Measurement of the differential gamma+2b-jet cross section and the ration sigma(gamma+2b-jets)/sigma(gamma plus b-jet) in p(p)over-bar collisions at root s=1.96 TeV

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

differential

γ

+

2b-jet

cross

section

and

the

ratio

σ

(

γ

+

2b-jets

)/

σ

(

γ

+

b-jet

)

in

p

p collisions

¯

at

√

s

=

1 .

96 TeV

D0

Collaboration

V.M. Abazov

af

,

B. Abbott

bp

,

B.S. Acharya

z

,

M. Adams

au

,

T. Adams

as

,

J.P. Agnew

ap

,

G.D. Alexeev

af

,

G. Alkhazov

aj

,

A. Alton

be

,

1

,

A. Askew

as

,

S. Atkins

bc

,

K. Augsten

g

,

C. Avila

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,

F. Badaud

j

,

L. Bagby

at

,

B. Baldin

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,

D.V. Bandurin

bv

,

S. Banerjee

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,

E. Barberis

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,

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J.F. Bartlett

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D. Lincoln

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R. Lipton

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H. Liu

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V.L. Malyshev

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http://dx.doi.org/10.1016/j.physletb.2014.09.007

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R. McCarthy

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a_LAFEX,_Centro_Brasileiro_de_Pesquisas_Físicas,_Rio_de_Janeiro,_Brazil b_Universidade_do_Estado_do_Rio_de_Janeiro,_Rio_de_Janeiro,_Brazil c_Universidade_Federal_do_ABC,_Santo_André,_Brazil

d_University_of_Science_and_Technology_of_China,_Hefei,_People’s_Republic_of_China e_Universidad_de_los_Andes,_Bogotá,_Colombia

f_Charles_University,_Faculty_of_Mathematics_and_Physics,_Center_for_Particle_Physics,_Prague,_Czech_Republic g_Czech_Technical_University_in_Prague,_Prague,_Czech_Republic

h_Institute_of_Physics,_Academy_of_Sciences_of_the_Czech_Republic,_Prague,_Czech_Republic i_Universidad_San_Francisco_de_Quito,_Quito,_Ecuador

j_LPC,_Université_Blaise_Pascal,_CNRS/IN2P3,_Clermont,_France

k_LPSC,_Université_Joseph_Fourier_Grenoble_1,_CNRS/IN2P3,_Institut_National_{Polytechnique}_de_Grenoble,_Grenoble,_France l_CPPM,_{Aix-Marseille}_Université,_CNRS/IN2P3,_Marseille,_France

m_LAL,_Université_Paris-Sud,_CNRS/IN2P3,_Orsay,_France n_LPNHE,_Universités_Paris_VI_and_VII,_CNRS/IN2P3,_Paris,_France o_CEA,_Irfu,_SPP,_Saclay,_France

p_IPHC,_Université_de_Strasbourg,_CNRS/IN2P3,_Strasbourg,_France q_IPNL,_Université_Lyon_1,_CNRS/IN2P3,_{Villeurbanne,}_France r_Université_de_Lyon,_Lyon,_France

s_III._{Physikalisches}_Institut_A,_RWTH_Aachen_University,_Aachen,_Germany t_{Physikalisches}_Institut,_Universität_Freiburg,_Freiburg,_Germany

u_II._{Physikalisches}_Institut,_{Georg-August-Universität}_Göttingen,_Göttingen,_Germany v_Institut_für_Physik,_Universität_Mainz,_Mainz,_Germany

w_{Ludwig-Maximilians-Universität}_München,_München,_Germany x_Panjab_University,_Chandigarh,_India

y_Delhi_University,_Delhi,_India

z_Tata_Institute_of_Fundamental_Research,_Mumbai,_India aa_University_College_Dublin,_Dublin,_Ireland

ab_Korea_Detector_Laboratory,_Korea_University,_Seoul,_Republic_of_Korea ac_CINVESTAV,_Mexico_City,_Mexico

ad_Nikhef,_Science_Park,_Amsterdam,_The_Netherlands ae_Radboud_University_Nijmegen,_Nijmegen,_The_Netherlands af_Joint_Institute_for_Nuclear_Research,_Dubna,_Russia

ag_Institute_for_Theoretical_and_Experimental_Physics,_Moscow,_Russia ah_Moscow_State_University,_Moscow,_Russia

ai_Institute_for_High_Energy_Physics,_Protvino,_Russia aj_Petersburg_Nuclear_Physics_Institute,_St._Petersburg,_Russia

ak_Institució_Catalana_de_Recerca_i_Estudis_Avançats_(ICREA)_and_Institut_de_Física_d’Altes_Energies_(IFAE),_Barcelona,_Spain al_Uppsala_University,_Uppsala,_Sweden

am_Taras_Shevchenko_National_University_of_Kyiv,_Kiev,_Ukraine an_Lancaster_University,_Lancaster_LA1_4YB,_United_Kingdom ao_Imperial_College_London,_London_SW7_2AZ,_United_Kingdom ap_The_University_of_Manchester,_Manchester_M13_9PL,_United_Kingdom aq_University_of_Arizona,_Tucson,_{AZ 85721,}_USA

(3)

ar_University_of_California_Riverside,_Riverside,_{CA 92521,}_USA as_Florida_State_University,_Tallahassee,_{FL 32306,}_USA at_Fermi_National_Accelerator_Laboratory,_Batavia,_{IL 60510,}_USA au_University_of_Illinois_at_Chicago,_Chicago,_{IL 60607,}_USA av_Northern_Illinois_University,_DeKalb,_{IL 60115,}_USA aw_Northwestern_University,_Evanston,_{IL 60208,}_USA ax_Indiana_University,_Bloomington,_{IN 47405,}_USA ay_Purdue_University_Calumet,_Hammond,_{IN 46323,}_USA az_University_of_Notre_Dame,_Notre_Dame,_{IN 46556,}_USA ba_Iowa_State_University,_Ames,_{IA 50011,}_USA bb_University_of_Kansas,_Lawrence,_{KS 66045,}_USA bc_Louisiana_Tech_University,_Ruston,_{LA 71272,}_USA bd_Northeastern_University,_Boston,_{MA 02115,}_USA be_University_of_Michigan,_Ann_Arbor,_{MI 48109,}_USA bf_Michigan_State_University,_East_Lansing,_{MI 48824,}_USA bg_University_of_Mississippi,_University,_{MS 38677,}_USA bh_University_of_Nebraska,_Lincoln,_{NE 68588,}_USA bi_Rutgers_University,_Piscataway,_{NJ 08855,}_USA bj_Princeton_University,_Princeton,_{NJ 08544,}_USA bk

StateUniversityofNewYork,Buffalo,NY 14260,USA

bl_University_of_Rochester,_Rochester,_{NY 14627,}_USA bm_State_University_of_New_York,_Stony_Brook,_{NY 11794,}_USA bn_Brookhaven_National_Laboratory,_Upton,_{NY 11973,}_USA bo_Langston_University,_Langston,_{OK 73050,}_USA bp_University_of_Oklahoma,_Norman,_{OK 73019,}_USA bq_Oklahoma_State_University,_Stillwater,_{OK 74078,}_USA br_Brown_University,_Providence,_{RI 02912,}_USA bs_University_of_Texas,_Arlington,_{TX 76019,}_USA bt_Southern_Methodist_University,_Dallas,_{TX 75275,}_USA bu_Rice_University,_Houston,_{TX 77005,}_USA

bv_University_of_Virginia,_{Charlottesville,}_{VA 22904,}_USA bw_University_of_Washington,_Seattle,_{WA 98195,}_USA

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Articlehistory: Received16May2014

Receivedinrevisedform19August2014 Accepted3September2014

Availableonline8September2014 Editor: H.Weerts

We present theﬁrstmeasurements ofthe differentialcross sectiond

σ

/dpγ_T for theproductionof an isolatedphotoninassociationwithatleasttwob-quarkjets.Themeasurementsconsiderphotonswith rapidities|yγ|<1.0 andtransversemomenta30<pγ_T<200 GeV.Theb-quarkjetsarerequiredtohave

pjet_T >15 GeV and_|yjet_|<1.5.The ratio ofdifferentialproductioncross sectionsfor

γ

+2 b-jetsto

γ

+b-jetasafunctionofpγ_T isalsopresented.Theresultsarebasedontheproton–antiprotoncollision data at√s=1.96 TeV collectedwiththe D0detectorattheFermilabTevatronCollider.Themeasured crosssectionsandtheirratiosarecomparedtothenext-to-leadingorderperturbativeQCDcalculationsas wellaspredictionsbasedonthekT-factorizationapproachandthosefromthe sherpa and pythia Monte

Carloeventgenerators.

In hadronic collisions, high-energy photons (

γ

) emerge unal-teredfromthehard parton–partoninteraction andtherefore pro-videacleanprobeoftheunderlyinghard-scatteringdynamics[1].

1 _Visitor_from:_Augustana_College,_Sioux_Falls,_SD,_USA. 2 _Visitor_from:_The_University_of_Liverpool,_Liverpool,_UK. 3 _Visitor_from:_DESY,_Hamburg,_Germany.

4 _Visitor_from:_Universidad_Michoacana_de_San_Nicolas_de_Hidalgo,_Morelia,

Mex-ico.

5 _Visitor_from:_SLAC,_Menlo_Park,_CA,_USA.

6 _Visitor_from:_University_College_London,_London,_UK.

7 _Visitor_from:_Centro_de_{Investigacion}_en_{Computacion, IPN,}_Mexico_City,_Mexico. 8 _Visitor_from:_Universidade_Estadual_Paulista,_São_Paulo,_Brazil.

9 _Visitor_from: _Karlsruher _Institut _für _Technologie _{(KIT), Steinbuch} _Centre _for

Computing(SCC),D-76128Karlsruhe,Germany.

10 _Visitor_from: _Oﬃce _of_Science, _U.S. _Department _of _Energy, _Washington, _DC

20585,USA.

11 _Visitor_from:_American_Association_for_the_Advancement_of_Science,

Washing-ton,DC 20005,USA.

12 _Visitor_from:_Kiev_Institute_for_Nuclear_Research,_Kiev,_Ukraine. 13 _Visitor_from:_University_of_Maryland,_College_Park,_Maryland_20742,_USA.

Photons produced inthese interactions (called direct or prompt) inassociationwithoneormorebottom(b)-quark jetsprovidean important test of perturbative Quantum Chromodynamics (QCD) predictionsatlargehard-scatteringscales Q andoverawiderange of parton momentum fractions. In addition, the study of these processesalsoprovidesinformationaboutthepartondensity func-tions (PDF) ofb quarks andgluons(g),whichstill have substan-tialuncertainties. In pp collisions,

¯

γ

+

b-jetevents areproduced primarily through the Compton process gb

→

γ

b, which domi-natesforlowandmoderatephotontransversemomenta(pγ_T),and through quark–antiquark annihilation followed by g

→

bb gluon

¯

splitting qq

¯

→

γ

g

→

γ

bb,

¯

which dominates at high pγ_T [2,3]. The ﬁnal state with b-quark pair production, pp

¯

→

γ

+

bb,

¯

is mainlyproducedviaqq

¯

→

γ

bb and

¯

gg

→

γ

bb scatterings

¯

[4].The

γ

+

2 b-jetprocessisacrucialcomponentofbackgroundin mea-surementsof,forexample,tt

¯

γ

coupling[5]andinsome searches for new phenomena. A series of measurements involving

γ

and b

(

c

)

-quarkﬁnal stateshavepreviously beenperformedbytheD0 andCDFCollaborations[3,6–9].

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Inthismeasurement,wefollowaninclusiveapproachby allow-ingtheﬁnalstate withanyadditionaljet(s) ontopofthestudied b-quark jets. Inclusive

γ

+

2 b-jet production mayalso originate frompartonicsubprocesses involvingpartonfragmentationintoa photon.However,usingphotonisolationrequirementssigniﬁcantly reducesthecontributionsfromsuchprocesses.Next-to-leading or-der(NLO)calculationsofthe

γ

+

2 b-jetproductioncrosssection, which includes all b-quark mass effects, have recently become available[4].Thesecalculationsarebasedonthefour-ﬂavor num-berscheme,whichassumesfourmasslessquarkﬂavorsandtreats theb quarkasamassivequarknotappearingintheinitialstate.

Thisletterpresentstheﬁrstmeasurement ofthecrosssection for associated production of an isolated photon with a bottom quark pair in pp collisions.

¯

The results are basedon data corre-sponding to an integrated luminosity of 8

.

7

±

0

.

5 fb−1 [10] col-lected with the D0 detector fromJune 2006 to September 2011 at the Fermilab Tevatron Collider at

√

s

=

1

.

96 TeV. The large datasample anduseof advancedphoton and b-jetidentiﬁcation tools [11–13] enable us to measure the

γ

+

2 b-jet production cross section differentially as a function of pγ_T for photons with rapidities

|

yγ

|

<

1

.

0 andtransversemomenta30

<

pγ_T

<

200 GeV, whiletheb jetsarerequiredtohavepjet_T

>

15 GeV and

|

yjet

|

<

1

.

5. This allows for probing the dynamics of the production process overawidekinematicrangenotstudiedbeforeinother measure-ments ofa vector boson

+

b-jet ﬁnal state. The ratio of differen-tialcrosssectionsfor

γ

+

2 b-jetproductionrelativeto

γ

+

b-jet productionisalsopresentedinthesamekinematicregionand dif-ferentially in pγ_T.The measurementof theratio ofcross sections leadstocancellationofvariousexperimentalandtheoretical uncer-tainties,allowing a moreprecise comparisonwiththetheoretical predictions.

TheD0detectorisageneralpurposedetectordescribedin de-tailelsewhere[14].Thesubdetectorsmostrelevanttothisanalysis are thecentral tracking system, composedof a siliconmicrostrip tracker (SMT) and a central ﬁber tracker embedded in a 1.9 T solenoidal magnetic ﬁeld, the central preshower detector (CPS), and the calorimeter. The CPS is located immediately before the inner layer of the central calorimeter and is formed of approx-imately one radiation length of lead absorber followed by three layers of scintillating strips. The calorimeter consists of a cen-tralsection(CC)withcoverage inpseudorapidityof

|

η

det

|

<

1

.

1,14

andtwoendcalorimeters(EC)extendingcoverage to

|

η

det

|

≈

4

.

2,

each housed in a separate cryostat, with scintillators between the CC andEC cryostats providingsamplingof developing show-ers for 1

.

1

<

|

η

det

|

<

1

.

4. The electromagnetic (EM) section of

thecalorimeterissegmentedlongitudinallyintofourlayers (EMi, i

=

1–4), withtransversesegmentation into cells ofsize

η

det

×

φ

det

=

0

.

1

×

0

.

1 (see footnote 14), except EM3 (near the EM

showermaximum),whereitis0

.

05

×

0

.

05.Thecalorimeterallows for a precise measurement of the energy of electrons and pho-tons, providing an energyresolutionof approximately4% (3%) at anenergyof30

(

100

)

GeV.The energyresponse ofthe calorime-tertophotonsiscalibratedusingelectrons from Z boson decays. Becauseelectrons andphotonsinteractdifferentlyinthe detector materialbeforethecalorimeter,additionalenergycorrectionsasa functionofpγ_T arederivedusingadetailed geant-based[15] sim-ulationoftheD0detectorresponse.Thesecorrectionsare

≈

2% for photoncandidatesofpγ_T

=

30 GeV,andsmallerforhigherpγ_T.

14 _The_polar_angle_θ_and_the_azimuthal_angle_φ_are_deﬁned_with_respect_to_the

positivez axis,whichisalongtheprotonbeamdirection.Pseudorapidityisdeﬁned asη= −ln[tan(θ/2)].Also,ηdetandφdetarethepseudorapidityandtheazimuthal

anglemeasuredwithrespect,tothecenterofthedetector.

ThedatausedinthisanalysisarerequiredtosatisfyD0 exper-iment data quality criteriathat ensure the proper functioning of detectorsubsystems (calorimeter andtrackingdetectors aremost important for this analysis) [14] during data-taking. The data is collected using a combination of triggers requiring a cluster of energy in the EM calorimeter with loose shower shape require-ments. Thetriggereﬃciencyis

≈

96% for photoncandidateswith pγ_T

=

30 GeV and100% for pγ_T

40 GeV. Oﬄineevent selection requires areconstructed pp interaction

¯

vertex[16] within 60 cm of thecenter ofthe detectoralong the beamaxis.The eﬃciency of the vertex requirement is

≈ (

96–98

)

%, depending on pγ_T. The missingtransversemomentum intheeventisrequiredtobeless than 0

.

7pγ_T to suppressbackgroundfromW

→

e

ν

decays.Such a requirementishighlyeﬃcient(

≥

98%)forsignalevents.

Photoncandidatesare identifiedintheD0detectorasisolated clustersofenergydepositsinthecalorimeterwithsignificant en-ergy intheEM calorimeterlayersandno spatially-matchedtrack in the trackingsystem. The detaileddescription of photon selec-tion andisolation criteriacan befound inRefs. [3,6].The photon selection efficiency and acceptance are calculated using samples of

γ

+

b-jet events, generated with the sherpa [17] and pythia

[18] Monte Carlo (MC) event generators. The samples are pro-cessed througha geant-based[15]simulationoftheD0 detector. Simulated eventsare overlaid withdata eventsfrom random pp

¯

crossingstoproperlymodeltheeffectsofmultiple pp interactions

¯

and noise in data. We ensure that the instantaneous luminosity distribution inthe overlayevents issimilar to thedata.The eﬃ-ciency for photons to pass the identiﬁcationcriteria is

(

71–82

)

% withrelativesystematicuncertaintyof3%.

For the

γ

+

n b measurement (n

=

1

,

2), at leastn jets with pjet_T

>

15 GeV and

|

yjet

|

<

1

.

5 areselected.Jetsare reconstructed usingtheD0Run IIalgorithm[19]withaconeradiusof

R

=

0

.

5. A setof criteriaisimposed to ensurethat we havesuﬃcient in-formationtoidentifythejetasaheavy-ﬂavorcandidate:thejetis requiredtohaveatleasttwoassociatedtrackswithpT

>

0

.

5 GeV

andatleastonehitintheSMT,oneofthesetracksmustalsohave pT

>

1

.

0 GeV.Thesecriteriahavean eﬃciencyofabout90%fora

b jet.Lightjets(initiatedbyu,d and s quarksorgluons)are sup-pressedusingadedicatedheavy-flavor(HF)taggingalgorithm[13]. The HF tagging algorithm is based on a multivariate analysis (MVA) technique that combines information from the secondary vertex(SV) taggingalgorithms andtracks impactparameter vari-ables using an artificial neural network (NN) to define a single outputdiscriminant,MVAbl [13].Thisalgorithmutilizesthelonger

lifetimes ofHF hadronsrelativeto their lighter counterparts. The MVAbl hasacontinuousoutputvaluethattendstowardsoneforb

jetandzeroforlightjets.Eventswithatleasttwojetspassingthe MVAbl

>

0

.

3 selectionare considered inthe

γ

+

2 b-jetanalysis.

Dependingon pγ_T,thisselectionhasan eﬃciencyof

(

13–21

)

% for twob jetswithrelativesystematicuncertaintiesof

(

4–6

)

%, primar-ilyduetouncertaintiesonthedata-to-MCcorrection factors[13]. Only

(

0

.

2–0

.

4

)

% oflight-jetsaremisidentiﬁedasb jets.

Afterapplicationofallselectionrequirements,3816

γ

+

2 b-jet candidate(186,406

γ

+

b-jetcandidate)eventsremaininthedata sample. Inthese events,thereare twomain backgroundsources: jets misidentiﬁed as photons and light-ﬂavor jets mimicking HF jets. Toestimatethephotonpurity,the

γ

-NNdistributionindata isﬁttedtoalinearcombinationoftemplatesforphotonsandjets obtainedfromsimulated

γ

+

jet anddijetsamples.Anindependent ﬁtisperformedineach pγ_T bin,yieldingphotonfractionsbetween 62%and90%,asshowninFig. 1.Themainsystematicuncertainty inthe photonfractionsisduetothefragmentationmodel imple-mentedin pythia[20].Thisuncertaintyisestimatedbyvaryingthe productionrateof

π

0_and

_η

_mesons_by

_±

_{50% with}_respect_to_their

(5)

Fig. 1. PhotonpurityasafunctionofpγT intheselecteddatasample.Theerrorbars

includestatisticalandsystematicuncertaintiesaddedinquadrature.Thebinningis deﬁnedasinTable 1.

Fig. 2. (Coloronline.)DistributionofdiscriminantDMJLafterallselectioncriteriafor

arepresentativebinof30<pTγ<40 GeV.Theexpectedcontributionfromthelight

jetscomponenthasbeensubtractedfromthedata.Thedistributionsfortheb-jet andc-jettemplates(withstatisticaluncertainties)areshownnormalizedtotheir respectiveﬁttedfractions.

centralvalues[21],andfoundtobeabout6% atpγ_T

≈

30 GeV,and

≤

1% atpγ_T

70 GeV.

Thefractionofdifferentﬂavor jetsintheselecteddatasample isextractedusingadiscriminant, DMJL, withdistributions

depen-dent on the jet ﬂavors. It combines two discriminating variables associatedwith the jet, massof any secondary vertexassociated with the jet MSV and the probability for the jet tracks located

withinthejetconetocomefromtheprimary pp interaction

¯

ver-tex. The latter probability is found using the jet lifetime impact parameter(JLIP)algorithm,andisdenoted as PJLIP [16].The ﬁnal

DMJL discriminant [22] is deﬁnedas DMJL

=

0

.

5

× (

MSV

/

5 GeV

−

ln

(

PJLIP

)/

20

)

, where MSV and ln

(

PJLIP

)

are normalized by their

maximumvaluesobtainedfromthecorrespondingdistributionsin data.The datasample with two HF-tagged jetsis ﬁtted to

tem-Fig. 3. The2b-jetfractionindataasafunctionofpγT derivedfromthetemplate

ﬁttotheheavyquarkjetdatasampleafterapplyingallselections.Theerrorbars showbothstatisticalandsystematicaluncertaintiessummedinquadrature.Binning isthesameasgiveninTable 1.

plates consisting mainly of 2 b-jet and 2 c-jet events, as deter-minedfromMCsimulation.Theremainingjetﬂavorcontributions inthesample(e.g.,light

+

light-jets,light

+

b

(

c

)

-jets,etc.)aresmall andare subtractedfromthe data.Thefractions oftheserarerjet contributions are estimated from sherpa simulation (which has been found to provide a good description ofthe data), and vary in therange

(

5–10

)

%. The difference in thevalues of these frac-tions obtained from sherpa and pythia,

(

2–4

)

%, is assigned asa systematicuncertaintyonthebackgroundestimate.Thefractionof 2 b-jet events are determined by performing a two-dimensional (correspondingto the2 b-jetcandidates) maximumlikelihood ﬁt ofDMJLdistributionsof2 jeteventsindatausingthe

correspond-ing templatesfor2b-jets and2c-jets. Thesejet ﬂavortemplates areobtainedfromMCsimulations.Asanexample,theresultofone ofthesemaximumlikelihoodﬁtstoDMJLtemplatesispresentedin Fig. 2(with

χ

2

_/

_ndf

₌

₆

_.

₈₀

_/

_{5 for}_data/MC_agreement)._This_shows

theone-dimensional projectionontothe highestpT jet DMJL axis

ofthe2Dﬁt,normalizedtothenumberofeventsindata,for pho-tonswith30

<

pγ_T

<

40 GeV.An independentﬁtis performedin each pγ_T bin,resultinginextractedfractionsof2b-jetevents be-tween76% and87%,asshowninFig. 3.Therelativeuncertainties oftheestimated2b-jetfractionsrangefrom5%to14%,increasing athigherpγ_T andaredominatedbythelimiteddatastatistics.

Byvaryingindependentlytherequirementsonphotonandb-jet identificationcriteriafromvery loosetovery tightselections, we find no evidence of a correlation between the measured photon purityandthe2b-jetfraction. Theobtainedphotonpurityand2 b-jetfractionsarefoundtobeconsistentwithinuncertaintieswith thevaluesdeterminedusingphotonandb-jetidentificationcriteria usedwiththedefaultselections.

Theestimatednumbersofsignaleventsineach pγ_T binare cor-rectedforthe geometricandkinematicacceptance ofthephoton andjets.The combinedacceptanceforphotonandjetsare calcu-latedusing sherpa MCevents.Theacceptanceiscalculatedforthe photonssatisfying pγ_T

>

30 GeV,

|

yγ

|

<

1

.

0 at particle level.The particle level includes all stable particles asdeﬁned in Ref. [23]. Thejetsarerequiredtohavepjet_T

>

15 GeV and

|

yjet

_|

_<

₁

_.

_5._As_in

Refs. [3,6],in the acceptancecalculations, the photon is required tobe isolatedby Eiso

T

=

EtotT

(

0

.

4

)

−

E

γ

(6)

Fig. 4. (Coloronline.)Theγ+2 b-jetdifferentialproductioncrosssectionsasa func-tionofpγT.Theuncertaintiesonthedatapointsincludestatisticalandsystematic

contributions.Themeasurementsarecomparedtothe NLOQCD calculations[4] usingthe CT10nlo_nf4PDFs [26](solidline). The predictionsfrom sherpa[17], pythia[18]andthekT-factorizationapproach[29,30]arealsoshown.

Fig. 5. (Coloronline.)Theratioofthemeasuredγ+2 b-jetproductioncross sec-tionstothe referenceNLOwith CT10predictions.The uncertaintiesonthe data includebothstatistical(innererrorbar)andtotaluncertainties(fullerrorbar). Sim-ilarratiostoNLOcalculationsfor predictionswith sherpa [17], pythia[18]and kT-factorization[29,30]arealsopresentedalongwiththescaleuncertaintiesonNLO

andkT-factorizationpredictions.

isthetotal transverseenergyofparticles withina coneofradius

R

=

(

η

)

2

_{+ (φ)}

2

₌

₀

_.

_{4 centered}_on_the_photon_direction_and

Eγ_T isthephoton transverseenergy.Thesumoftransverseenergy in the cone includes all stable particles [23]. The acceptance is driven by selection requirements in

|

η

det

|

(appliedto avoidedge

effectsinthecalorimeterregions usedforthemeasurement)and

|φ

det

|

(toavoid periodic calorimeter module boundaries), photon

|

η

γ

_|

_and _pγ

T, and bin-to-bin migration effects due to the ﬁnite

energy resolution of the EM calorimeter. The combined photon andjetsacceptancewithrespecttothe pT andrapidityselections

variesbetween66% and77% indifferentpγ_T bins.Uncertaintieson theacceptanceduetothejetenergyscale[24],jetenergy

resolu-tion,andthedifferencebetweenresultsobtainedwith sherpa and pythia_are_in_the_range_of

₍

_8–12

₎

_%.

The data,correctedforphoton andjet acceptance, reconstruc-tioneﬃcienciesandtheadmixtureofbackgroundevents,are pre-sented at the particle level by unfolding for effects of detector resolution,photon andb-jetdetectionineﬃciencies.The differen-tial crosssectionsof

γ

+

2 b-jetproduction are extractedinﬁve bins of pγ_T.They are given in Table 1.The datapoints are plot-tedatthevaluesof pγ_T forwhichthevalue ofasmooth function describing thedependence ofthecross section on pγ_T equals the averagedcrosssectioninthebin[25].

The crosssectionsfall by morethan twoorders ofmagnitude intherange30

<

pγ_T

<

200 GeV.Thestatisticaluncertaintyonthe results rangesfrom4.3% inthe ﬁrst p_Tγ binto 9% inthe last pγ_T bin,whilethetotalsystematicuncertaintyrangesupto20%.Main sourcesofsystematicuncertaintyarethephotonpurity(upto8%), photonandtwob-jetacceptance(upto14%),b-jetfraction(upto 13%), andintegrated luminosity (6%) [10]. At higher pγ_T, the un-certainty is dominatedby the fractions of b-jet events andtheir selectioneﬃciencies.

NLO perturbative QCD predictions, with the renormalization scale

μ

R, factorization scale

μ

F, and fragmentation scale

μ

f all

settopγ_T,arealsogiveninTable 1.Theuncertaintyfromthescale choice is

(

15–20

)

% and isestimatedthrougha simultaneous vari-ationofallthreescalesbyafactoroftwo,i.e.,for

μ

R,F,f

=

0

.

5pγT

and 2pγ_T. The predictions utilize CT10nlo_nf4 PDFs [26] and are corrected for non-perturbative effects of parton-to-hadron frag-mentation and multiple parton interactions. The latter are eval-uated using sherpa and pythia MC samples with their standard settings [17,18]. The overall correction variesfrom about0

.

90 at 30

<

pγ_T

<

40 GeV toabout0

.

95 athighpγ_T,andanuncertaintyof

2% is assignedto accountfor differencesbetweenthetwo MC generators.NLOpredictionsbasedonMSTW2008[27]arecloseto thosemadewithNNPDF2.3[28]andareslightlyhigher(upto7% atsmall pγ_T)thanthepredictionsusingCT10.

ThepredictionsbasedonthekT-factorizationapproach[29,30]

and unintegrated parton distributions [31] are also given in Ta-ble 1.ThekT-factorizationformalismcontainsadditional

contribu-tions tothecrosssectionsduetoresummationofgluonradiation diagrams with k2

T above a scale

μ

2 of

O(

1 GeV

)

, where kT

de-notesthetransversemomentumoftheradiatedgluon.Apartfrom this resummation, the non-vanishing transverse momentum dis-tribution of the colliding partons are taken into account. These effects leadtoa broadeningofthe photontransversemomentum distributioninthisapproach[29].Thescaleuncertaintiesonthese predictions vary from about31% at 30

<

pγ_T

<

40 GeV to about 50%inthehighestpγ_T bin.

Table 1alsocontainspredictionsfromthe pythia[18]MCevent generatorwiththe cteq6.1LPDFset.Itincludesonly2

→

2 matrix elements(ME)withgb

→

γ

b andqq

¯

→

γ

g scatterings(deﬁnedat LO)andwithg

→

bb splitting

¯

inthepartonshower (PS).Wealso provide predictions ofthe sherpa MC event generator [17] with the cteq6.6MPDF set[32].For

γ

+

b production, sherpa includes alltheMEswithonephotonanduptothreejets,withatleastone b-jetin ourkinematicregion.Inparticular,itaccountsforan ad-ditionalhardjetthataccompaniesthephotonassociatedwith2b jets.ComparedtoanNLOcalculation,thereisanadditionalbeneﬁt ofimposing resummation(further emissions)throughthe consis-tent combinationwiththePS.Matchingbetweenthe MEpartons andthePSjetsfollowstheprescriptiongiveninRef.[33]. System-atic uncertainties are estimated by varying the ME-PS matching

(7)

Fig. 6. (Coloronline.)Theγ+b-jetdifferentialproductioncrosssectionsasa func-tionofpγT.Theuncertaintiesonthedatapointsincludestatisticalandsystematic

contributionsaddedinquadrature.The measurementsarecomparedtothe NLO QCDcalculations[4]usingthe cteq6.6MPDFs[32](solidline).Thepredictionsfrom sherpa[17], pythia[18]andkT-factorization[29,30]arealsoshown.

scale by

±

5 GeV around the chosen central value.15 _As _a _result, the sherpa cross sectionsvary up to

±

7%, the uncertainty being largestintheﬁrstpγ_T bin.

Allthetheoreticalpredictionsareobtainedincludingthe isola-tionrequirementonthephotonEiso_T

<

2

.

5 GeV.Thepredictionsare comparedtodatainFig. 4asafunctionof pγ_T.Theratiosofdata totheNLOQCDcalculationswithCT10andofdifferentQCD pre-dictionsorMC simulation tothe sameNLO QCD calculationsare showninFig. 5asafunctionofpγ_T.

ThemeasuredcrosssectionsarewelldescribedbytheNLOQCD calculationsandthepredictionsfromthekT-factorizationapproach

in the full studied pγ_T region considering the experimental and theoretical uncertainties. Both of these predictions show consis-tent behavior, although the predictions from the kT-factorization

approachsuffer fromlarger uncertainties. pythia predicts signiﬁ-cantlylowerproductionratesandamoresteeplyfalling pγ_T distri-butionthanobservedindata. sherpa performsbetterindescribing thenormalizationathighpγ_T,butunderestimatesproductionrates comparedtothatobservedindataatlow pγ_T.

In addition to measuring the

γ

+

2 b-jet cross sections, we alsoobtainresultsfortheinclusive

γ

+

b-jetcrosssection inthe same pγ_T bins. Here we follow the same procedure as described inthe previous similarD0 measurement [3].However, asforthe

γ

+

2 b-jet crosssectionmeasurement,we nowusethemost re-centHF tagging algorithm [13]. The measured cross sections are showninFig. 6,andarecomparedtovariouspredictionsinFig. 7. Dataandpredictions arealso presentedinTable 2. Thevaluesof theobtained

γ

+

b-jetcrosssectionareconsistentwithour previ-ouslypublishedresults[3].

Weuse

σ

(

γ

+

2 b-jet

)

and

σ

(

γ

+

b-jet

)

cross sectionsto cal-culate their ratio in bins of p_Tγ. Fig. 8 shows the pγ_T spectrum of the measured ratio. The systematic uncertainties on the ra-tio vary within

(

11–15

)

%, being largest at high pγ_T. The major sourcesofsystematicuncertaintiesareattributedtothejet

accep-15 _We_choose_the_following_ME-PS_matching_parameters:_the_energy_scale _Q 0=

15 GeV andthespatialscaleD=0.4,whereD istakentobeoftheradiusofthe photonisolationcone.

Fig. 7. (Coloronline.)Theratioofγ+b-jetproductioncrosssectionstoNLOwith CT10predictionsfordataandtheoreticalpredictions.Theuncertaintiesonthedata includebothstatistical(innererrorbar)andtotaluncertainties(fullerrorbar).The ratiostotheNLOcalculationswithpredictionsfrom sherpa[17], pythia[18]and kT-factorization[29,30]arealsopresentedalongwiththescaleuncertaintiesonNLO

andkT-factorizationpredictions.

Fig. 8. (Coloronline.)Theratioofmeasuredcrosssectionsforγ+2 b-jettoγ+b-jet production asa functionof pγT comparedtotheoretical predictions.The

uncer-taintiesonthedatapoints includeboth statistical(innererrorbar)and thefull uncertainties(fullerrorbar).ThemeasurementsarecomparedtotheNLOQCD cal-culations[4].Thepredictionsfrom sherpa[17], pythia[18]andkT-factorization[29, 30]arealsoshownalongwiththescaleuncertaintiesonNLOandkT-factorization

predictions.

tances andthe estimationof b-jetand 2b-jet fractions obtained fromthetemplateﬁts tothedata.Fig. 8 alsoshowscomparisons with various predictions. The measurements are well described by the calculations done by NLO QCD and kT-factorization

pre-dictionstakingintoaccount theexperimental andtheoretical un-certainties. The scale uncertainties on the NLO calculations are typically

15%, while they vary upto 35% at high pγ_T for the kT-factorization approach. The predictions from sherpa describe

(8)

Table 1

Thedifferentialγ+2 b-jetproductioncrosssectionsdσ/dpγT inbinsofp

γ

T for|ηγ|<1.0,p

jet

T >15 GeV and|yjet|<1.5 togetherwithstatisticaluncertainties(δstat),total

systematicuncertainties(δsyst)andtotaluncertainties(δtot)whichareobtainedbyaddingδstatandδsystinquadrature.Thelastfourcolumnsshowtheoreticalpredictions obtainedwithNLOQCD,kTfactorization,andwiththe pythia andthe sherpa eventgenerators.

pγ_T bin (GeV) pγ_T(GeV) dσ/dpγ_T (pb/GeV)

Data δstat(%) δsyst(%) δtot(%) NLO kTfact. pythia sherpa

30–40 34.5 2.24×10−1 _4.3 ₊₁₉_/₋₁₇ ₊₁₉_/₋₁₈ ₂_.₃₉_×₁₀−1 ₂_.₂₀_×₁₀−1 ₈_.₉₆_×₁₀−2 ₁_.₂₃_×₁₀−1 40–50 44.6 9.80×10−2 _5.4 ₊₁₈_/₋₁₅ ₊₁₉_/₋₁₆ ₁_.₀₈_×₁₀−1 ₉_.₉₆_×₁₀−2 ₄_.₉₉_×₁₀−2 ₆_.₇₉_×₁₀−2 50–65 56.6 4.52×10−2 _6.2 ₊₁₅_/₋₁₄ ₊₁₆_/₋₁₆ ₄_.₅₁_×₁₀−2 ₄_.₃₁_×₁₀−2 ₁_.₉₉_×₁₀−2 ₃_.₂₉_×₁₀−2 65–90 75.2 1.54×10−2 _7.2 ₊₁₄ /−14 +16/−16 1.49×10−2 ₁ .48×10−2 ₅ .57×10−3 ₁ .19×10−2 90–200 118.3 1.93×10−3 _9.1 ₊₁₉ /−18 +21/−21 1.67×10−3 ₁ .96×10−3 ₅ .12×10−4 ₁ .45×10−3 Table 2

Thedifferentialγ+b-jetproductioncrosssectionsdσ/dpγT inbinsofp

γ

T for|ηγ|<1.0,p

jet

T >15 GeV and|yjet|<1.5 togetherwithstatisticaluncertainties(δstat),total

systematicuncertainties(δsyst),andtotaluncertainties(δtot)thatareobtainedbyaddingδstatandδsystinquadrature.Thelastfourcolumnsshowtheoreticalpredictions obtainedwithNLOQCD,kT-factorization,andwiththe pythia andthe sherpa eventgenerators.

pγ_T bin (GeV) pγ_T(GeV) dσ/dpγ_T (pb/GeV)

30–40 34.5 1.51 2.3 12 12 1.52 1.69 1.23 1.46 40–50 44.6 5.83×10−1 _2.4 ₁₁ ₁₂ ₅_.₀₆_×₁₀−1 ₅_.₇₀_×₁₀−1 ₄_.₂₃_×₁₀−1 ₅_.₆₅_×₁₀−1 50–65 56.6 1.92×10−1 _2.8 ₉ ₁₀ ₁_.₇₅_×₁₀−1 ₁_.₉₈_×₁₀−1 ₁_.₆₃_×₁₀−1 ₂_.₀₂_×₁₀−1 65–90 75.2 6.06×10−2 _3.3 ₉ ₉ ₄_.₉₃_×₁₀−2 ₅_.₄₃_×₁₀−2 ₄_.₂₇_×₁₀−2 ₅_.₄₁_×₁₀−2 90–200 118.3 6.15×10−3 _3.3 ₁₃ ₁₃ ₄ .83×10−3 ₅ .68×10−3 ₃ .76×10−3 ₅ .05×10−3 Table 3

Theσ(γ+2 b-jet)/σ(γ+b-jet)crosssectionratioinbinsofpγT for|ηγ|<1.0,p

jet

T >15 GeV and|yjet|<1.5 togetherwithstatisticaluncertainties(δstat),totalsystematic

uncertainties(δsyst)andtotaluncertainties(δtot)whichareobtainedbyaddingδstatandδsystinquadrature.Thelastfourcolumnsshowtheoreticalpredictionsobtainedwith NLOQCD,kTfactorization,andwiththe pythia andthe sherpa eventgenerators.

pγT bin (GeV) p

γ

T(GeV) σ(γ+2 b)/σ(γ+b)

30–40 34.5 1.48×10−1 _2.3 ₊₁₄ /−6 +14/−6 1.58×10−1 ₁ .42×10−1 ₇ .25×10−2 ₈ .42×10−2 40–50 44.6 1.68×10−1 _2.5 ₊₁₃ /−7 +13/−8 2.04×10−1 ₁ .89×10−1 ₁ .18×10−1 ₁ .20×10−1 50–65 56.6 2.36×10−1 _2.8 ₊₁₂_/₋₈ ₊₁₂_/₋₈ ₂_.₅₉_×₁₀−1 ₂_.₃₄_×₁₀−1 ₁_.₂₂_×₁₀−1 ₁_.₆₃_×₁₀−1 65–90 75.2 2.54×10−1 _3.3 ₊₁₁_/₋₈ ₊₁₂_/₋₁₀ ₃_.₀₅_×₁₀−1 ₂_.₉₂_×₁₀−1 ₁_.₃₀_×₁₀−1 ₂_.₂₀_×₁₀−1 90–200 118.3 3.14×10−1 _3.4 ₊₁₅_/₋₁₄ ₊₁₅_/₋₁₅ ₃_.₅₂_×₁₀−1 ₃_.₆₇_×₁₀−1 ₁_.₃₆_×₁₀−1 ₂_.₈₇_×₁₀−1

The Pythia modeldoesnot performwell indescribing theshape andunderestimatesratiosacrossallthebins.Experimentalresults aswell as theoretical predictions for the ratios are presented in

Table 3.

Insummary, we havepresented theﬁrst measurement ofthe differential cross section of inclusive production of a photon in associationwithtwo b-quark jetsasa function of pγ_T atthe Fer-milabTevatron pp Collider.

¯

Theresultscoverthekinematicrange 30

<

pγ_T

<

200 GeV,

|

yγ

|

<

1

.

0,pjet_T

>

15 GeV,and

|

yjet

|

<

1

.

5.The measuredcrosssectionsareinagreementwiththeNLOQCD cal-culationsand predictionsfromthe kT-factorization approach.We

havealsomeasuredtheratioofdifferential

σ

(

γ

+

2 b-jet

)/

σ

(

γ

+

b-jet

)

inthesamepγ_T range.Theratioagreeswiththepredictions fromNLOQCDandkT-factorizationapproachwithinthetheoretical

andexperimentaluncertaintiesinthefullstudied pγ_T range.These results can be used to further tune theory, MC event generators and improve the description of background processes in studies oftheHiggsboson andsearches fornewphenomenabeyondthe Standard Model at the Tevatron and the LHC in ﬁnal states in-volving the production of vector bosons in association with two b-quarkjets.

Acknowledgements

We are grateful to the authorsof the theoretical calculations, H.B. Hartanto,L. Reina,A. LipatovandN. Zotov,forproviding pre-dictionsandformanyusefuldiscussions.

We thankthe staffsatFermilab andcollaborating institutions, andacknowledgesupport fromthe DOEandNSF(USA);CEAand CNRS/IN2P3 (France); MON, Rosatom and RFBR (Russia); CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); DAE and DST (India); Colciencias(Colombia);CONACyT(Mexico);NRF(Korea);FOM(The Netherlands);STFCandtheRoyalSociety(UnitedKingdom);MSMT and GACR (Czech Republic); BMBF andDFG (Germany); SFI (Ire-land);TheSwedishResearchCouncil(Sweden);andCASandCNSF (China).

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