Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Test
of
CP
invariance
in
vector-boson
fusion
production
of
the
Higgs
boson
in
the
H
→
τ τ
channel
in
proton–proton
collisions
at
√
s
=
13
TeV with
the
ATLAS
detector
.TheATLASCollaboration
a r t i c l e i n f o a b s t ra c t
Articlehistory:
Received14February2020
Receivedinrevisedform26March2020 Accepted9April2020
Availableonline16April2020 Editor:M.Doser
A test ofCPinvariance in Higgsbosonproduction viavector-bosonfusion isperformed inthe H→
τ τ decaychannel.ThistestusestheOptimalObservablemethodandiscarriedoutusing36.1fb−1of
√s
=13TeV proton–proton collisiondatacollectedbytheATLASexperimentattheLHC. Contributions
fromCP-violatinginteractionsbetweentheHiggsbosonandelectroweakgaugebosonsaredescribedby
aneffectivefieldtheory,inwhichthe parameterd governs˜ thestrengthofCPviolation. Nosign ofCP
violationisobservedinthedistributionsoftheOptimalObservable,andd is˜ constrainedtotheinterval
[−0.090,0.035]atthe68%confidencelevel(CL),comparedtoanexpectedintervalofd˜∈ [−0.035, 0.033]
basedupontheStandardModelprediction.Noconstraintscanbesetond at˜ 95%CL,whileanexpected
95%CLintervalofd˜∈ [−0.21, 0.15]fortheStandardModelhypothesiswasexpected.
©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense
(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
Contents
1. Introduction . . . 1
2. Theoreticalframeworkandmethodology . . . 2
3. ATLASdetector . . . 3
4. Simulatedeventsamples . . . 4
5. Eventselection . . . 4 6. Backgroundestimation . . . 6 7. Systematicuncertainties . . . 8 8. Fittingprocedure . . . 8 9. Results . . . 9 10. Conclusion . . . 11 Acknowledgements . . . 11 References . . . 12 1. Introduction
One of the central puzzles in physics today is the observed baryon asymmetry oftheuniverse. Theviolation ofinvarianceof fundamentalinteractionsunderthetransformationofcharge con-jugation (C) and its combination with parity (CP) is one of the threenecessarySakharov conditions [1] toexplain thedynamical generationofthebaryonasymmetry.Inthe StandardModel(SM) ofparticlephysics, CPviolation (CPV)isintroduced via the
com- E-mailaddress:atlas.publications@cern.ch.
plex phase inthequark mixing(CKM) matrix [2,3].1 It isable to describeall observationsofCPVinthe K -, B-, and D-meson sys-tems [4–15]. However, the measured size of the complex phase and the derived magnitudeof CPV in the early universe are in-sufficientto explaintheobserved valueofthebaryon asymmetry within the SM [16–20] and, mostprobably, new sources of CPV beyondtheSMneedtobeintroduced.
1 EffectsofpossibleCPVintheneutrinosectorandinthestronginteractionare notconsideredinthisstatement.
https://doi.org/10.1016/j.physletb.2020.135426
0370-2693/©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
2 The ATLAS Collaboration / Physics Letters B 805 (2020) 135426
The investigationof Higgsboson productionand decayatthe LHCoffersanovelopportunitytosearchfornewsourcesofCPVin theinteractionoftheHiggsbosonwithotherSMparticles.No ob-servableeffectofCPVisexpectedintheproductionordecayofthe SM Higgsboson.Hence anyobservation ofCPviolation involving theobservedHiggsboson[21,22] wouldbeanunequivocalsignof physicsbeyondtheSM.
The measured Higgs boson productioncross sections, branch-ingratios,andderived constraintsoncoupling-strengthmodifiers, assuming thetensorstructureofthe SM,agree withthe SM pre-dictionswithinthecurrentprecision [23–25].Investigationsofspin andCPquantumnumbersstronglyindicatethattheobserved par-ticleisofscalarnatureandthatthedominantcouplingstructureis CP-evenandconsistentwiththeSM expectation [26–28]. Various measurementshavebeenusedintheframeworkofeffectivefield theoriestoderivelimitsonWilsoncoefficientswhichmultiply CP-evenandCP-oddoperatorsandmodifythestructureandstrength of the coupling of the Higgs boson to gluons and electroweak gauge bosons. These include measurements of differential cross sections as functions of CP-even observables in the decay H→
γ γ [29],measurements ofeventratesinspecificeventcategories and phase-space regions in the decay H→Z Z∗ [30], and mea-surementsofthe V H invariant massinHiggsbosonproductionin associationwitha weakgaugeboson V (V=W±, Z ) [31]. These analyses useCP-evenobservablesandeventrateinformationand hence are not directly sensitive to possible interference between theCP-evenSM operatorsandnewCP-oddoperators. Theshapes of distributions of CP-odd andCP-even observables (without ex-ploitingCP-evenrateinformation)havebeenusedtosetlimitson CP-oddandCP-evencouplingsoftheHiggsbosontogaugebosons. Thisisdonebyinvestigatingthedecay H→V V∗(V=W±, Z), us-ingonlyinformationfromthedecay [27,32] andcombiningitwith informationfromvector-bosonfusion(VBF)orassociated V H
pro-duction[33,34].AnotheranalysisusingthedecayH→τ τ exploits informationfromVBF andV H production [35]. The shapeofthe distributionofa single CP-oddobservableconstructed from kine-maticinformationinVBFproductionin H→τ τ candidateevents hasbeen previously usedto seta limit onthe parameterd [˜ 36], which governs the strength of CPV in an effective field theory ansatz as described in Section 2. This analysis constrained d to ˜
the interval [−0.11,0.05] atthe 68% confidence level(CL) using ATLASdatacollectedat√s=8 TeV in2012,whilea68%CL inter-valofd˜∈ [−0.16,0.16] wasexpected. No hintsofCPVhavebeen observedinthesestudies.
InthisLetter,adirecttestofCPinvarianceinHiggsboson pro-duction via VBF is presented in the H→τ τ channel, based on proton–proton collision data corresponding to an integrated lu-minosityof 36.1 fb−1 collected withthe ATLAS detectorat √s =
13 TeV in the years 2015 and 2016. A CP-odd Optimal Observ-able [37–39] is employed. The Optimal Observable combines the information from the multidimensional phase space in a single quantity calculated from leading-order matrix elements for VBF production, independent of the decay mode of the Higgs boson. VBFproductionprovidesapromisingphysicsprocesstotestCP in-varianceinthe H V V vertex [40].Thedecaymode H→τ τ allows the selection of signal events with a good signal-to-background ratioandthe reconstruction ofthe four-momentumof theHiggs bosoncandidatewithadequateprecision.
Inthe presentwork a direct testof CP invarianceis obtained throughameasurementofthemeanvalueoftheCP-oddOptimal Observable, neglecting possible effects from rescattering by new lightparticlesinloops [40].Ameasurementoftheparameterd is ˜
alsoperformed.Limitsond are ˜ derivedbyanalysingtheshapesof distributionsoftheOptimalObservablemeasuredin H→τ τ can-didateeventswithtwo jetsinthe finalstate consistentwithVBF production.The eventselection, estimationofbackground
contri-butions, and systematic uncertainties closely follow the analysis employed fortheobservationofthe H→τ τ decay [41].Inorder toincreasethesignal-to-backgroundratio,thefinaleventselection utilizesmultivariatediscriminants.
2. Theoreticalframeworkandmethodology
The effectiveLagrangian Leff considered is theSM Lagrangian augmented with CP-odd operators of mass dimension six, in-volving the Higgsfield andelectroweak gauge fields.No CP-even dimension-sixoperators builtfromthesefieldsare takeninto ac-count. All interactions between the Higgs boson and other SM particles(fermionsandgluons)areassumedtobeaspredictedin the SM,i.e.the couplingstructure ingluon–gluon fusion produc-tionandinthedecayintoa pairof τ-leptonsisconsideredtobe thesameasintheSM.Thetheoretical ansatzconsideredandthe methodology is the same as in Ref. [36], which contains further details. After electroweaksymmetry breaking,the Lagrangian can bewritteninthemassbasis oftheHiggsboson H , photon A and
weakgaugebosons W±and Z as inRef. [42]: Leff=LSM+ ˜gH A AHA˜μνAμν+ ˜gH A ZHA˜μνZμν
+ ˜gH Z ZHZ˜μνZμν+ ˜gH W WHW˜+μνW−μν,
where V μν and V μν˜ =μνρσ Vρσ (with V=W±, Z, A) denotethe field strength and dual field strength tensors, respectively. Only two of the four couplings g˜H V V are independent due to con-straints imposed by U(1)Y andSU(2)IW,L invariance. Theycan be
expressedintermsoftwodimensionlesscouplingsd and ˜ d˜B asin Refs. [43,44]: ˜ gH A A= g 2mW (˜d sin2θW + ˜dBcos2θW) ˜ gH A Z= g 2mW sin 2θW(˜d− ˜dB) ˜ gH Z Z= g 2mW (˜d cos2θW+ ˜dBsin2θW) ˜ gH W W= g mW ˜ d,
where g is theSU(2)couplingconstantandθW istheweakmixing angle. Adopting the arbitrary choice d˜= ˜dB yields the following relations2: ˜ gH A A= ˜gH Z Z= 1 2g˜H W W= g 2mW ˜ d and g˜H A Z=0.
Inaneffectivefieldtheory(EFT),thecouplingparametersarereal valued. However, rescatteringeffectsfromnewparticles inloops, withmasseslowerthan thescaleofnewphysics assumedinthe EFT, may introduce an imaginary part [40]. Such effects are not considered in theanalysispresented here, asd is ˜ assumedto be realvalued.
The strengthofCP violationinVBFHiggs bosonproductionis thendescribedbyasingle parameterd. ˜ Thecorrespondingmatrix elementMforVBFproductionisthesumofaCP-even contribu-tion MSM fromthe SMandaCP-oddcontributionMCP-odd from thedimension-sixoperatorsconsidered:
M=MSM+ ˜d·MCP-odd,
wherethe dependenceond has ˜ explicitly beenfactoredout. The squaredmatrixelementhasthreecontributions:
2 The parameterd is˜ relatedto the parameterκˆ
W= ( ˜κW/κSM)tanα usedin the investigation of CP properties in the decay H→W W∗ via d˜= − ˆκW =
−( ˜κW/κSM)tanα.Thechoiced˜= ˜dB yieldsκˆW= ˆκZ asassumedinthe
|M|2= |M
SM|2+ ˜d·2 Re(M∗SMMCP-odd)+ ˜d2· |MCP-odd|2. The first term |MSM|2 and third term d˜2· |MCP-odd|2 are both CP-even and hence are not a source of CPV. The second term ˜
d·2Re(M∗SMMCP-odd)stemsfromtheinterferenceofthetwo con-tributions to the matrix element and is CP-odd, representing a possiblenew sourceof CPVin the Higgssector. The interference term integrated over a CP-symmetric part of phase space van-ishesandthereforedoesnot contribute tothe totalcross section andobservedeventyieldafterCP-symmetricselection criteriaare applied. The third term increases the total cross section by an amount quadratic in d, ˜ but this is not exploited in the analysis presentedhereastheobservedratecanalsobeinfluencedby ad-ditionalCP-conservingnewphysics.
The final state consisting of the reconstructed decay of the Higgs boson and the two tagging jets corresponding to the VBF topologycan be characterizedby seven phase-spacevariables, by fixingthemassoftheHiggsboson,neglectingjetmasses,and ex-ploiting momentum conservation in the plane transverse to the beamline.TheconceptoftheOptimalObservable(Oopt)combines the information from the seven-dimensional phase space into a single observable,which isshown tohave thehighestsensitivity tosmallvaluesoftheparameterofinterestandneglects contribu-tionsproportionaltod˜2inthematrixelement.
TheOptimalObservable forthedeterminationofd is ˜ givenby theratiooftheinterferenceterminthematrixelementtotheSM contribution:
Oopt=
2 Re(M∗SMMCP-odd)
|MSM|2
.
Inorderto make an almostmodel-independent testof CP in-variance,the meanvalue oftheOptimal Observablecan be mea-sured.If no CPV ispresent in the H V V vertex, then the expec-tation value of the Optimal Observable vanishes: Oopt=0, as the Optimal Observable is a CP-odd (and T-oddˆ 3) variable. Since theinitial state of VBF productionof theHiggs boson isnot CP-symmetric,this argument assumes that effects fromrescattering arenegligible [40].Thus an observationofa non-vanishingmean value or an asymmetry in the Optimal Observable distribution wouldindicatephysicsbeyondtheSM,eitherstemmingfromCPV, ororiginatingfromrescatteringeffects(i.e.newparticlesbeingon themass shell in loop correctionsto the H V V vertex). Example distributionsoftheOptimal Observable forsignal eventsafterthe fulleventselection,asdescribedinSection5,areshownfor vari-ousvaluesofd in ˜ Fig.1.In theSM thedistributionissymmetric andhasameanvalueofzero,whereasanon-vanishingvalueofd˜
causesan asymmetryandanon-vanishingmeanvalue ofthe Op-timalObservable.
Thevalues ofthe leading-order matrixelements (ME) needed forthe calculation of the Optimal Observable are extractedfrom HAWK [45–47]. The evaluationrequiresthe four-momentaofthe Higgsbosonandthetwotaggingjets ( j j).Themomentumfraction
x1 (x2) of theinitial-state partonfromthe protonmoving inthe positive(negative) z-direction (alongthebeam)canbederivedby exploitingenergy–momentum conservationfromtheHiggsboson andtaggingjetfour-momentaas
xreco1,2 =m√H j j s e
±yH j j,
wheremH j j ( yH j j) isthe invariant mass(rapidity) obtainedfrom thevectoriallysummedfour-momentaofthetaggingjetsandthe Higgsboson.Sincetheflavouroftheinitial- andfinal-statepartons
3 T denotesˆ thenaivetimereversalaccordingtoRef. [40],whichinvertsthe di-rectionsofmomentaandspins.
Fig. 1. DistributionoftheOptimalObservable forsignaleventsforthreeexample valuesofd after˜ event reconstructionand applicationofthe fulleventselection usedtodefinethesignalregion(seeSection5).Non-vanishingvaluesofd cause˜ an asymmetryandanon-vanishingmeanvalue.
cannot be determined experimentally, the sum over all possible flavour configurations i j →klH weighted by the CT10 leading-orderpartondistributionfunctions(PDFs) [48] is calculated sepa-ratelyforthematrixelementsinthenumeratoranddenominator:
2 Re(M∗SMMCP-odd)= i,j,k,l fi(x1)fj(x2)2 Re((MSMi j→klH)∗Mi jCP-odd→klH) |MSM|2= i,j,k,l fi(x1)fj(x2)|MSMi j→klH|2.
Thebestestimateandconfidenceintervalsford in ˜ thisanalysis aredeterminedbyafitofthepredicteddistributionoftheOptimal Observabletothatmeasuredindata.IthasbeenshowninRef. [36] thattheOptimalObservableyieldsasignificantlyhighersensitivity inthedeterminationofd than ˜ theCP-oddsigneddifferenceinthe azimuthal angle φj j betweenthetwotaggingjets, assuggested inRef. [44].
3. ATLASdetector
The ATLAS experiment [49–51] at the LHC is a multipurpose particle detector with a forward–backward symmetric cylindrical geometry and a near 4π coverage in solid angle.4 It consists of
an inner tracking detectorsurroundedby a thinsuperconducting solenoidprovidinga2 T axialmagneticfield,electromagneticand hadron calorimeters,and a muon spectrometer. The inner track-ing detectorcoversthepseudorapidity range|η|<2.5. Itconsists ofsiliconpixel,siliconmicrostrip,andtransitionradiationtracking detectors. Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic(EM)energymeasurementswithhighgranularity. Asteel/scintillator-tilehadroncalorimetercoversthecentral pseu-dorapidity range(|η|<1.7). The endcapandforwardregions are instrumentedwithLArcalorimetersforboththeEMandhadronic energy measurements up to |η|=4.9. The muon spectrometer surrounds the calorimeters and is based on three large air-core toroidalsuperconducting magnetswitheight coilseach.The field integralofthetoroidsrangesbetween2.0and6.0 T macrossmost
4 ATLASuses aright-handedcoordinatesystemwith itsoriginat thenominal interactionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeam pipe.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y-axis pointsupwards.Cylindricalcoordinates(r,φ)areusedinthetransverseplane,φ beingtheazimuthalanglearoundthez-axis.Thepseudorapidityisdefinedinterms ofthepolarangleθas η≡ −ln tan(θ/2).Angulardistanceismeasuredinunitsof R≡( η)2+ ( φ)2.
4 The ATLAS Collaboration / Physics Letters B 805 (2020) 135426
Table 1
OverviewofsimulationtoolsusedtogeneratesignalandbackgroundprocessesandtomodeltheUEPS.DetailsonthetunesusedintheUEPSmodelcanbefoundin Ref. [41].ThePDFsetsarealsosummarized.AllHiggsbosoneventsweregeneratedassumingmH=125 GeV.Alternativeeventgeneratorsand configurationsusedto
estimatesystematicuncertaintiesareshowninparentheses.Thepredictionorderinthelastcolumnreferstothecrosssectionusedtonormalizetheeventsample. Process Matrixelement
(alternative)
PDF set UEPSmodel
(alternativemodel)
Predictionorderfortotalcrosssection VBF H Powheg-Boxv2 [59–63] PDF4LHC15 NLO [64] Pythia8 [65] approx. NNLO QCD + NLO EW [45,46,66]
(Herwig 7 [67,68])
ggF H Powheg-Boxv2 PDF4LHC15 NNLO Pythia8 N3LO QCD + NLO EW [69–72]
NNLOPS [73–75] (Herwig 7)
V H Powheg-Boxv2 [76] PDF4LHC15 NLO Pythia8 qq/qg→V H: NNLO QCD + NLO EW [77,78] gg→Z H: NLO + NLL QCD [79,80] tt H¯ MG5_aMC@NLO 2.2.2 [81,82] NNPDF3.0LO [83] Pythia8 NLO QCD + NLO EW [84–89]
W/Z +jets Sherpa2.2.1 [90] NNPDF3.0NNLO Sherpa2.2.1 [91] NNLO [92,93]
(MG5_aMC@NLO 2.2.2) (Pythia 8)
Electroweak W/Z j j Sherpa2.2.1 NNPDF3.0NNLO Sherpa2.2.1 LO
V V/Vγ∗ Sherpa2.2.1 NNPDF3.0NNLO Sherpa2.2.1 NLO
tt¯ Powheg-Boxv2 [94] CT10 [48] Pythia6.428 [95] NNLO+NNLL [96]
W t Powheg-Boxv1 [97] CT10 Pythia6.428 NLO [97]
ofthedetector.Themuonspectrometerincludesasystemof preci-siontrackingchambersandfastdetectorsfortriggering.The inte-gratedluminosityrecordedbyATLASisobtainedwiththeLUCID-2 detector [52].
A two-level trigger system is used to select events [53]. The first-level trigger is implemented in hardware and uses a subset ofthedetectorinformationtoreducetheacceptedratetoatmost 100 kHz.Thisisfollowedbyasoftware-basedtriggerthatreduces the accepted event rate to 1 kHz on average depending on the data-takingconditions.
4. Simulatedeventsamples
Samplesofsignalandbackgroundeventsweresimulatedusing variousMonteCarlo (MC)eventgenerators.Thegeneratorsandthe PDFsetsusedforthehard-scatteringprocessandthemodelsused forthepartonshowers,hadronization,andunderlying-event activ-ity (UEPS)aresummarizedinTable1.Inaddition,theorderofthe totalcross-sectioncalculationisgiven.
OnlyHiggsbosonproductionviaVBFisconsideredassignal, in-cludingthesignalsobservedasH→τ τ decayandH→W W∗→
ννdecay.TheanalysisisnotsensitivetoCPVinthe H→W W∗
decayvertexandtheshapeoftheOptimalObservable isthesame forthe H→W W∗→ νν and H→τ τ → 4ν decaymodes re-gardlessofthevalueofd. ˜ TheotherHiggsbosonproductionmodes –gluon–gluonfusion (ggF H ), V H , t¯t H – areconsidered as back-ground in this analysis, and all couplings other than the H V V
coupling were set to SM values. All SM signal and background samplesused inthisanalysisare thesameasthose employedin Ref. [41],andthesamenormalizationofthosesamplesisused.The only exception is the normalization of the electroweak Z j j
pro-cess. Here, theleading-order (LO) cross section calculatedby the Sherpa2.2.1 generator [54–57] ismultiplied bya factorof1.7to matchthecross-sectionvaluemeasuredby theATLAS experiment at √s=13 TeV [58]. An uncertainty of 25% from the measured cross-sectionoftheelectroweakZ j j process isappliedtothe nor-malization.
To simulatethe presence of non-vanishing values ofd in ˜ the
H V V vertex, amatrix-element reweighting methodis appliedto the VBF SM signal sample. The weightis defined asthe ratioof the squaredME value of theVBF process associatedwith a spe-cific amountof CPmixing(given interms ofd) ˜ to that obtained fromtheSM. Toextractthe weights,the leading-orderMEs from HAWK are used for the 2→2+H and 2→3+H processes
separately. The MEs are evaluated using the four-momenta and particleidentification codes ofthe initial- and final-statepartons and the Higgs boson of each event. The reweighting procedure has been validated [36] against samples generated with
Mad-Graph5_aMC@NLO [98] andprovestobeagoodapproximationof a full NLO description of the process withnon-vanishing values ofd.˜
For all samples, a full simulation of the ATLAS detector re-sponse [99] usingthe Geant4 program [100] wasperformed. The effect of multiple pp interactions in the same and neighbouring bunch crossings(pile-up) was included by overlaying minimum-bias events simulated with Pythia 8 using the MSTW2008LO PDF [101] andtheA2set [102] oftunedparametersoneach gener-ated signalandbackgroundevent.The numberofoverlaid events was chosen such that the distribution of the average number of interactions per pp bunch crossinginthesimulationmatchesthat observedindata.
5. Eventselection
In this analysis, events with at leasttwo jetsand a H→τ τ
decay candidate in the final state are selected.Decays ofthe τ -leptonswithallcombinationsofleptonic(τ→ νν¯ with=e, μ) and hadronic(τ→hadronsν) final states are considered. In the following, the eventpreselection, which closelyfollows Ref. [41], is summarized and the analysis strategy using gradient boosted decisiontrees(BDTs) [103] isdescribed.Afterdataquality require-ments [104],theintegratedluminosityofthe√s=13 TeV dataset used is 36.1 fb−1. The definitionof the reconstructed objects as wellasthetriggersusedinthisanalysiscorrespondtothoseused inRef. [41],wheremoredetailsaregiven.
Depending on the reconstructed decay modes of the two τ -leptons,eventsareseparatedintofouranalysischannels:the dilep-tonic same-flavour (τlepτlep SF), the dileptonic different flavour (τlepτlep DF), the semileptonic (τlepτhad), and the fully hadronic (τhadτhad)channel.Allchannelsrequireanexactnumberof identi-fiedandisolated τ-leptondecaycandidates,i.e.electrons,muons, and visible products of hadronic τ decays (τhad-vis), as defined in Ref. [41], corresponding to their respective final state. Events with additional τ-lepton decay candidates are rejected. This en-sures that theselected datasamples inthe fourchannelsdo not overlap.The two τ-leptondecaycandidatesare requiredtobe of oppositeelectricchargeandtofulfiltherequirementsonthe trans-versemomentumgiveninTable2.
The eventselection forthe four analysis channels is summa-rizedinTable2.Inthe τlepτlepand τhadτhadchannels,onlyevents with missingtransverse momentum Emiss
T >20 GeV are selected torejecteventswithoutneutrinocandidates.Tosuppressthelarge backgroundfrom Z→ productioninthe τlepτlepSFchannel,the requirementon EmissT istightened.Furthermore,an additional re-quirement is imposed on the quantity Emiss, hardT , obtained from
Table 2
Summaryoftheeventselectionrequirementsforthefouranalysischannels.InthecaseofthepTrequirementsonthe τ-leptondecaycandidates,theasteriskmarksthe lowestpTthreshold,whichvariesdependingonthetriggerused.DetailsofthisaregiveninRef. [41].Thetransversemomentumofthevisibledecayproductsofthe τ-lepton candidatewiththehigher(lower)transversemomentumisdenotedbypτ1
T (p τ2
T).TheinputvariablesusedfortheBDTtrainingandtheBDTscorethresholdusedtodefine thesignalregionsarealsoreported.
Channel τlepτlepSF τlepτlepDF τlepτhad τhadτhad
Preselection Two isolatedτ-lepton decay candidates with opposite electric charge pτ1 T >19∗/15∗GeV(μ/e) p e T>18 GeV p τhad T >30 GeV p τ1 T >40 GeV pτ2 T >10/15∗GeV(μ/e) p μ T>14 GeV p τlep T >21∗GeV p τ2 T >30 GeV mcoll τ τ >mZ−25 GeV mT<70 GeV 0.8< Rτ τ<2.5 30<m<75 GeV 30<m<100 GeV | ητ τ| <1.5 Emiss
T >55 GeV EmissT >20 GeV EmissT >20 GeV
Emiss, hardT >55 GeV
Nb-jets=0 VBF topology Njets≥2, p j2 T >30 GeV, mj j>300 GeV,| ηj j| >3 pj1 T >40 GeV p j1 T >70 GeV,|ηj1| <3.2 BDT input variables mMMC τ τ , mj j, Rτ τ, Cj j(τ1), Cj j(τ2), ptotT mvis τ τ, m τ1,EmissT T , p j3 T C(φmiss)/ √ 2 φτ τ EmissT /p τ1 T, E miss T /p τ2 T m vis τ τ,| ητ τ| p τ τEmiss T T ,| ητ τ|
Signal region BDTscore>0.78 BDTscore>0.86 BDTscore>0.87
an Emiss
T calculation considering only contributions from recon-structed objectsandneglecting contributions frominner-detector tracksoriginating fromthe vertexof thehard-scattering process, butnot associated withany of the reconstructed objects. In ad-dition,arequirementon theinvariant massofthe twolight lep-tons, m, is applied in the τlepτlep channels. A requirement on thedi-τ mass calculated inthe collinear approximation [105] of
mcoll
τ τ >mZ−25 GeV isintroduced inthe τlepτlep channelsto en-sureorthogonalitybetweenthisanalysisandtheanalysisof H→ W W∗→ νν[106],whichhasasimilarfinalstate.Inthe τlepτlep and τlepτhadchannels, thetop quarkbackgroundissuppressedby requiring that no jet with pT>25 GeV and |η|<2.5 contains
b-hadrons (b-jets). A multivariate algorithm [107,108] is used to identifyandselect b-jets withaworkingpointcorrespondingtoan averageefficiencyof85%,asmeasuredonasamplefromtopquark pairproduction.Lowtransversemass5 (mT<70 GeV) isrequired inthe τlepτhad channel to reject events with leptonic W decays. Requirementsontheangulardistancebetweenthevisibleproducts ofthetwoselected τ-leptondecays, Rττ , andtheir pseudorapid-itydifference,| ητ τ|,areappliedinthe τhadτhadchanneltoreject non-resonantbackgroundevents.
ToselectHiggsbosoneventsproducedbyVBF,all channels re-quireatleasttwojetswithtransversemomentum oftheleading jet pj1
T >40 GeV andofthesubleadingjet p j2
T >30 GeV,a large invariantmassofthetwoleadingjets, mj j>300 GeV,anda pseu-dorapidity separation of | ηj j|>3. In the τhadτhad channel, the requirements on the leading jet are raised to pj1
T >70 GeV and |ηj1|<3.2 to achieve a uniform trigger selection efficiency as a functionof pj1
T .Thisselection isreferred toastheVBF event se-lectioninthefollowing.
To construct a region enriched in VBF signal events, BDTs trained to discriminate between the VBF signal and the back-groundsareused inallchannels. Kinematicvariables usedinthe BDTtrainingcanbecategorizedasfollows:
5 Thetransverse massisdefinedasm T=
2p
TEmissT · (1−cos φ),where φ istheazimuthalseparationbetweenthedirectionsoftheleptonandthemissing transversemomentum.
• Properties of the Higgs boson which discriminate against all backgroundprocesseswithoutaHiggsboson:thevisiblemass of the di-τsystem, mvisτ τ , the transverse momentum of the
τ τEmissT system, pτ τE miss T
T , and the reconstructed Higgsboson mass, mMMCτ τ , determined using the missing-mass calculator (MMC) [109].
• Propertiesofaresonant di-τdecaywhichdiscriminateagainst processes with jets that are misidentified as τ-decay can-didates (referred to as “Misidentified τ”): the angular dis-tance Rττ , the difference in pseudorapidity | ητ τ|, and
the difference in azimuth φτ τ between the two visible τ -leptons.Inaddition,thetransversemomentumratio Emiss
T /p τ1 T (EmissT /pτ2 T ) between the E miss
T and the leading (subleading)
τ-candidate aswell asthe transverse massof the EmissT and theleading τ-candidate, mτ1,EmissT
T ,isused.Furthermore,the az-imuthalcentralityofEmissT , C(φmiss)/√2,whichquantifies the angular directionof the missing transverse momentum rela-tivetothevisible τ-decayproductsinthetransverseplane,is constructed.6
• Properties oftheVBF topology: mj j,the totaltransverse mo-mentum ptotT ,which is definedasthe transversemomentum of the system composed of all objects in a VBF event (τ1,
τ2, j1, j2, EmissT ), η-centralities, Cj j(τ1) and Cj j(τ2), of each
τ-candidaterelative to thepseudorapidity ofthetwo leading jets,7 and thetransverse momentum of the third leading jet
pj3
T whichissettozeroforeventswithexactlytwojets. The most important variables in the training are mMMCτ τ , mj j, and Cj j(τ1). The resulting BDT score (BDTscore) distributions are shown in Fig. 2 for events surviving the VBF event selection
6 C(φmiss)isdefinedas(A+B)/√A2+B2,whereA=sin(φ
Emiss
T −φτ2)/sin(φτ1−
φτ2)andB=sin(φτ1− φEmiss
T )/sin(φτ1− φτ2). 7 C j j(τ)=exp −4 (ηj1−ηj2)2 ητ−ηj1+η2 j2 2
,where ητ, ηj1and ηj2arethe
pseu-dorapiditiesofthe τ-candidateandthetwoleadingjets,respectively.Thisvariable hasavalue ofunitywhentheobjectishalfwayin ηbetweenthetwojets,1/e whentheobjectisalignedwithoneofthejets,and<1/ewhentheobjectisnot betweenthejetsin η.
6 The ATLAS Collaboration / Physics Letters B 805 (2020) 135426
Fig. 2. Post-fitBDTscoredistributionsaftertheVBFeventselectionforthe(a) τlepτlepSF,(b) τlepτlepDF,(c) τlepτhadand(d) τhadτhadanalysischannels.Theratiosofthedata tothepredictionareshowninthelowerpanels.TheobservedVBFsignal(μ =0.73,d˜= −0.01)isshownwiththesolidredlineonthetopofthehistogramstack.“Other bkg”denotesallbackgroundcontributionsnotlistedexplicitlyinthelegend.ThedashedlineshowstheobservedVBFsignalscaledupbyafactorof40andisnotpartof thehistogramstack.Thesizeofthecombinedstatistical,experimental,andtheoreticaluncertaintiesinthebackgroundisindicatedbythehatchedbands.
and show the ability of the BDT to separate the signal process from background processes. All figures in this Letter use signal strength μ (defined as the ratio of the measured cross section timesbranchingratiototheSMpredictionfortheVBFsignal pro-cess),backgroundnormalizations, andsystematicuncertainties as fittedbythefinalstatisticalanalysisdiscussedinSection8and re-ferred to aspost-fit. The signal purityincreases athighvalues of BDTscore.A thresholdvalue ofBDTscore isusedto define thefinal signalregion (SR)ineachchannel.Thisthresholdischosentoyield ahighsignalsignificanceandisgiveninTable2foreachchannel. Theefficiencyofthesignal selectionrelativetotheVBFevent se-lectionis 32%(27%) forthe τlepτlep SF (τlepτlep DF)channel, 29% forthe τlepτhadchannel,and49%forthe τhadτhad channel.The ef-ficiencyforthesumofbackgroundprocesses,on theother hand, is1.5%(0.8%)forthe τlepτlep SF(τlepτlepDF)channel,0.4%forthe
τlepτhadchannel,and1.1%forthe τhadτhad channel.IneachSRthe OptimalObservableisthenusedtoprobeforCPV.Nodependence ofthe meanvaluesof theOptimal Observable onBDTscore is ob-served,confirmingthattheSRselectioncriteriadonotintroducea CPasymmetry.
6. Backgroundestimation
Severalbackgroundprocessescontribute totheSReventyields in thefour analysis channels. The dominantcontributions in the
τlepτlepDF, τlepτhad,and τhadτhadchannelsarisefrom Z→τ τ pro-ductionandfromlight- andheavy-flavourjetsthat are misidenti-fiedaspromptleptonic orhadronic τ decays.Themisidentified τ
decaysinthe τlepτlepand τlepτhad channelsoriginatelargelyfrom
W +jets production with smaller contributions frommultijet and top quarkproduction,whileinthe τhadτhad channelthe contribu-tionfrommultijetproductiondominates.Inthe τlepτlepSFchannel thecontributionfromZ→ productionisdominant.Other back-ground contributions in all analysis channels originate from top quark pairandassociated W t production (denoted by “tt¯/W t” in thefollowing),dibosonproduction,andotherHiggsboson produc-tionmodes.
Background contributions withprompt leptonic orhadronic τ
decaysareestimatedfromsimulation,whiletheestimationofthe background contribution from misidentified τ decays is mostly data-driven [41]. Dedicated control regions (CR) are defined in datatonormalizethepredictionsofthefollowingbackground pro-cesses: Z→τ τ (for all channels), tt¯/W t and Z→ (only for the τlepτlepchannels),andthemisidentified τ decays(onlyforthe
τhadτhad channel).All other backgroundprocesseswithprompt τ decays (including other Higgsboson production modes) are nor-malizedtotheirSMprediction.
Toconstructa CRfor Z→τ τ production,theSRrequirement on the BDTscore (given in Table 2) is inverted for each analysis channel. This CR is called the “low-BDTscore CR” in the
follow-Fig. 3. Post-fitmMMC
τ τ distributionsinthelow-BDTscoreCRforthe(a) τlepτlepSF,(b) τlepτlepDF,(c) τlepτhadand(d) τhadτhadanalysischannels.Theratiosofthedatatothe predictionareshowninthelowerpanels.ThecontaminationoftheCRbysignalisnegligible.“Otherbkg”denotesallbackgroundcontributionsnotlistedexplicitlyinthe legend.Thesizeofthecombinedstatistical,experimental,andtheoreticaluncertaintiesinthebackgroundisindicatedbythehatchedbands.Therightmostbinsineachof thesubfiguresincludeeventyieldswithmMMC
τ τ valueslargerthantheshownrange.
ing. Since the purity of Z→τ τ production in the low-BDTscore CR ranges from 30% to 54% depending on the analysis channel,
Z→τ τ production is normalized to data in the Z boson mass peak of the mMMC
τ τ distributions, shown in Fig. 3. In the fit the Z→τ τ normalization is correlated across all analysis channels and the fit yields a normalization factor of 0.93±0.08. To en-surethat the normalization is valid in the SR, the modelling of the Z -boson and jet kinematic properties was checked in a val-idation region which is composed of Z → events with kine-maticpropertiessimilartothoseofthe Z→τ τ eventsintheVBF regionof each analysischannel. This region isdefined by select-ing two same-flavour leptons of opposite charge witha dilepton mass of m>80 GeV and low missing transverse momentum (Emiss
T <55 GeV).All VBFselection requirementsgiveninTable2 areapplied aswell. As inRef. [41], a slightpositive slope inthe ratio of the data to the Sherpa simulation as a function of mj j isobserved. In this analysis, the simulated Z→τ τ and Z →
eventsare reweighted to the observed mj j distribution after the VBFeventselection,whichresultsinasmallchangeinthe accep-tanceof Z→τ τ and Z→ eventsintheSR.
Ineach ofthetwo τlepτlep channels,atop quarkCRisdefined by inverting the veto on b-tagged jets and not applying the se-lectiononthe BDTscore. Thenormalizationof t¯t/W t production is constrained by the event yield in these CRs, corresponding to a normalizationof 1.16±0.06 from the combined fit to the data. Additionally,another CRisdefinedtonormalizethe Z→ pro-cessforthe τlepτlepSFchannel.Again,theselectionontheBDTscore
isnotapplied,andtherequirementonthedileptoninvariantmass is changed to 80<m<100 GeV. The observed event yield in the Z→ CRconstrainsthe normalizationofsimulated Z →
eventsinthe τlepτlepSFchannelto1.0±0.4.
In the τhadτhad channel, the background from misidentified hadronic τ decays is dominated by multijet events. This back-ground process is modelled using a template extracted from
τhad-vis candidates with one, two, orthree associated tracks that pass all selection requirements, but fail the opposite-charge re-quirement.Before thefinalfit,thetemplateisnormalizedtodata by a fit ofthe | ητ τ| distribution afterthe preselection, but
re-movingtherequirementon| ητ τ|.Inthefinalfitthetemplateis
normalized to datain the mMMC
τ τ distribution ofthe low-BDTscore
CRinthe τhadτhad channel.Then, themultijetbackgroundis nor-malizedwithafactorof0.99±0.09 relativetothepre-fit normal-ization.
The modelling of the Optimal Observable distribution forthe background processes is validated in all CRs. Fig. 4 shows Opti-malObservabledistributionsinthelow-BDTscoreCRforallanalysis channels, where thebackgroundprocesses havebeen normalized totheresultofthefit.Neithertheobservednorthepredicted dis-tributionsinanyCRshowhintsofanasymmetryornon-vanishing mean values of the Optimal Observable caused by event recon-structionandselectionwithinuncertainties.Thedataandthe pre-dicted distributions are observed to be compatiblewithin uncer-tainties hereaswell as inthe top quark and Z→ CRsof the
8 The ATLAS Collaboration / Physics Letters B 805 (2020) 135426
Fig. 4. Post-fitOptimalObservabledistributionsinthelow-BDTscore CRforthe(a) τlepτlepSF,(b) τlepτlepDF,(c) τlepτhad and(d) τhadτhadanalysischannels.Theratiosof thedatatothepredictionareshowninthelowerpanels.ThecontaminationoftheCRbysignalisnegligible.“Otherbkg”denotesallbackgroundcontributionsnotlisted explicitlyinthelegend.Thesizeofthecombinedstatistical,experimental,andtheoreticaluncertaintiesinthebackgroundisindicatedbythehatchedbands.
7. Systematicuncertainties
Theeffectsofthesystematicuncertaintiesontheyieldsinboth the SRsand CRsand onthe shape of theOptimal Observable in theSRs,aswell asthe mMMC
τ τ distributions intheCRs,are
evalu-atedfollowingtheproceduresinRef. [41].Nosourcesofsystematic uncertaintiesintroduceasignificantasymmetryintheOptimal Ob-servable distribution. The sources of uncertainty can be grouped into two categories: experimental and theoretical. The dominant experimentaluncertaintiesstemfromthedeterminationofthejet energy resolution and scale [110], the τhad-vis energy scale and resolution [111], andthe τhad-vis reconstruction andidentification efficiencies [112]. Other sources of uncertainty are the electron (muon) energy (momentum) scale and resolution, lepton identi-fication and isolation [113–115], missing transverse momentum reconstruction [116], b-tagging efficiency [107,117], modelling of pile-up, and luminosity measurement [118]. The luminosity un-certainty of 2.1% [118] is only applied to the VBF signal and to background processes normalized to theoretical predictions. Un-certaintiesinbackgroundsfrommisidentified τ-leptonsarisefrom the limited statisticalprecision ofthe data-driven templates and corrections used, fromclosure tests performed in regions where the τ-leptonsarerequiredtohavethesamecharge,andfromthe subtractionoftheelectroweakcontributions.
Theoretical uncertainties affecting the total cross section are evaluatedfortheHiggsbosonproductioncrosssectionsforggF H ,
V H , and t¯t H production by varying the QCD factorization and
renormalizationscalesaswellasthePDFmodelfollowingthe rec-ommendationsinRef. [119].Also,uncertaintiesinthe H→τ τ and
H→W W∗ branchingratiosareconsidered [119].Theoretical un-certainties in the MC modelling are considered forthe VBF and gluon–gluon fusionproduction ofthe Higgs bosonas well asfor
Z→τ τ production. For all simulated background contributions other than Z →τ τ, no theoretical uncertainties are considered, as their impact is negligible. Uncertainties in MC modelling are assessed bya comparisonbetweennominalandalternativeevent generators andUEPS models,asindicated inTable 1. Inaddition, the effects of QCD factorization and renormalizationscale varia-tions,matching-scalevariations(inthecaseof Z→τ τ only),and PDF model uncertainties are evaluated. As an additional uncer-tainty in the Z→τ τ and Z → processes, the full difference between thesample reweighted to the observed mj j distribution andthe sample without reweighting isapplied to thefull analy-sis.Anuncertaintytoaccountforthesignalreweightingprocedure described inSection 4wasconsideredandfoundtobenegligible. TheuncertaintyduetolimitedMCsamplesizeisevaluatedforthe sumofallMC-basedbackgroundprocessesineachanalysisbin. 8. Fittingprocedure
The estimate of d is ˜ obtained using a binned maximum-likelihood fit (ML-fit) performed simultaneously on the SRs and all introduced CRs, which are included in order to constrain background normalizations and nuisance parameters describing
the systematic uncertainties. The ML-fit uses the distribution of the Optimal Observable in each of the four high-BDTscore SRs, one for each analysis channel. The mMMC
τ τ distributions in the
low-BDTscore region for each channel are included in the ML-fit, andso are the eventyields in the Z → (τlepτlep SF) and top quark(τlepτlep SFandDF)CRs.
Theinclusionofthe mMMC
τ τ distributionsinthelow-BDTscore
re-gionsprovidesthemainconstraintonthe Z→τ τ normalization, whichisfreetofloatintheML-fit.The Z→ backgroundinthe
τlepτlep SF channel and top quark backgrounds in the τlepτlep SF andDFchannelsare alsofreetofloat,andtheir contributionsare constrainedbytheinclusionofCRsintheML-fit.
Thenormalization ofthe signal isnot constrained inthe ML-fit,sothat theanalysisonlyexploitstheshapeofthedistribution of the Optimal Observable in the estimation of d. ˜ Any possible model-dependenceofthe crosssectionon CP-mixing scenariosis notexploited.TherelativecontributionofthetwoHiggsboson de-caymodes(H→τ τ and H→W W∗)tothesignal(relevantonly forthe τlepτlep channel) isassumed to be correctlypredicted by theSM.Allother Higgsbosonproductionmodesforthesedecays areconsideredasbackgroundandarenormalizedtotheirSM pre-dictedyields.
TheML-fitusesa binnedlikelihood functionL(x; μ,θ ),which isafunctionofthedatax,thefree-floatingsignalstrength μ,and nuisanceparametersθ corresponding tothesystematic uncertain-tiesmentioned in Section 7.The likelihood function is evaluated foreach d hypothesis ˜ using the relevant reweighted signal tem-platesdefinedinSection4,withthebackgroundmodelunchanged, andanegativelog-likelihood(NLL)curve canthenbeconstructed asafunctionofd.˜
The parameter of interest, d, ˜ is obtained at the point where theNLLcurvereachesaminimum.Centralconfidenceintervalsare obtainedbyreadingoffthepointsontheNLLcurvewhichexceed theminimumvaluebyacertainamount.
9. Results
ForaCP-evenHiggsboson,themeanvalueoftheOptimal Ob-servable forthesignalandbackgroundprocessesisexpectedtobe zeroifanyeffectsfromtherescatteringofnewparticlesinloops canbeneglected.However, CP-violatingeffectscouldresultinthe meanvalueoftheOptimalObservable indatadeviatingfromzero, allowinganalmostmodel-independenttestforCP-violatingeffects inthismeasurement.
TheobservedvaluesforthemeanoftheOptimalObservable in data,alongwiththeir statisticaluncertainties,are summarizedin Table3forthefourchannelsinthisanalysis,aswellastheir com-bination.Thecombinedmeanisobtainedbyweighting themean value of each individual channel by the inverse of its respective variance. These values are fully consistent with zero, so no evi-denceofCPVisobserved.
ToextractconfidenceintervalsfortheCP-mixing parameterd, ˜
theML-fitdescribedinSection8iscarriedout.Thepost-fit distri-butionsoftheOptimalObservable inthevariousanalysischannels are shownin Fig. 5.Here thevalue ofthe parameter of interest ˜
d, thevalues ofthenuisance parameters,andthe normalizations ofthesignalandbackgroundprocesseshavebeenadjustedwithin theirallowedconstraintstominimizetheNLLcurve.Valuesofthe NLLareevaluatedinstepsof ˜d=0.01,andthesmallestvalueof theNLLisobservedatd˜= −0.01.Thisisthevalueofd that ˜ isused forthepost-fitdistributionsandeventyields.Basedupon interpo-lationsbetweenthediscreteevaluationsofthevariousNLLvalues asafunction ofd, ˜ thebest estimatorford is ˜ −0.013+−0.0480.077.This value isconsistent with theSM expectationof zero,andno evi-denceofCPV isobserved usingthisapproach. Thebest-fit signal strengthfromtheML-fitis μ =0.73±0.47.
Table 3
MeanvaluesoftheOptimalObservable withstatisticaluncertaintiesthatare ob-servedindataforthefouranalysischannelSRsandtheircombination.
Channel Optimal observable
τlepτlepSF −0.54±0.72
τlepτlepDF 0.71±0.81
τlepτhad 0.74±0.78
τhadτhad −1.13±0.65
Combined −0.19±0.37
While the predicted background distributions for the Opti-malObservable are not perfectlysymmetric,they are statistically consistent with a symmetric distribution. This slight asymmetry causes the expected confidence intervalsfor d to ˜ also be asym-metric.
Tables 4 and 5 display the fitted event yields of the signal (μ=0.73,d˜= −0.01) andvarious background processes for the SRs of each channel, along with the corresponding number of events observed in data. For reference, the signal yields for the SMexpectation(μ=1,d˜=0)arealsoshown.
Theobservedandexpected NLL curvesareshowninFig.6(a) asafunctionofd. ˜ Theexpectedcurvesareobtainedinatwo-step process:firstly,nuisanceparametersandbackgroundnormalization factors are constrained via a ML-fit to all analysis CRs, exclud-ing the SRs; then another fit isperformed inall SRsand CRsto pseudo-datawhich were createdwiththe best-fitparameter val-ues from the first step. This two-step process ensures that the nuisanceparametersandthebackgroundnormalizationfactorsfor theexpectedsensitivityaresetto valuesthatare consistentwith theobserveddataintheanalysisCRs.Theexpected NLL curveis shownford˜=0 and μ =1 andrepresentsthebestestimateofthe sensitivityoftheanalysisbasedonSMexpectations.Another NLL curve withd˜ =0 and the signal strength μ set to the observed value of0.73 is alsoshowninorderto demonstratethedecrease insensitivityduetothelowerthanexpectedeventyields(see Ta-bles4and5).AlsoshownforcomparisoninFig.6(a)isthepre-fit expected NLL curve, which is obtained using a pseudo-dataset where the eventyields and distributions in theSRs and CRsare set to the SM expectations for both the signal (with d˜=0 and
μ=1)andbackgroundprocesses.Thisdemonstratesthatthe pre-ferredvaluesofthenuisanceparametersandnormalizationfactors basedontheobserveddatainthebackgroundCRsintheexpected NLL curveresultinadecreaseinsensitivitytod when ˜ compared withthepre-fitexpectedcurve.
Theeffectofsystematicuncertaintiesonthesensitivitytod can ˜
beseeninFig.6(b).Here,theexpected NLL curvesareshownfor ˜
d=0 and μ =1,withandwithouttheeffectofsystematic uncer-tainties.Toassesstheimpactofsystematicuncertaintiesstemming from jet reconstruction, τ-lepton identification, and MC sample size,expected NLL curvesarealsoshownwherethenuisance pa-rameterscorrespondingtothesystematicuncertaintiesinquestion havebeenremovedfromthelikelihoodfunction.Itisevidentthat the experimental uncertainties related to jet reconstruction have thelargesteffectonthesensitivityofthisanalysistod.˜
Toobtaininsightintothepreferredvaluesofd obtained ˜ forthe individualOptimal Observable distributionsinthedifferent analy-sis channels, NLL curvesfor eachindividual channel are shown inFig.6(c),andcomparedwiththecombinedresult.Forthese in-dividual NLL curves,onlyeventyieldinformationfromtheother three signal regions that are not beingfeatured is used, so that thedistributionofeventsintheOptimalObservable intheseother signal regions is not exploited in the ML-fit. For these individ-ualchannel NLL curves,thesignal strengthisconstrainedtobe positive sothattheML-fit isstableandinsensitiveto eventyield fluctuationsinthe individualchannel SRsthat arise fromsmaller
10 The ATLAS Collaboration / Physics Letters B 805 (2020) 135426
Fig. 5. Post-fitdistributionsoftheevent yields(dividedbythe binwidth)as afunctionoftheOptimal Observable inthe SRsfor the(a)τlepτlep SF,(b)τlepτlep DF, (c)τlepτhadand(d)τhadτhadanalysischannels.Thevaluesofd,˜ thesignalstrength μ,thenormalizationofbackgroundprocesses,andnuisanceparametersfortheeventyield predictionaresettothosewhichminimizetheNLL.Theratiosofthedatatothepredictionareshowninthelowerpanels.Thesizeofthecombinedstatistical,experimental andtheoreticaluncertaintiesinthepredictedeventyieldsisindicatedbythehatchedbands.
Table 4
Post-fiteventyieldsintheSRsforthe τlepτlepSFand τlepτlepDFanalysischannels. TheZ→ anddibosonbackgroundsaregroupedtogetherinasinglebackground categoryforthe τlepτlepDFchannel.Forcomparison,theexpectedsignalyieldsfor theSMexpectation(μ =1,d˜=0)arealsoshown.
Process τlepτlepSF τlepτlepDF
Data 26 30 VBF H→τ τ/W W (μ=0.73,d˜= −0.01) 3.3 ± 2.1 5.1 ±3.1 VBF H→τ τ/W W (μ=1,d˜=0) 4.5 ± 2.9 6.9 ±4.4 Z→τ τ 6.6 ± 3.7 8.2 ±3.8 Fake lepton 0.02± 0.20 2.3 ±0.7 t¯t + single top 3.8 ± 2.3 10.6 ±5.5 Z→ 11 ±18 1.8 ±1.1 Diboson 0.70± 0.59 ggF H / V H / tt H, H¯ →τ τ/W W 0.49± 0.48 0.70±0.30 Sum of backgrounds 23 ±17 23.6 ±6.1
samples.Thisconstraintisresponsiblefortheplateauinthe NLL curveoccurringatnegativevaluesinthe τlepτhadchannel.
Anobserved68%CLintervalofd˜∈ [−0.090,0.035] isobtained fromtheobserved NLL curveusingOptimalObservable distribu-tions inall SRs.Thecorresponding expectedinterval, basedupon the expected NLL curve for d˜ =0 and μ =1 in Fig. 6(a) is
Table 5
Post-fiteventyieldsintheSRsfor the τlepτhad and τhadτhad analysischannels. Theline “Other backgrounds”includes topquark (t¯t and single top), diboson, and Z→ backgrounds.BackgroundsfromW(→τhadν)+jetsproductioninthe τhadτhad channelarealso includedin“Other backgrounds”.Forcomparison,the expectedsignalyieldsfortheSMexpectation(μ =1,d˜=0)arealsoshown.
Process τlepτhad τhadτhad
Data 30 37 VBF H→τ τ (μ=0.73,d˜= −0.01) 11.8± 7.4 8.9±5.6 VBF H→τ τ (μ=1,d˜=0) 16 ±10 12.3±7.7 Z→τ τ 7.8± 3.5 15.5±5.2 Fake lepton/τ 6.2± 1.0 5.4±2.7 ggF H / V H / t¯t H, H→τ τ 2.1± 1.5 2.8±1.4 Other backgrounds 2.8± 3.1 2.3±0.8 Sum of backgrounds 19.0± 5.5 26.0±6.6 ˜
d∈ [−0.035,0.033].This representsan improvementon the con-fidence interval ford set ˜ in Ref. [36]. Whileno observed 95% CL intervalford can ˜ bequoted,thecorrespondingexpectedintervalis ˜
d∈ [−0.21,0.15] at95% CL.Theasymmetryintheseexpected in-tervalsstemsfromtheslightlyasymmetricOptimalObservable dis-tribution ofthe backgroundestimates in the SRs, caused by the limitedsamplesizesforthebackgroundpredictions.
Fig. 6. (a)Theobserved NLL curveasafunctionofd values.˜ Forcomparison,expected NLL curvesarealsoshown. Theconstraintsonthenuisanceparametersand normalizationfactorsarefirstdeterminedinaCR-onlyfit,andthenafittopseudo-datacorrespondingtothesenuisanceparameters,normalizationfactors,andtod˜=0,μ = 1 ord˜=0,μ =0.73 isperformedtoobtainthese NLL curves.Apre-fitexpected NLL isalsoshown,usingpseudo-datacorrespondingtod˜=0 and μ =1 inthesignal andcontrolregions.(b)Theexpected NLL curves(d˜=0,μ =1)comparingthesensitivityofthefitwithandwithoutsystematicuncertainties.Forcomparison,othercurves areshownwhichremovetheeffectofjet-basedsystematicuncertainties, τ-basedsystematicuncertainties,andMCstatisticaluncertainties.(c)Theobserved NLL curves foreachanalysischannelasafunctionofd,˜ comparedwiththecombinedresult.Fortheindividualanalysischannel NLL curves,onlyeventyieldinformationintheother SRsisused,ensuringthattheOptimalObservable distributionsintheotherSRsdonotinfluencethepreferredvalueofd.˜ Thesignalstrengthisconstrainedtobepositivein theseindividualchannel NLL curves.Forallfigures,thedashedhorizontallinesshowthevaluesof NLL usedtodefinethe68%and95%confidenceintervals.
The intervals based upon the pre-fit expected NLL curve in Fig.6(a),wherethenuisanceparametersandbackground normal-izationfactorsdo nottake into accountthe observeddata inthe CRs,ared˜∈ [−0.032,0.031]at68%CLandd˜∈ [−0.12,0.10]at95% CL.
10. Conclusion
TheCPinvarianceoftheHiggsbosoncouplingtovectorbosons has been tested in the VBF H→τ τ process in 36.1 fb−1 of √
s=13 TeV proton–protoncollisiondataobtainedwiththeATLAS detectorat theLHC. In this analysis, an Optimal Observable was usedandconfidenceintervalsweresetontheCP-mixing parame-terd.˜
Since the mean of the Optimal Observable observed in data isconsistent withzero,andtheobtainedconfidenceintervalsfor ˜
d are consistentwiththeStandardModelvalued˜=0,noevidence ofCPviolation isobserved fromthisanalysis. Dueto lower than expectedsignal yields in data, noconstraints on d can ˜ be setat 95% CL,whilethecorrespondingStandardModelexpectationisd˜∈ [−0.21,0.15].Anobserved 68% CLinterval ofd˜∈ [−0.090,0.035] isobtained, whilethecorrespondinginterval basedonthe expec-tationisd˜∈ [−0.035,0.033].
Declarationofcompetinginterest
Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.
Acknowledgements
We thank CERN forthe very successfuloperation of the LHC, aswell as thesupport staff fromour institutionswithout whom ATLAScouldnotbeoperatedefficiently.
WeacknowledgethesupportofANPCyT,Argentina;YerPhI, Ar-menia;ARC,Australia;BMWFWandFWF,Austria; ANAS, Azerbai-jan; SSTC,Belarus;CNPqandFAPESP,Brazil; NSERC,NRCandCFI, Canada;CERN;CONICYT,Chile;CAS,MOSTandNSFC,China; COL-CIENCIAS,Colombia;MSMTCR,MPOCRandVSCCR,Czech Repub-lic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRT, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Cen-ter, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway;MNiSW andNCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russia Federation;JINR;MESTD, Serbia;MSSR,Slovakia; ARRSandMIZŠ, Slovenia;DST/NRF,SouthAfrica; MINECO,Spain;SRCand
Wallen-12 The ATLAS Collaboration / Physics Letters B 805 (2020) 135426
berg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom;DOEandNSF,UnitedStatesofAmerica. Inaddition, in-dividualgroupsandmembershavereceivedsupport fromBCKDF, Canarie, Compute Canada and CRC, Canada; ERC, ERDF, Horizon 2020,MarieSkłodowska-CurieActionsandCOST,EuropeanUnion; Investissementsd’AvenirLabex,Investissementsd’AvenirIdex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya and PROMETEO Programme Generalitat Valenciana,Spain;GöranGustafssons Stiftelse,Sweden;TheRoyal SocietyandLeverhulmeTrust,UnitedKingdom.
The crucial computingsupport fromall WLCG partners is ac-knowledged gratefully,in particularfromCERN, theATLAS Tier-1 facilities atTRIUMF(Canada),NDGF(Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA(Germany), INFN-CNAF (Italy), NL-T1 (Netherlands),PIC (Spain), ASGC (Taiwan), RAL (UK) andBNL (USA),theTier-2facilitiesworldwideandlargenon-WLCGresource providers.Majorcontributorsofcomputingresourcesarelisted in Ref. [120].
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