Measurement and interpretation of differential cross sections for Higgs boson production at root s=13 TeV

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SISTEMA DE BIBLIOTECAS DA UNICAMP

REPOSITÓRIO DA PRODUÇÃO CIENTIFICA E INTELECTUAL DA UNICAMP

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https://www.sciencedirect.com/science/article/pii/S037026931930228X

DOI: 10.1016/j.physletb.2019.03.059

Direitos autorais / Publisher's copyright statement:

©2019

by Elsevier. All rights reserved.

DIRETORIA DE TRATAMENTO DA INFORMAÇÃO

Cidade Universitária Zeferino Vaz Barão Geraldo

CEP 13083-970 – Campinas SP

Fone: (19) 3521-6493

http://www.repositorio.unicamp.br

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Physics Letters B 792 (2019) 369–396

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

and

interpretation

of

differential

cross

sections

for

Higgs

boson

production

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

Article history:

Received16December2018

Receivedinrevisedform24March2019 Accepted29March2019

Availableonline3April2019 Editor:M.Doser

Keywords:

Differentialcrosssections Combination

Higgsbosoncouplingmodiﬁers

Differential Higgs boson (H) production cross sections are sensitive probes for physics beyond the standardmodel.Newphysicsmaycontributeinthegluon-gluonfusionloop,thedominantHiggsboson productionmechanismattheLHC,andmanifestitselfthroughdeviationsfromthedistributionspredicted bythe standardmodel.Combinedspectrafor theH_→

γ γ

,H_→ZZ,andH_→bb decaychannelsand theinclusiveHiggsbosonproductioncrosssectionarepresented,basedonproton-protoncollisiondata recordedwiththeCMSdetectorat√s=13TeV correspondingtoanintegratedluminosityof35.9 fb−1. The transversemomentumspectrumisused toplacelimits ontheHiggsbosoncouplingstothe top, bottom,and charmquarks, as wellas its directcouplingto thegluon ﬁeld.No signiﬁcantdeviations fromthestandardmodelareobservedinanydifferentialdistribution.Themeasuredtotalcrosssectionis 61.1±6.0(stat)±3.7(syst) pb,andtheprecisionofthemeasurementofthedifferentialcrosssectionof theHiggsbosontransversemomentumisimprovedbyabout15%withrespecttotheH→

γ γ

channel alone.

1. Introduction

The Higgs boson (H), whose existence is predicted by the Brout–Englert–Higgs mechanism [1–3], is responsible for elec-troweaksymmetrybreakinginthestandardmodel(SM).Sincethe discovery [4–6] ofaparticlecompatiblewiththeSMHiggsboson attheCERNLHC,extensiveeffort hasbeendedicatedtothe mea-surementofitspropertiesandcouplings.

Inthisanalysiswe measuretheinclusiveanddifferentialcross sections for the production of Higgs bosons. Comparedwith in-clusivemeasurements [7–9], differential distributions provide ex-tended information on the Higgs boson couplings, which can be extractedby ﬁttingparametrizedspectratoa combinationof dif-ferentialcrosssections.WhentheHiggsbosoncouplingstoquarks andtootherbosonsarevariedwithrespecttotheirSMvalues, dis-tortionsof thepredicteddifferential crosssection spectraappear, which are particularly pronounced in the transverse momentum (pT)distribution.

AprecisemeasurementoftheHiggsbosoncouplingsrepresents animportanttestoftheSM,asthecouplingsaresensitiveto sev-eral SM extensions [10,11]. While the couplings to the top ( yt) and bottom ( yb) quarks are known with fair precision, there is

_{E-mail address:}_cms_-publication_-committee_-chair_@cern_.ch_.

stilla relativelylargeuncertaintyinthemeasurementofthe cou-plings to lighterquarks such asthecouplingto the charmquark ( yc).Aproof-of-conceptstudydetermininglimitsonthe modiﬁca-tion of the SM Higgs boson coupling ( ySM_c ) to the charm quark,

κ

c

=

yc/ySMc , from the Higgs boson transverse momentum (pHT) distributionwas performedin Ref. [12]. ReinterpretingtheATLAS Collaboration measurements in Ref. [13], this analysis yields the overall bounds

κ

c

∈ [−

16

,

18

]

at95% conﬁdencelevel (CL).Using thesamedataset,areinterpretationofasearchbytheATLAS Col-laborationfortheH

→

J

/

ψ

γ

channel [14] yields

|

κ

c

|

<

429 at95% CL [15]. Morerecently,studies fromtheATLAS Collaboration [16,

17], using datacollected at

√

s

=

13TeV corresponding to an in-tegratedluminosityof36

.

1fb−1,yieldanobservedupperlimiton the H

→

J

/

ψ

branching fractionof 3

.

5

×

10−4 _at _95% _{CL that} _is an improvement of about a factor two with respect to the re-sult obtained in Ref. [14], and an observed upper limit on the product of the production cross section and branching fraction

σ

(

pp

→

ZH

)

B(

H

→

cc

)

of110 timestheSMvalueat95%CL. Both the ATLAS and CMS Collaborations have reported mea-surementsofdifferentialHiggsbosonproductioncrosssectionsat

√

s

=

8 and 13TeV [18–28].The CMSCollaborationhasmeasured differential Higgs boson production cross sections in the H

→

γ γ

[25] andH

→

ZZ(∗)

→

4

(

=

e or

μ

) [27] decaychannels us-ingdatarecordedbytheCMSexperimentin2016at

√

s

=

13TeV, correspondingtoan integratedluminosity of35

.

9fb−1.Wereport https://doi.org/10.1016/j.physletb.2019.03.059

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measurementsofdifferentialcrosssectionsobtainedbycombining theseresults.Additionally,weincludeasearchfortheHiggsboson producedwithlarge pT anddecayingtoabottomquark-antiquark (bb)pair [29] inthecombinationofthe pH

T spectra.The differen-tialcrosssectionsforthefollowingobservablesarecombined: pH_T, theHiggs bosonrapidity

|

yH

|

,the numberof hadronicjets Njets, andthetransversemomentumoftheleadinghadronicjet pjet_T .

We interpret the pH

T spectrum in terms of Higgs boson cou-plings.Inordertotakeintoaccountasmanydegreesoffreedomas possible,multiplecouplingsarevariedsimultaneously.Wepresent resultsobtainedby varyingsimultaneously(i) themodiﬁerofthe Higgsbosoncouplingtothecharmquark

κ

c andthebottomquark

κ

b,(ii)themodiﬁeroftheHiggsbosoncouplingtothetopquark

κ

t andthecoeﬃcient cg ofthe anomalousdirect couplingtothe gluonﬁeldintheheavytopquarkmasslimit,and(iii)

κ

t and

κ

b.

The SM production cross sectionsand decayrates depend on the Higgs boson mass mH. We assume a Higgs boson mass of 125

.

09GeV forallmeasurementsinthispaper,basedonthe com-binedATLASandCMSmeasurementusingproton-protoncollision datacollectedin2011and2012 [8].

2. Theoreticalpredictions

Differentialcrosssectionsmaybeusedtoconstrainmodel pa-rameters.InthecaseofHiggsbosonproductionvia gluonfusion, thedominant productionmode atthe LHC,ﬁnite quark mass ef-fectsandmoderatevariationstoHiggsbosoncouplingsmay man-ifestthemselvesthroughdistortionsofthe pH

T spectrum.We inter-pretthe pH_T spectrum forgluon fusion in termsof modiﬁcations of the couplings of the Higgs boson using two models: one tai-loredtoheavyquarksandthussensitivetoeffectsathighpT [30, 31],andthe other considering the effectoflighter quarks inthe gluonfusionloop [12].The crosssectionforHiggsboson produc-tioninassociation withtop quarksistakentoscale quadratically with

κ

t.Theother productionprocessesaretakentobe indepen-dent of thesecouplings. The couplingmodiﬁers are described in thecontextofthe

κ

-framework [32]:

κ

i

=

yi

ySM

i

,

(1)

where yi is theHiggsbosoncouplingto particlei. TheSM value ofany

κi

isequalto1.

Recent developments in pT resummation procedures have al-lowed more accurate calculations of the pH_T spectrum when in-cluding the effects of lighter quarks on Higgs boson production via gluon fusion [33–36]. The pH

T spectrum for gluon fusion has beencalculatedforsimultaneousvariationsof

κ

c and

κ

b [12], tak-inginto accountthe interferenceofthetop quarkloop withthat from the bottom and charm quarks in the gluon fusion produc-tionloop,providinganovelapproachtoconstrainthesecouplings viathepH_T spectrum.Weparameterizethevariationscomputedin Ref. [12] withaquadraticpolynomialforeachbinofthepH

T spec-trum.TheHiggsbosoncouplingtothetopquarkisﬁxedtoitsSM valueinthismodel.ThecalculationsfromRef. [12] aregivenupto thescaleofthe Higgsbosonmass,andthusthe H

→

bb channel (forwhich thelower limit ofthe pH

T spectrum is 350GeV) isnot usedasinputfortheresultsobtainedwiththismodel.

A second model producing simultaneous variations of

κ

t, cg, and

κ

b by adding dimension-6 operators to the SM Lagrangian has been built in Refs. [30,31]. This study employs an analytic resummationperformeduptonext-to-next-to-leading-logarithmic (NNLL)orderinordertoobtainthe pH_T spectrumat next-to-next-to-leading order

+

NNLL (NNLO

+

NNLL) accuracy.The dimension-6

operator whose coefficient is cg yields a direct coupling of the Higgs field to the gluon field with the same underlying tensor structure as in the heavy-top mass limit. In the SM, the value of cg equals 0.The introduction ofcg in theeffective Lagrangian is given in Ref. [31] and the inclusive cross section is given by

σ

12cg

+

κ

t

2

σ

SM.Twootheroperatorsareincludedinthe La-grangianto describemodiﬁcationsofthetopandbottomYukawa couplings with coeﬃcients

κ

t and

κ

b, respectively. While the model allows simultaneous variation of all three coupling modi-ﬁers, we consideronly simultaneousvariations of

κ

t andcg,and of

κ

t and

κ

b.The precomputedspectrafromRef. [30] areusedas inputandparametrizedusingaquadraticpolynomial.

3. TheCMSdetector

The central feature of the CMS apparatus is a superconduct-ing solenoid of6 m internal diameter, providing a magneticﬁeld of 3.8 T. Withinthe solenoidvolume are asilicon pixeland strip tracker, a lead tungstate crystalelectromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrel andtwoendcap sections.Forwardcalorimeters extendthe pseudorapidity(

η

)coverageprovidedbythebarrelandendcap de-tectors.Muonsaredetectedingas-ionizationchambersembedded inthesteelﬂux-returnyokeoutsidethesolenoid.Amoredetailed description oftheCMSdetector,together witha deﬁnitionofthe coordinate systemusedandtherelevant kinematicvariables, can befoundinRef. [37].

4. Inputstothecombinedanalysis

For all the analyses used as input to the combination (H

→

γ γ

[25], H

→

ZZ(∗)

→

4

[27], and H

→

bb [29]), the data set

corresponds to an integratedluminosity of35

.

9fb−1 recorded by the CMSexperiment in2016. The H

→

bb decay channel is only includedinthecombinationofthepH

T spectra,improvingthe mea-surements atthe higher end of the distribution where the data from the H

→

γ γ

and H

→

ZZ decay channels are limited. All analyses provide the parametrization of the folding matrix Mk_ji (which isthe probability for an eventin generator-level bin i to be reconstructed in bin j and category k) in terms of a com-mongenerator-levelbinning,thatisusedforthecombinedspectra. Given the limited statisticalprecision in the individual channels, the results ofthe H

→

ZZ and H

→

bb channels individually are reportedforacoarserbinning,whichisprovidedinTables1–4for eachoftheobservables.Thisbinningcoincideswiththebinningat thereconstructionlevel.

The SM prediction for the differential cross sections is sim-ulated with MadGraph5_amc@nlo v2.2.2 [38] for each of the fourdominantHiggsbosonproductionmodes:gluon-gluon fusion (ggH),vector bosonfusion,associatedproductionwithaW/Z bo-son, andassociatedproductionwitha topquark-antiquarkpair.A contributionfromHiggsbosonproductioninassociationwith bot-tomquarksisnotsimulated,butincludedassumingitsacceptance is equal to that from Higgs boson production via gluon fusion. Thematrixelementcalculationincludestheemissionofuptotwo additional partons and is performed at NLO accuracy in pertur-bative quantum chromodynamics (QCD). Events are interfaced to pythia8.205 [39] forpartonshoweringandhadronizationwiththe CUETP8M1 [40] underlyingeventtune.Thematrixelement calcu-lationismatchedtothepartonshowerfollowingtheprescription in Ref. [41]. A weight depending on pH_T and Njets is applied to simulated ggH events to matchthe predictions from the nnlops program [42,43], as discussed in Ref. [9]. The set of parton dis-tribution functionsused in all simulations isNNPDF3.0 [44]. The hadronicjetsare clusteredfromtheparticle-ﬂow candidates [45]

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The CMS Collaboration / Physics Letters B 792 (2019) 369–396 371

Table 1

Thereconstruction-levelbinningfor

p

H

T fortheH→γ γ,H→ZZ,andH→bb channels.Thisbinningcoincideswiththe binningoftheunfoldedcrosssectionsinwhichtheindividualresultsarereported.

Channel pH

T binning (GeV)

H→γ γ [0, 15) [15, 30) [30, 45) [45, 80) [80, 120) [120, 200) [200, 350) [350, 600) [600,∞) H→ZZ [0, 15) [15, 30) [30, 80) [80, 200) [200,∞)

H→bb None [350, 600) [600,∞)

inthe caseofdata andsimulation, andfromstableparticles ex-cludingneutrinosinthecaseofgeneratedevents,usingtheanti-kT clustering algorithm [46] with a distance parameter of 0

.

4. The measurementsarereportedintermsofkinematicobservables de-ﬁned before the decay of the Higgs boson, i.e. at the generator level.

Eachof the analyses used asinput to the combination corre-sponds to a different ﬁducial phase space deﬁnition and applies adifferenteventcategorization.InthecaseoftheH

→

γ γ

anal-ysis, theﬁducial phase spaceis deﬁnedby requiringthe ratioof the leading (subleading) photon pT to the diphoton mass to be greaterthan1

/

3 (1

/

4). Inaddition,foreachphoton candidatethe scalarsumofthe generator-level pT of stableparticlescontained inaconeofradius

R

=

0

.

3 aroundthecandidateisrequiredto be less than 10GeV, where

R

=

√

(

η

)

2

+ ( φ)

2 is the angu-lar separation between particles and

φ

is the azimuthal angle between two particles in radians. The selected photon pairs are categorized according to their estimated relative invariant mass resolution [25].In the caseof the H

→

ZZ analysis,the 4-lepton massis required to be greater than 70GeV, the leading Z boson candidate invariant mass must be greater than 40GeV, and lep-tonsmust be separatedin angular space by at least

R

>

0

.

02. Furthermore,atleast two leptons must each havea pT

>

10GeV andat least one a pT

>

20GeV.The selected events are catego-rizedaccording totheir lepton conﬁgurationin theﬁnal state (4 electrons, 4 muons, or 2 electrons and2 muons). In the caseof theH

→

bb analysis,theanalysisstrategyrequiresthepresenceof asingleanti-kTjetwithadistanceparameterof0

.

8,pT

>

450GeV, and

|

η

|

<

2

.

5.Forthisanalysis, thedataisnotunfoldedtoa fidu-cialphase space. Softand wide-angleradiation isremoved using thesoft-drop grooming algorithm [47,48]. The jet massafter ap-plicationofthesoft-dropalgorithm,mSD,peaksclosetotheHiggs bosonmass in the caseof signal events.To avoidfinite-cone ef-fectsandthenonperturbativeregimeofthemSD calculation,events are selected based on the dimensionless mass scale variable for QCD jetsdefined as

ρ

=

log

m2_SD

/

p2_T

[47], whichrelates the jet pT to the jet mass. Events with isolated electrons, muons, or

τ

leptonswith pT

>

10GeV and

|

η

|

<

2

.

5 arevetoedinorderto re-ducethe backgroundfromSM electroweak processes,andevents withamissingtransversemomentumgreaterthan140GeV are ve-toedinorderto reducethebackgroundfromtopquark-antiquark pairproduction.Additionally,aselectioncriterionisappliedbased onthe compatibilityofthe single anti-kT jet with havinga two-prong substructure [49–52]. Events are categorized according to theirlikelihoodofconsistingoftwob quarks,whichiscomputed usingthedouble-b taggeralgorithm [53].

Minormodiﬁcations are applied to the individual analyses in Refs. [25,27,29] to provide the inputs used for the combination ofdifferential observables. ForH

→

γ γ

, an additional bin, pH

T

>

600GeV,isincludedinthe pH

T spectrum.ForH

→

ZZ,thebinning is modiﬁed for multiple kinematicobservables to align with the binningoftheH

→

γ γ

analysis.Furthermore,thebranching frac-tionsofthetwoZ bosonstothevariousleptonconfigurationsare fixedtotheirSMvalues,whereasinRef. [27] theseareallowedto float.ForH

→

bb thesignal issplit intotwo pT binsatthe gen-erator level: the ﬁrstwith 350

≤

pT

<

600GeV,where the lower

Table 2

Thebinningfor

N

jetsfortheH→γ γandtheH→ZZ channels.This binningcoincideswiththebinningoftheunfoldedcrosssectionsin whichtheindividualresultsarereported.

Channel Njetsbinning

H→γ γ 0 1 2 3 ≥4

H→ZZ 0 1 2 ≥3

limit has beenextended downwards withrespect to the individ-ual analysis, and thesecond an overﬂow bin with pT

≥

600GeV, which aligns with the binning of the other channels. At the re-construction level two bins are employed, with 450

≤

pT

<

600 and pT

≥

600GeV,which is aslight modification withrespect to thebinningusedinRef. [29].Theredefinitionofthereconstructed pTcategoriesnecessitatesareevaluationofthebackgroundmodel, which is performedusing the same procedure asin the original analysis. Forthe purposeofthe combinationinthisanalysis, the fiducial measurements from the H

→

γ γ

and H

→

ZZ channels areextrapolatedtotheinclusivephasespace [38,42,43].

5. Statisticalanalysis

The cross sections are extracted through a simultaneous ex-tended maximumlikelihoodﬁtto thediphotonmass,four-lepton mass, and mSD distributions in all the analysis categories ofthe H

→

γ γ

,H

→

ZZ,andH

→

bb channels,respectively.

The number of expected signal events nsig _in _a _given recon-structedkinematicbini,givenanalysiscategoryk andgivendecay channelm isobtainedfrom:

nsig_i ,km

(

σ

|θ) =

n

gen_bins

j=1

σ

jL

(

θ )

B

mMkmji

(

θ ),

(2)

where:

•

j isakinematicbinindexatthegeneratorlevel;

•

ngen_bins is thenumber of kinematicbins atthe generator level, whichisthesameforalldecaychannels;

• σ

is the set of differential cross sections at the generator level,and L istheintegratedluminosity ofthesamples used inthisanalysis;

• B

m_is_the_branching_fraction_of_the_decay_channel_m._The over-all effectofthebranching fractionuncertainties onthe com-binedspectraisbelow1%,andhasbeenneglected.

•

Mkm

ji is the foldingmatrix, which isdetermined from Monte Carlo simulation; note that the corresponding matrix M

km neednotbesquare;thenumberofreconstructedbinsmaybe smallerthanthenumberofbinsatthegeneratorlevel;and

• θ

isthesetofnuisanceparameters.

The bin-to-bin migrations are taken into account via the folding matrix,effectively allowing unfoldingof the detectoreffects. Fol-lowingtheprescriptioninRef. [54],weﬁndthatnoregularization oftheunfoldingprocedureisneeded.

Anextendedlikelihoodfunctionforasingledecaychannelm is constructed:

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Table 3

Thebinningfor|yH|fortheH→γ γ andtheH→ZZ channels.Thisbinningcoincideswiththebinningoftheunfolded crosssectionsinwhichtheindividualresultsarereported.

Channel |yH|binning

H→γ γ [0.0, 0.15) [0.15, 0.30) [0.30, 0.60) [0.60, 0.90) [0.90, 1.20) [1.20, 2.50] H→ZZ [0.0, 0.15) [0.15, 0.30) [0.30, 0.60) [0.60, 0.90) [0.90, 1.20) [1.20, 2.50]

Table 4

Thebinningfor

p

jetT fortheH→γ γandtheH→ZZ channels.Thisbinningcoincideswiththebinning oftheunfoldedcrosssectionsinwhichtheindividualresultsarereported.

Channel pjetT binning (GeV)

H→γ γ [0, 30) [30, 55) [55, 95) [95, 120) [120, 200) [200,∞) H→ZZ [0, 30) [30, 55) [55, 95) [95,∞)

L

m

(

σ

|θ) =

nreco_bins,m

i=1 nm cat

k=1 nm O

l=1

pdf_ikm

(

O

_lm

|

σ

,

θ )

N_obsiklm

×

Poisson

N_obsikm

nsig_i ,km

(

σ

|θ) +

nbkg_i ,km

(

θ )

,

(3)

where:

• O

m _is _the_observable, _{i.e. the}_diphoton _mass,_the_four-lepton mass, ormSD for the H

→

γ γ

, H

→

ZZ, and H

→

bb decay channels,respectively;

•

nreco_bins,misthenumberofreconstructedbins,nm_cat isthenumber ofcategoriesforthedecaychannel(see theindividual analy-ses [25,27,29] formoredetails),andnm

O isthenumberofbins

forobservable

O

;

•

Niklm

obs isthenumberofobservedeventsreconstructedin kine-maticbin i,category k andobservable binl, and Nikm_obs isthe samebutsummedoverallbinsoftheobservable;

•

nbkg_i ,km isthenumberofexpectedbackgroundevents;and

•

pdf_ikm

(

O

m_l

|

σ

,

θ)

is the probability density function for the

observable,based onthe signal andbackgrounddistributions oftheobservablewhicharedeterminedviasimulation. In order to combine the decay channels, the likelihoods for the individualdecaychannelsaremultiplied:

L

(

σ

|θ) =

nc

m=1

L

m

(

σ

|θ)

pdf

(

θ ),

(4)

wherenc is thenumber ofdecay channelsincluded inthe com-bination,

L

m isthelikelihoodformulafromEq. (3) speciﬁctothe decaychannelm,andpdf

(

θ )

istheprobabilitydensityfunctionof thenuisanceparameters. Fortheindividual analyses,the number of categories, invariant mass bins, and even the number of re-constructed bins maydiffer, although the number of bins atthe generatorlevelandtheir binningneedto bealignedbetween de-cay channels. Notethat a single commonsetof differentialcross sectionsandnuisanceparametersisﬁttedtothedatainalldecay channelssimultaneously.

Theteststatisticq,whichisasymptoticallydistributedasa

χ

2_, isdeﬁnedas [55,56]: q

(

σ

)

= −

2 ln

⎛

⎜

⎝

L

σ

ˆθ

σ

L

ˆ

σ

ˆθ

⎞

⎟

⎠ .

(5)

The quantities

ˆ

σ

and

ˆθ

are theunconditional maximum likeli-hoodestimatesfor theparameters

σ

and

θ

,respectively,while

ˆθ

_{σ denotes} the maximum likelihood estimate for

θ

conditional onthevaluesof

σ

.

TheHiggsbosoncouplingmodiﬁersareﬁttedviaalargely anal-ogous procedure. In the likelihood function (4), the differential crosssections

σ

are replacedby parametrizationsoftheoretical spectra,insteadofallowingthemtobedeterminedintheﬁt:

σ

→

σ

(

κ

a

,

κ

b

),

(6)

where

κ

aand

κ

b arethecouplingmodiﬁerstobeﬁtted.

6. Systematicuncertainties

Theexperimentalsystematicuncertaintiesfromtheinput anal-yses are incorporatedin thecombinationasnuisanceparameters in theextended likelihood ﬁt andare proﬁled.Among the decay channels, correlations are taken into account for the systematic uncertainties in the jet energy scale and resolution, and the in-tegratedluminosity.Detaileddescriptionsoftheexperimental sys-tematicuncertaintiesperdecaychannelcanbefoundinRefs. [25,

27,29].

Themeasurementismadeforthefullphasespaceratherthan limited to a ﬁducial phase space (as is the casefor the original H

→

γ γ

andH

→

ZZ analyses).Thismeansthat theuncertainties intheacceptancesfortheindividualanalysesandinthebranching fractions mayaffect theresults. Theeffect ofthe acceptance un-certainties perbinontheoverall uncertainty,includingtheeffect oftheHiggscouplingmodiﬁersontheacceptances,islessthan1% andsothisisneglected inthecombination.Forcertain measure-mentstheproductioncrosssectionsofnon-ggH productionmodes are assumed to be their respective SM value. In thesecases, the uncertaintyintheinclusiveproductioncrosssectionfromnon-ggH modes, determinedtobeabout2.1% [57],hasbeentakeninto ac-countasanuisanceparameter.

The theoretical predictions described in Section 2 are subject totheoreticaluncertaintiesfromtherenormalisationscale

μ

Rand the factorisationscale

μ

F.The standardapproach toevaluate the impact ofthese uncertainties isto compute an envelopeof scale variations,andtoassigntheextremaoftheenvelopeasthe uncer-tainty.Tothisend,

μ

R and

μ

F areindependently variedbetween 0

.

5,1,and2 timestheirnominalvalue,whereasthefraction μR_μF is constrainednottobelessthan0

.

5 orgreaterthan2

.

0.Asthe the-oretical spectrainthe

κ

t/cg/

κ

b caseandthe

κ

c/

κ

b casecontain a resummation,theuncertaintyintheresummationscale Q isalso considered, andit isevaluatedby varying Q from 0

.

5 to 2 times itscentralvalue(whilekeeping

μ

Fand

μ

Rattheirrespective cen-tralvalues).Thetheoreticaluncertaintiesareassignedbyapplying the minimumandmaximumscale variations per bin.The result-inguncertaintiesforthespectraundervariationsof

κ

band

κ

cand variations of

κ

t, cg, and

κ

b areshown inTables 5and6, respec-tively.

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Table 5

Uncertaintiesinthepredicted

p

H

T spectrarelatedtovariationsoftheoryparametersfortheκb andκccase.

Binning (GeV) [0, 15) [15, 30) [30, 45) [45, 80) [80, 120)

scale(%) 8.9% 6.6% 18.1% 22.0% 21.6%

Table 6

Uncertaintiesinthepredicted

p

HTspectrarelatedtovariationsoftheoryparametersfortheκt,

c

g,andκbcase.

Binning (GeV) [0, 15) [15, 30) [30, 45) [45, 80) [80, 120) [120, 200) [200, 350) [350, 600) [600, 800)

scale_(%) _12.7% _7.4% _9.5% _12.8% _17.4% _19.3% _20.9% _23.4% _8.2%

Theoreticaluncertainties are subjecttobin-to-bin correlations. Weadopta procedure thatproduces a correlation coeﬃcient

ρab

directlyfromtheindividualscalevariations:

ρ

ab

=

i

(

σ

a,i

−

σ

a

)(

σ

b,i

−

σ

b

)

i

(

σ

a,i

−

σ

a

)

2

i

(

σ

b,i

−

σ

b

)

2

,

(7)

where

σa

(b),iisthecrosssection inbina (b)oftheithscale vari-ation,

σa

(b) isthemeancrosssection inbina (b),and

ρab

isthe

resultingcorrelation coeﬃcientbetweenbina andb.The correla-tionstructureischaracterizedbystrongcorrelationsamongbinsat moderatepH_T (15

≤

pH_T

≤

600GeV).OnlythebinswithpH_T

<

15 and pH_T

>

600GeV areanti-correlatedwiththebinsatmoderatepH_T. 7.Results

7.1.Totalcrosssectionand

B

γ γ

/BZZ

ThetotalcrosssectionforHiggsbosonproduction,basedona combinationoftheH

→

γ γ

andH

→

ZZ channels,ismeasuredto be61

.

1

±

6

.

0(stat)

±

3

.

7(syst) pb,obtainedbyapplyingthe treat-ment described in Section 4 to the inclusive cross section (i.e. witha single bin, both atgenerator andat reconstruction level). Themeasuredtotalcrosssectionsfromtheindividualchannelsare 64

.

0

±

9

.

6 pb forH

→

γ γ

and58

.

2

±

9

.

8 pb forH

→

ZZ;the combi-nationimprovestheprecisionby27%withrespecttotheH

→

γ γ

channelindividually.The likelihoodscansfortheindividualdecay channelsandtheir combinationare shownin Fig.1 (upper). The combinationresultagreeswiththeSMvalueof55

.

6

±

2

.

5 pb [57]. Ameasurementof thebranching fractionforone decay chan-nelis degenerate witha measurement of thetotal cross section. However, theratioof branching fractionsfortwo decaychannels canbe measuredwhileproﬁling thetotalcrosssection. Theratio oftheH

→

γ γ

andH

→

ZZ branchingfractions,

B

γ γ

/

BZZ

,is mea-suredtobe0

.

092

±

0

.

018(stat)

±

0

.

010(syst).Thisisinagreement withtheSMpredictionof0

.

086

±

0

.

002 [57].Thelikelihoodscan for

B

γ γ

/

BZZ

isshowninFig.1(lower).

7.2.Combinationsofdifferentialobservables

TheunfoldeddifferentialcrosssectionsfortheobservablespH_T, Njets,

|

yH

|

, and pjetT are shown in Figs. 2, 3, 4, and 5, respec-tively.Fig.2(lower)showsthedifferentialcrosssection of pH_T for Higgsboson productionviagluonfusion; forthisresult, the non-gluon-fusionproduction modesare considered to be background, constrainedtotheSM predictionswiththeirrespective uncertain-ties. The numerical values for the spectra in Figs. 2–5 are given inAppendix A and the corresponding bin-to-bin correlation ma-tricesare givenin AppendixB.Fortheobservables pH

T, Njets,and pjet_T ,therightmostbinisan overﬂowbin,whichisnormalizedby the binwidth ofthe second-to-rightmost bin.Overall no signiﬁ-cantdeviationsfromtheSMpredictions areobserved.Forthe pH T

Fig. 1. Scanofthetotalcrosssectionσtot(upper)andoftheratioofbranching frac-tionsBγ γ/BZZ(lower),basedonacombinationoftheH→γ γ andH→ZZ anal-yses.Themarkersindicatetheonestandarddeviationconﬁdenceinterval.

CYRM-2017-002 refers toRef. [57].

spectrum,thedominantsourceofuncertaintyisthestatisticalone; inparticular, thesystematicuncertaintyisabouthalfthe statisti-cal uncertainty in therightmost bin, andmuch smaller than the statisticaluncertaintyinallotherbins.Thetotaluncertaintyinthe combinationperbinvariesbetween30and40%.Comparedtothe measurementintheH

→

γ γ

channelalone,thedecreasein

(7)

uncer-Fig. 2. Measurementofthetotaldifferentialcrosssection(upper)andthe differ-entialcross section ofgluonfusion (lower)as afunction ofpH

T. The combined spectrumisshownasblackpointswitherrorbarsindicatinga1standard devia-tionuncertainty.Thesystematiccomponentoftheuncertaintyisshownbyablue band.ThespectrafortheH→γ γ,H→ZZ,andH→bb channelsareshownin red,blue,andgreen,respectively.ThedottedhorizontallinesintheH→ZZ chan-nelindicatethe coarserbinningofthismeasurement.Therightmostbins ofthe distributionsareoverﬂowbins;thenormalizationsofthecrosssectionsinthese binsareindicatedintheﬁgure.

CYRM-2017-002 refers

toRef. [57].

taintyachievedbythecombinationismostnotableinthelow-pT region.ThecontributionoftheH

→

bb channeltotheoverall pre-cisionofthecombinationismostsigniﬁcantinthelast pH_T bin. 7.3. FitsofHiggsbosoncouplingmodiﬁers:

κ

bvs.

κ

c

Fig.6(upper)showsthe oneandtwostandard deviation con-tours of the ﬁts of the

κ

b/

κ

c parametrization from Ref. [12] to data,assumingthebranchingfractionsaredependentontheHiggs

Fig. 3. Measurementofthedifferentialcrosssectionasafunctionof

N

jets.The com-binedspectrumisshownasblackpointswitherrorbarsindicatinga1standard deviationuncertainty.Thesystematiccomponentoftheuncertaintyisshownbya blueband.ThespectrafortheH→γ γandH→ZZ channelsareshowninredand blue,respectively.ThedottedhorizontallinesintheH→ZZ channelindicatethe coarserbinningofthismeasurement.

CYRM-2017-002 refers

toRef. [57].

Fig. 4. Measurementofthedifferentialcrosssectionasafunctionof|yH|.The com-binedspectrumisshownasblackpointswitherrorbarsindicatinga1standard deviationuncertainty.Thesystematiccomponentoftheuncertaintyisshownbya blueband.ThespectrafortheH→γ γandH→ZZ channelsareshowninredand blue,respectively.

CYRM-2017-002 refers

toRef. [57].

bosoncouplings,i.e.,

B = B(

κ

b,

κ

c),andthatthereareno beyond-the-SM contributions. The substructure on the combined scan showsa ringshapearound theorigin, inagreementwiththeSM predictionwithinonestandarddeviation.

(8)

Fig. 5. Measurementofthedifferentialcrosssectionasafunctionof

p

jetT.The com-binedspectrumisshownasblackpointswitherrorbarsindicatinga1standard deviationuncertainty.Thesystematiccomponentoftheuncertaintyisshownbya blueband.ThespectrafortheH→γ γandH→ZZ channelsareshowninredand blue,respectively.ThedottedhorizontallinesintheH→ZZ channelindicatethe coarserbinningofthismeasurement.Therightmostbinofthedistributionisan overﬂowbin;thenormalizationofthecrosssectioninthatbinisindicatedinthe ﬁgure.

CYRM-2017-002 refers

toRef. [57].

Inordertoassesstheconstraintobtainedonlyfromthe knowl-edgeofthepH

T distribution,thetotalwidthandtheoverall normal-izationare proﬁled in theﬁt. Thisis effectivelyaccomplished by implementingthebranchingfractionsfortheH

→

γ γ

andH

→

ZZ channelsasnuisance parameters with no prior constraint, i.e. as freeparameters.TheresultofthisﬁtisshowninFig.6(lower).As expected,therangeofallowed valuesof

κ

b and

κ

c ismuchwider thaninthecaseofcoupling-dependentbranchingfractions.

Conﬁdenceintervalscan be seton

κ

b and

κ

c byproﬁling one couplingandscanningovertheother.Theresultsofthese single-couplingscansareshowninFigs.7and8.Theobserved(expected) limitsat95%CL intheone-dimensionalscansare:

−

1

.

1

<

κ

b

<

1

.

1

(

−

1

.

3

<

κ

b

<

1

.

3

),

−

4

.

9

<

κ

c

<

4

.

8

(

−

6

.

1

<

κ

c

<

6

.

0

),

(8) inthecaseofbranchingfractionsthatdependon

κ

b and

κ

c,and

−

8

.

5

<

κ

b

<

18

(

−

8

.

8

<

κ

b

<

15

),

−

33

<

κ

c

<

38

(

−

31

<

κ

c

<

36

),

(9) in the case of the branching fractions implemented as nuisance parameters withno prior constraint. Forthe coupling-dependent branching fractions,the resultsare shaped predominantly by the constraintsfromthetotalwidthratherthan bydistortions ofthe pH_T spectrum.Ifthe branchingfractions areﬁxed to their SM ex-pectations,theone-dimensionalscansyieldthefollowingexpected limitsat95%CL:

−

3

.

5

<

κ

b

<

5

.

1

,

−

13

<

κ

c

<

15

.

(10) Theseintervals are comparableto those in Ref. [12], where

κ

c

∈

[−

16

,

18

]

at95% CL, notingthat the resultshere are basedon a

Fig. 6. Simultaneousﬁt todataforκb and κc,assumingacouplingdependence ofthe branching fractions (upper) and the branching fractions implemented as nuisanceparameterswithnopriorconstraint(lower).Theonestandarddeviation contourisdrawnforthecombination(H→γ γandH→ZZ),theH→γ γchannel, andtheH→ZZ channelinblack,red,andblue,respectively.Forthecombination thetwostandarddeviationcontourisdrawnasablackdashedline,andthe shad-ingindicatesthenegativelog-likelihood,withthescaleshownontherighthand sideoftheplots.

largerdataset.Theintervalsobtainedarecompetitivewiththe in-tervalsfromotherdirectsearchchannelssummarizedinSection1. 7.4. FitsofHiggsbosoncouplingmodiﬁers:

κ

tvs.cgand

κ

tvs.

κ

b

Theﬁtsare repeatedinawayanalogoustothat ofSection7.3

but with

κ

t, cg, and

κ

b, the coeﬃcients of the dimension-6 op-eratorsaddedto theSM Lagrangian,asthe parametersofthe ﬁt, using the parametrization obtained fromRefs. [30,31]. The com-bined log-likelihood scan for

κ

t vs. cg, assuming branching frac-tionsthatdependonthecouplings,isshowninFig.9(upper).The normalizationofthespectrumis,byconstruction,equaltotheSM normalization forthe set of coeﬃcients satisfying12cg

+

κ

t

1. TheshapeoftheparametrizedpH

T spectrums iscalculatedby nor-malizingthedifferentialcrosssectionto1:

si

(

κ

t

,

cg

)

=

σ

i

(

κ

t

,

cg

)

j

σ

j

(

κ

t

,

cg

)

(9)

Fig. 7. Likelihoodscanofκbwhileprofilingκc(upper),andofκcwhileprofilingκb (lower).Thefilledmarkersindicatethelimitsat95%CL.Thebranchingfractionsare considereddependentonthevaluesofthecouplings.

where

σi

is the parametrization in bin i. Inserting the expected parabolic dependence of

σi

(

κ

t,cg) reveals that the shape of the parametrizationfor

κ

t/cgvariationsbecomesafunctionoftheratio ofthe twocouplings, si

(

cg/

κ

t).Thus the dependenceofthe like-lihoodontheradialdistance

√

κ

2

t

+

c2g stemsfromconstraintson the overall normalization, whereas the dependence on the slope cg/

κ

t stems from constraints on the shape of the distribution. The dependence of the likelihood on the slope becomes appar-ent in Fig. 9 (lower), where the branching fractions are imple-mented as nuisance parameters with no prior constraint in the ﬁt. Except at small values of the couplings, the constraint on the couplings comes from their ratio. The two symmetric sets ofcontours are dueto a symmetryof theparametrization under

(

κ

t,cg)

→ (−

κ

t,

−

cg).The constraintfromthe H

→

γ γ

channel individuallyishereslightlystrongerthanthecombination;this ef-fect,notobservedinexpectedﬁts,stemsfromoppositedeviations intheH

→

γ γ

andH

→

ZZ pH_T spectrathatcanceloutinthe com-bination.

Fig. 10 (upper) shows the combined log-likelihood scan as a function of

κ

t and

κ

b, withbranching fractions scaling appropri-ately with the coupling modiﬁers and Fig. 10 (lower) with the branchingfractions implementedasnuisanceparameterswithno

Fig. 8. Likelihoodscanofκbwhileprofilingκc(upper),andofκcwhileprofilingκb (lower).Thefilledmarkersindicatethelimitsat95%CL.Thebranchingfractionsare implementedasnuisanceparameterswithnopriorconstraint.

prior constraint. Asthe H

→

γ γ

branching fractiondepends lin-early on

κ

t, the constraints on the H

→

γ γ

channel and the combinationinFig.10(upper)are notsymmetricwithrespectto the

κ

t axis.Forthebranching fractions implementedasnuisance parameters with noprior constraint, the parametrizationis sym-metricunder

(

κ

t

,

κ

b)

→ (−

κ

t,

−

κ

b),whichexplainstheobserved symmetryinFig.10(lower).

8. Summary

A combination ofdifferential cross sections forthe Higgs bo-son transverse momentum pH_T, the number of jets, the rapidity of the Higgsboson, andthe pT of the leading jet has been pre-sented,usingproton-protoncollisiondatacollectedat

√

s

=

13TeV with the CMS detector, corresponding to an integrated luminos-ityof35

.

9 fb−1.Thespectraobtainedarebasedondatafromthe H

→

γ γ

, H

→

ZZ, andH

→

bb decaychannels. The precision of thecombinedmeasurementofthedifferentialcrosssectionof pH_T is improved by about 15% with respect to the H

→

γ γ

chan-nel alone. The improvementis larger inthe low-pH

T region than in the high-pH_T tails.No signiﬁcant deviations from the standard model are observed in any differential distribution. Additionally,

(10)

Fig. 9. Simultaneousﬁttodataforκtand

c

g,assumingacouplingdependenceofthe branchingfractions(upper)andthebranchingfractionsimplementedasnuisance parameterswithnopriorconstraint(lower).Theonestandarddeviationcontouris drawnforthecombination(H→γ γ,H→ZZ,andH→bb),theH→γ γchannel, andtheH→ZZ channelinblack,red,andblue,respectively.Forthecombination thetwostandarddeviationcontourisdrawnasablackdashedline,andtheshading indicatesthenegativelog-likelihood,withthescaleshownontherighthandside oftheplots.

thetotalcrosssectionforHiggsbosonproductionbasedona com-binationoftheH

→

γ γ

andH

→

ZZ channelsismeasuredto be 61

.

1

±

6

.

0(stat)

±

3

.

7(syst) pb.

Thespectraobtainedare interpretedinthe

κ

-framework [32], in which simultaneous variations of

κ

b and

κ

c,

κ

t and

κ

b, and

κ

t and the anomalous direct coupling to the gluon ﬁeld cg are ﬁttedtothepH_T spectra.Thelimitsobtainedfortheindividual cou-plingsare

−

1

.

1

<

κ

b

<

1

.

1 and

−

4

.

9

<

κ

c

<

4

.

8 at95%conﬁdence level,assumingthebranchingfractionsscalewiththeHiggsboson couplingsfollowingthestandardmodelprediction.Forthecharm coupling

κ

c inparticular,theseboundsarecomparablewiththose obtainedfromdirectsearcheswithcharmquarksintheﬁnalstate. Acknowledgements

We thank Fady Bishara, Ulrich Haisch, Pier Francesco Monni, Emanuele Re, Massimiliano Grazzini, Agnieszka Ilnicka, Michael Spira, and Marius Wiesemann for guidance regarding their pre-dictions of the Higgs boson transverse momentum spectra. We

Fig. 10. Simultaneousﬁttodataforκtand κb,assumingacouplingdependence ofthe branching fractions (upper) and the branching fractions implemented as nuisanceparameterswithnopriorconstraint(lower).Theonestandarddeviation contourisdrawnforthecombination(H→γ γ,H→ZZ,andH→bb),theH→γ γ channel,andtheH→ZZ channelinblack,red,andblue,respectively.Forthe com-binationthetwostandarddeviationcontourisdrawnasablackdashedline,and theshadingindicatesthenegativelog-likelihood,withthescaleshownontheright handsideoftheplots.

congratulate our colleagues in the CERN acceleratordepartments fortheexcellent performanceofthe LHCandthankthetechnical andadministrativestaffs atCERNandatother CMSinstitutesfor their contributions to the successof the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel oftheWorldwideLHCComputingGridfordeliveringsoeffectively thecomputinginfrastructureessentialtoouranalyses.Finally,we acknowledgetheenduringsupportfortheconstruction and oper-ation of the LHC and the CMS detector provided by the follow-ing fundingagencies:BMBWF andFWF(Austria); FNRSandFWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIEN-CIAS(Colombia);MSESandCSF(Croatia);RPF(Cyprus);SENESCYT (Ecuador);MoER,ERCIUT,andERDF(Estonia);AcademyofFinland, MEC,andHIP(Finland);CEAandCNRS/IN2P3(France);BMBF,DFG, and HGF (Germany); GSRT (Greece); NKFIA (Hungary); DAE and DST (India);IPM(Iran); SFI(Ireland);INFN (Italy); MSIPandNRF (Republic ofKorea); MES (Latvia); LAS (Lithuania);MOE andUM (Malaysia); BUAP, CINVESTAV,CONACYT, LNS, SEP, andUASLP-FAI

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(Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pak-istan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON,ROSATOM,RAS,RFBR,andNRCKI(Russia);MESTD(Serbia); SEIDI, CPAN, PCTI, and FEDER (Spain); MoSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand);TUBITAK and TAEK (Turkey);NASU andSFFR(Ukraine);STFC(UnitedKingdom);DOEandNSF(USA).

Individuals have received support from the Marie-Curie pro-gramme and the European Research Council and Horizon 2020 Grant, contract No. 675440 (European Union); the A.G. Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy 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.-FNRS and FWO (Belgium) under the “Excellence of Science – EOS” – be.h project n. 30820817; the Ministry of Education, Youth and Sports(MEYS)oftheCzechRepublic;theLendület(“Momentum”) ProgrammeandtheJánosBolyaiResearchScholarshipofthe Hun-garian Academy of Sciences, the New National Excellence Pro-gram ÚNKP, the NKFIA research grants 123842, 123959, 124845, 124850, and 125105 (Hungary); the Council of Science and

In-dustrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund,the MobilityPlus programmeofthe Ministry of Science and Higher Education, the National Science Centre (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 Program by Qatar National Research Fund; the Programa Estatalde Fomentode laInvestigación CientíficayTécnica de Ex-celencia María de Maeztu, grant MDM-2015-0509 and the Pro-grama Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF; theRachadapisekSompotFundforPostdoctoralFellowship, Chula-longkornUniversityandtheChulalongkornAcademic intoIts2nd CenturyProject AdvancementProject(Thailand);theWelch Foun-dation,contractC-1845;andtheWestonHavensFoundation(USA). Appendix A. Tablesforthedifferentialcrosssection

measurements

TablesA.1–A.5showthemeasureddifferentialcrosssectionsfor theconsideredobservables.

Table A.1

Differentialcrosssections(pb/GeV)fortheobservable

p

H T. pH T (GeV) 0–15 15–30 30–45 45–80 80–120 120–200 200–350 350–600 >600 H→γ γ 1.0+₋00..33 1+ 0.3 −0.3 0.5+ 0.2 −0.2 0.3+ 0.1 −0.1 0.1+ 0.05 −0.05 0.03+ 0.01 −0.01 0.01+ 2.8×10−3 −2.5×10−3 −3.4×10−5+ 3.8×10−4 −3.1×10−4 −1.9×10−4+ 2.4×10−4 −2.4×10−4 H→ZZ 0.7+₋00..33 1+ 0.4 −0.3 0.4+ 0.1 −0.1 0.08+ 0.03 −0.02 3.3×10−4+ 2.6×10−3 −2.6×10−3 H→bb None 9.6×10−4+1.2×10−3 −1.2×10−3 1.1×10−4+ 1.2×10−4 −1.1×10−4 Comb. 0.8+₋00..22 1+ 0.2 −0.3 0.6+ 0.2 −0.2 0.3+ 0.1 −0.09 0.1+ 0.05 −0.04 0.03+ 0.01 −0.01 0.01+ 2.6×10−3 −2.4×10−3 −2.8×10−6+ 3.7×10−4 −2.8×10−4 5.8×10−5+ 1.0×10−4 −1.0×10−4 Table A.2

Differentialcrosssectionsofgluonfusion(ggH)(pb/GeV)fortheobservable

p

HT,withnon-ggH productionmodesﬁxedtotheirSMprediction. pH T (GeV) 0–15 15–30 30–45 45–80 80–120 120–200 200–350 350–600 >600 Comb. 0.8+0.2 −0.2 1+ 0.2 −0.3 0.5+ 0.2 −0.2 0.2+ 0.1 −0.09 0.1+ 0.05 −0.04 0.02+ 0.01 −0.01 8.3×10− 3+2.6×10−3 −2.4×10−3 −1.6×10− 4+3.4×10−4 −2.6×10−4 3.5×10− 5+5.8×10−5 −5.7×10−5 Table A.3

Differentialcrosssections(pb)fortheobservable

N

jets.

Njets 0 1 2 3 ≥4 H→γ γ 50+₋88..51 14+ 5.1 −4.9 4.8×10−1+ 2.7 −2.7 3.1+ 2.0 −2.0 1.3+ 8.8×10−1 −9.3×10−1 H→ZZ 41+₋98..10 8.7+ 5.2 −4.3 6.9+ 3.7 −3.0 1.2+ 2.1 −2.1 Combination 47+₋66..24 11+ 3.7 −3.4 3.5+ 1.9 −1.7 1.8+ 1.7 −1.5 1.2+ 8.3×10−1 −8.8×10−1 Table A.4

Differentialcrosssections(pb)fortheobservable|yH|.

|yH| 0–0.15 0.15–0.3 0.3–0.6 0.6–0.9 0.9–1.2 1.2–2.5 H→γ γ 42+11 −11 39+−1211 31−+79..05 28+−98..17 24+ 12 −10 18+ 7.4 −7.2 H→ZZ 39+17 −14 35+ 18 −14 34+ 11 −9.8 45+ 13 −11 13+−86..98 13+ 6.7 −5.4 Combination 41+9.1 −8.9 38+ 9.7 −9.2 32+ 7.0 −6.0 35+ 7.1 −6.6 17+ 7.4 −6.5 15+ 5.1 −4.7 Table A.5

Differentialcrosssections(pb/GeV)fortheobservable

p

jetT .

pjetT (GeV) 30–55 55–95 95–120 120–200 >200 H→γ γ 1.6×10−1+2.0×10−1 −2.1×10−1 2.0×10−1+ 9.2×10−2 −9.3×10−2 1.3×10−1+ 9.5×10−2 −9.2×10−2 1.5×10−5+ 1.8×10−2 −1.7×10−2 2.9×10−2+ 9.1×10−3 −9.2×10−3 H→ZZ 4.8×10−1+2.4×10−1 −2.0×10−1 7.7×10−2+ 8.8×10−2 −6.9×10−2 8.0×10− 2+5.9×10−2 −4.4×10−2 Combination 3.2×10−1+1.4×10−1 −1.3×10−1 1.3×10− 1+7.7×10−2 −6.1×10−2 1.1×10− 1+8.4×10−2 −8.1×10−2 −4.2×10− 3+1.7×10−2 −1.6×10−2 2.7×10− 2+8.7×10−3 −8.9×10−3

(12)

Appendix B.Correlationmatricesforthecombinationsof differentialobservables

Figs.B.1–B.4 show the correlation matricesforthe considered observables.

Fig. B.1. Bin-to-bincorrelationmatrixofthe

p

H

T spectrum(upper)andofthe

p

H T spectrumofgluonfusion(ggH),wherethenon-ggH contributionsareﬁxedtothe SMexpectation(lower).

Fig. B.2. Bin-to-bin correlation matrix of the Njetsspectrum.

Fig. B.3. Bin-to-bin correlation matrix of the|yH|spectrum.

Fig. B.4. Bin-to-bin correlation matrix of the pjetT spectrum.

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TheCMSCollaboration

A.M. Sirunyan,

A. Tumasyan

Yerevan Physics Institute, 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,

A. Taurok,

W. Waltenberger,

J. Wittmann,

C.-E. Wulz

1

,

M. Zarucki

Institut für Hochenergiephysik, Wien, Austria

V. Chekhovsky,

V. Mossolov,

J. Suarez Gonzalez

Institute for Nuclear Problems, Minsk, Belarus

E.A. De Wolf,

D. Di Croce,

X. Janssen,

J. Lauwers,

M. Pieters,

H. Van Haevermaet,

P. Van Mechelen,

N. Van Remortel

Universiteit Antwerpen, Antwerpen, Belgium

S. Abu Zeid,

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

Vrije Universiteit Brussel, Brussel, Belgium

D. Beghin,

B. Bilin,

H. Brun,

B. Clerbaux,

G. De Lentdecker,

H. Delannoy,

B. Dorney,

G. Fasanella,

L. Favart,

R. Goldouzian,

A. Grebenyuk,

A.K. Kalsi,

T. Lenzi,

J. Luetic,

N. Postiau,

E. Starling,

L. Thomas,

C. Vander Velde,

P. Vanlaer,

D. Vannerom,

Q. Wang

Université Libre de Bruxelles, Bruxelles, Belgium

T. Cornelis,

D. Dobur,

A. Fagot,

M. Gul,

I. Khvastunov

2

,

D. Poyraz,

C. Roskas,

D. Trocino,

M. Tytgat,

W. Verbeke,

B. Vermassen,

M. Vit,

N. Zaganidis

Ghent University, Ghent, Belgium

H. Bakhshiansohi,

O. Bondu,

S. Brochet,

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,

S. Wertz,

J. Zobec

Université Catholique de Louvain, Louvain-la-Neuve, Belgium

F.L. Alves,

G.A. Alves,

M. Correa Martins Junior,

G. Correia Silva,

C. Hensel,

A. Moraes,

M.E. Pol,

P. Rebello Teles

Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil

E. Belchior Batista Das Chagas,

W. Carvalho,

J. Chinellato

3

,

E. Coelho,

E.M. Da Costa,

G.G. Da Silveira

4

,

D. De Jesus Damiao,

C. De Oliveira Martins,

S. Fonseca De Souza,

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

3

,

F. Torres Da Silva De Araujo,

A. Vilela Pereira

Universidade do Estado do Rio de Janeiro, Rio de Janeiro, 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

,

S.S. Padula

a

a_{Universidade Estadual}_{Paulista, São}_Paulo,_Brazil b_Universidade_{Federal do ABC, São}_Paulo,_Brazil