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

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

Articlehistory:

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.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

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-mailaddress: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

0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

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

κ

iisequalto1.

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]

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

Table 1

Thereconstruction-levelbinningforpH

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

ThebinningforNjetsfortheH→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_{isthebranchingfractionofthedecaychannelm.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

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

ThebinningforpjetT 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 theobservable, i.e. thediphoton mass,thefour-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 5and

6

,

The CMS Collaboration / Physics Letters B 792 (2019) 369–396 373

Table 5

UncertaintiesinthepredictedpH

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

UncertaintiesinthepredictedpHTspectrarelatedtovariationsoftheoryparametersfortheκt,cg,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

ρ

ab 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

σ

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

σ

a(b) isthemeancrosssection inbina (b),and

ρ

ab 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 referstoRef. [57].

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

→

γ γ

channelalone,thedecreasein

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 referstoRef. [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. MeasurementofthedifferentialcrosssectionasafunctionofNjets.The

com-binedspectrumisshownasblackpointswitherrorbarsindicatinga1standard deviationuncertainty.Thesystematiccomponentoftheuncertaintyisshownbya blueband.ThespectrafortheH→γ γandH→ZZ channelsareshowninredand blue,respectively.ThedottedhorizontallinesintheH→ZZ channelindicatethe coarserbinningofthismeasurement.CYRM-2017-002 referstoRef. [57].

Fig. 4. Measurementofthedifferentialcrosssectionasafunctionof|yH|.The

com-binedspectrumisshownasblackpointswitherrorbarsindicatinga1standard deviationuncertainty.Thesystematiccomponentoftheuncertaintyisshownbya blueband.ThespectrafortheH→γ γandH→ZZ channelsareshowninredand blue,respectively.CYRM-2017-002 referstoRef. [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.

The CMS Collaboration / Physics Letters B 792 (2019) 369–396 375

Fig. 5. MeasurementofthedifferentialcrosssectionasafunctionofpjetT.The

com-binedspectrumisshownasblackpointswitherrorbarsindicatinga1standard deviationuncertainty.Thesystematiccomponentoftheuncertaintyisshownbya blueband.ThespectrafortheH→γ γandH→ZZ channelsareshowninredand blue,respectively.ThedottedhorizontallinesintheH→ZZ channelindicatethe coarserbinningofthismeasurement.Therightmostbinofthedistributionisan overflowbin;thenormalizationofthecrosssectioninthatbinisindicatedinthe figure.CYRM-2017-002 referstoRef. [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.7and

8

.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

)

Fig. 7. Likelihoodscanofκbwhileprofilingκc(upper),andofκcwhileprofilingκb

(lower).Thefilledmarkersindicatethelimitsat95%CL.Thebranchingfractionsare considereddependentonthevaluesofthecouplings.

where

σ

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

σ

i

(

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,

The CMS Collaboration / Physics Letters B 792 (2019) 369–396 377

Fig. 9. Simultaneousfittodataforκtandcg,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

(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)fortheobservablepH 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)fortheobservablepHT,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)fortheobservableNjets.

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)fortheobservablepjetT .

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

The CMS Collaboration / Physics Letters B 792 (2019) 369–396 379

Appendix B.Correlationmatricesforthecombinationsof differentialobservables

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

Fig. B.1. Bin-to-bincorrelationmatrixofthe pH

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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The CMS Collaboration / Physics Letters B 792 (2019) 369–396 381

TheCMSCollaboration

A.M. Sirunyan,

A. Tumasyan

YerevanPhysicsInstitute,Yerevan,Armenia

W. Adam,

F. Ambrogi,

E. Asilar,

T. Bergauer,

J. Brandstetter, M. Dragicevic,

J. Erö,

A. Escalante Del Valle,

M. Flechl,

R. Frühwirth

1

, V.M. Ghete, J. Hrubec, M. Jeitler

1

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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

InstitutfürHochenergiephysik,Wien,Austria

V. Chekhovsky,

V. Mossolov,

J. Suarez Gonzalez

InstituteforNuclearProblems,Minsk,Belarus

E.A. De Wolf,

D. Di Croce,

X. Janssen, J. Lauwers,

M. Pieters,

H. Van Haevermaet, P. Van Mechelen,

N. Van Remortel

UniversiteitAntwerpen,Antwerpen,Belgium

S. Abu Zeid,

F. Blekman,

J. D’Hondt,

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K. Deroover,

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VrijeUniversiteitBrussel,Brussel,Belgium

D. Beghin, B. Bilin,

H. Brun,

B. Clerbaux,

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G. Fasanella, L. Favart,

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J. Luetic,

N. Postiau,

E. Starling,

L. Thomas,

C. Vander Velde,

P. Vanlaer,

D. Vannerom,

Q. Wang

UniversitéLibredeBruxelles,Bruxelles,Belgium

T. Cornelis,

D. Dobur,

A. Fagot,

M. Gul,

I. Khvastunov

2

, D. Poyraz,

C. Roskas, D. Trocino,

M. Tytgat,

W. Verbeke,

B. Vermassen,

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N. Zaganidis

GhentUniversity,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

UniversitéCatholiquedeLouvain,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

CentroBrasileirodePesquisasFisicas,RiodeJaneiro,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

UniversidadedoEstadodoRiodeJaneiro,RiodeJaneiro,Brazil

S. Ahuja

a

, C.A. Bernardes

a

,

L. Calligaris

a

, T.R. Fernandez Perez Tomei

a

,

E.M. Gregores

b

,

P.G. Mercadante

b

,

S.F. Novaes

a

,

S.S. Padula

a

a_{UniversidadeEstadualPaulista,SãoPaulo,Brazil} b_{UniversidadeFederaldoABC,SãoPaulo,Brazil}