,
Y. Mao,
S.J. Qian,
D. Wang
StateKeyLaboratoryofNuclearPhysicsandTechnology,PekingUniversity,Beijing,China
Y. Wang
TsinghuaUniversity,Beijing,China
C. Avila,
A. Cabrera,
C.A. Carrillo Montoya,
L.F. Chaparro Sierra,
C. Florez,
C.F. González Hernández,
M.A. Segura Delgado
UniversidaddeLosAndes,Bogota,Colombia
J.D. Ruiz Alvarez
UniversidaddeAntioquia,Medellin,Colombia
N. Godinovic,
D. Lelas,
I. Puljak,
T. Sculac
UniversityofSplit,FacultyofElectricalEngineering,MechanicalEngineeringandNavalArchitecture,Split,Croatia