Measurements of differential jet cross sections in proton-proton collisions at sqrt(s)

33 Pages·2013·0.96 MB·English

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP/2012-343
2013/06/05
CMS-QCD-11-004
Measurements of differential jet cross sections in
√
proton-proton collisions at s = 7TeV with the CMS
detector
3
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The CMS Collaboration
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[ Measurementsofinclusivejetanddijetproductioncrosssectionsarepresented. Data
√
2 from LHC proton-proton collisions at s = 7TeV, corresponding to 5.0fb−1 of inte-
v grated luminosity, have been collected with the CMS detector. Jets are reconstructed
0
up to rapidity 2.5, transverse momentum 2TeV, and dijet invariant mass 5TeV, us-
6
6 ing the anti-kT clustering algorithm withdistance parameter R = 0.7. Themeasured
6 cross sections are corrected for detector effects and compared to perturbative QCD
.
2 predictionsatnext-to-leadingorder,usingfivesetsofpartondistributionfunctions.
1
2
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: SubmittedtoPhysicalReviewD
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(cid:13)c 2013CERNforthebenefitoftheCMSCollaboration. CC-BY-3.0license
∗SeeAppendixAforthelistofcollaborationmembers

1
1 Introduction
Eventswithhightransversemomentumjetsinproton-protoncollisionsaredescribedbyquan-
tum chromodynamics (QCD) in terms of parton-parton scattering, where the outgoing scat-
teredpartonsmanifestthemselvesashadronicjets. Measurementsoftheinclusivejetanddijet
cross sections can be used to test the predictions of perturbative QCD, constrain parton dis-
tribution functions (PDFs) of the proton, differentiate among PDF sets, and look for possible
deviationsfromthestandardmodel.
Inthispaper,measurementsofthedouble-differentialinclusivejet(p+p → jet+X)anddijet
(p+p → jet+jet+X)productioncrosssectionsarereportedasfunctionsofjetrapidityyand
√
either jet transverse momentum p or dijet invariant mass M , at s = 7TeV. The data were
T jj
collectedwiththeCompactMuonSolenoid(CMS)detectorattheCERNLargeHadronCollider
(LHC)duringthe2011runandcorrespondtoanintegratedluminosityof5.0fb−1,twoordersof
magnitudelargerthanthepublishedLHCresultsfromthe2010run[1–3]. Jetsarereconstructed
uptorapidity2.5, transversemomentum2TeV, anddijetinvariantmass5TeV. Themeasured
crosssectionsarecorrectedfordetectoreffectsandcomparedtothenext-to-leading-orderQCD
predictions.
2 Apparatus
TheCMScoordinatesystemhasitsoriginatthecenterofthedetector,withthezaxispointing
along the direction of the counterclockwise beam. The azimuthal angle is denoted as φ, the
polarangleasθ,andthepseudorapidityisdefinedasη = −ln[tan(θ/2)]. Thecentralfeature
of the CMS detector is a superconducting solenoid, of 6m internal diameter, that produces an
axialmagneticfieldof3.8T.Withinthefieldvolumeareasiliconpixelandstriptracker,alead
tungstate crystal electromagnetic calorimeter (ECAL) and a brass/plastic scintillator hadronic
calorimeter. Outsidethefieldvolumeandintheforwardregion(3 < |η| < 5)isaniron/quartz-
fiber hadronic calorimeter. Muons are measured in gas ionization detectors embedded in the
steel return yoke outside the solenoid, in the pseudorapidity range |η| < 2.4. A detailed de-
scriptionoftheCMSapparatuscanbefoundinRef.[4].
3 Jet reconstruction
The rapidity y and the transverse momentum p of a jet with energy E and momentum(cid:126)p =
T
(cid:113)
(p ,p ,p ) are defined as y = (1/2)ln[(E+p )/(E−p )] and p = p2 +p2. The inputs to
x y z z z T x y
the jet clustering algorithm are the four-momentum vectors of the reconstructed particle can-
didates. Each such candidate is constructed using the particle-flow technique [5], which com-
bines the information from several subdetectors and is calibrated to account for the nonlinear
and nonuniform response of the CMS calorimetric system to hadrons. Jets are reconstructed
using the anti-k clustering algorithm [6] with distance parameter R = 0.7. The clustering is
T
performed using four-momentum summation with the FASTJET package [7], where the cho-
sen distance parameter allows for the capture of most of the parton shower and improves
the dijet mass resolution with respect to smaller sizes. The total transverse energy ΣE and
T
missing transverse energy (cid:126)Emiss are used in the event selection and are derived from the re-
T
constructed particle-flow objects. They are defined as ΣE = ∑ E , with E = E sinθ , and
T i Ti Ti i i
(cid:126)Emiss = −∑ (E sinθ cosφxˆ +E sinθ sinφyˆ),wherethesumreferstoallparticlecandidates
T i i i i i i i
andxˆ,yˆ aretheunitvectorsinthedirectionofthe xandyaxes.
2 4 Datasamplesandeventselection
The reconstructed jets require a small additional energy correction, mostly due to thresholds
on reconstructed tracks and clusters in the particle-flow algorithm, and various reconstruc-
tion inefficiencies. These jet energy corrections are derived using simulated events, generated
by PYTHIA6 (version 6.4.22) [8] and processed through the CMS detector simulation based on
GEANT4 [9], and in situ measurements with dijet, photon+jet, and Z+jet events [10]. These
jet energy corrections correct reconstructed jets to the hadron level, as opposed to the par-
ton level. An offset correction is also applied to account for the extra energy from additional
proton-proton interactions within the same or neighboring bunch crossings (in-time and out-
of-time pileup) [10]. The pileup effects are important for the lowest-p jets (10% jet energy
T
scale correction and 1% systematic uncertainty [11] for jets with p ∼ 100GeV) and progres-
T
sively decrease with jet p . For jets with p > 200GeV the pileup effects are negligible. The
T T
jetenergycorrectiondependsonη and p ofthejet,andisappliedasamultiplicativefactorto
T
thejetfour-momentumvector. Thefactoristypicallybetween1.0and1.2andisapproximately
uniform in η. For a jet p = 100GeV the factor is 1.1, decreasing towards 1.0 with increasing
T
p . The typical jet p resolution is 10% at p = 100GeV. The dijet mass M is calculated from
T T T jj
the corrected four-momentum vectors of the two jets with the highest p (leading jets). The
T
relative dijet-mass resolution, estimated from the simulation, ranges from 7% at M = 0.2TeV
jj
to3%at M = 3TeV.
jj
4 Data samples and event selection
The data samples used for this measurement were collected with single-jet high-level triggers
(HLT) [12] that require at least one jet in the event to have p > 60, 110, 190, 240, or 370GeV,
T
respectively, in corrected jet transverse momentum. The online jet reconstruction uses only
calorimetricinformationandtheresultingHLTjetstypicallyhaveworseenergyresolutionthan
theofflineparticle-flowjets. Thelower-p triggerswereprescaledandthecorrespondinginte-
T
gratedluminosityofeachtriggersample,L ,islistedinTable1. Intheofflineanalysis,events
eff
are required to have at least one well reconstructed proton-proton interaction vertex [13]. In
ordertosuppressnonphysicaljets,i.e.,jetsresultingfromnoiseintheelectromagneticand/or
hadroniccalorimeters,thejetsarerequiredtosatisfythefollowingidentificationcriteria. Each
jet should contain at least two particles, one of which is a charged hadron, and the jet energy
fraction carried by neutral hadrons and photons should be less than 90%. These criteria have
anefficiencyofgreaterthan99%forphysicaljets,whiletheprobabilityforanonphysicaljetto
passthecriteriaislessthan10−6.
Table1: Theintegratedluminosityforeachofthedatasamples.
Min. jettrigger p 60 110 190 240 370
T
(GeV)
Jettriggername Jet60 Jet110 Jet190 Jet240 Jet370
L (pb−1) 0.41 7.3 152 512 4980
eff
The inclusive single-jet cross section measurements are made in five rapidity regions of size
∆|y| = 0.5 over the range 0.0–2.5. Jets that do not satisfy the jet identification criteria are
discardedandeventsarerequiredtocontainatleastonejetthatsatisfiesthesecriteria. Inorder
toavoidanytriggerbias,thejetsareadditionallyrequiredtohave p > 110,200,300,360,and
T
510GeVforthefivesingle-jetHLTtriggersused,respectively. Figure1(left)showsthetrigger
efficiency as a function of the jet p , for the central rapidity bin |y| < 0.5 and for the highest
T
triggerthreshold. Theefficiencyofeachtriggerpathhasbeenmeasuredusingeventscollected
3
withalowerthresholdsingle-jettriggerandconfirmedwitheventscollectedwithsingle-muon
triggers.
Background events due to instrumental noise, beam halo effects, or proton-proton collisions
with leptons in the final state that might survive the jet identification criteria are further sup-
pressed by requiring Emiss/ΣE < 0.3. Hard QCD processes do not generate true Emiss and
T T T
because of the good energy resolution the measured values of Emiss in such events are small
T
compared to the total transverse energy. Hence, the distribution of the variable Emiss/ΣE
T T
peaks close to zero for QCD events, while some background events give larger values. Fig-
ure 2 (left) shows a typical distribution of the variable Emiss/ΣE for events with at least one
T T
jetwith p > 510GeV,collectedwiththe370GeVsingle-jettrigger. Thedatapointsexceedthe
T
QCD predictions at large values of Emiss. This tail is dominated by processes such as Z+jet(s),
T
where the Z boson decays to neutrinos, and W+jet(s), where the W boson decays to leptons.
Noeventsfrominstrumentalandbeamhaloeffectswerefoundtosurvivethejetidentification
criteria, and therefore the additional Emiss/ΣE selection only removes events from processes
T T
thatproducetrue Emiss.
T
For the dijet measurement, at least two jets with p > 60GeV and p > 30GeV and sat-
T1 T2
isfying the tight identification criteria are required. If either of the two leading jets fails the
identification criteria, the event is discarded. The dijet measurement is performed in five
rapidity regions of size ∆|y | = 0.5, defined by the maximum absolute rapidity y =
max max
sign(|max(y ,y )|−|min(y ,y )|)·max(|y |,|y |) of the two leading jets in the event. The
1 2 1 2 1 2
use of the variable |y| ≡ |y | divides the phase space of the dijet system into exclusive
max max
rapiditybins,whichcorrespondtodifferentscatteringanglesinthecenter-of-massframe.
Low values of |y| probe s-channel scattering at large angles, while large values of |y|
max max
probe t-channel scattering at small angles. For each rapidity bin the trigger efficiency is ex-
pressedasafunctionof M ,andtheeventsarerequiredtosatisfyaminimummassthreshold,
jj
whichincreaseswith|y| . Figure1(right)showsthetriggerefficiencyforthecentralrapidity
max
binandforthehighesttriggerthreshold. Becauseofthedijettopology,nofurthercutisneeded
onthe Emiss/ΣE variable,ascanbeseeninFig.2(right).
T T
Efficiency 0.81 sC = M7 STeV Efficiency 0.81 sC = M7 STeV
Trigger 0.6 anLti -=k T5 .R0 =fb 0-1.7 Trigger 0.6 anLti -=k T5 .R0 =fb 0-1.7
|y| < 0.5 |y| < 0.5
0.4 0.4 max
Jet370 Jet370
0.2 0.2
0 0
250 300 350 400 450 500 550 600 650 700 400 600 800 1000 1200 1400
Jet p (GeV) M (GeV)
T jj
Figure 1: Trigger efficiency as a function of the jet p (left) and dijet mass M (right) for the
T jj
370GeVsingle-jettriggerandforthecentralrapiditybins.
5 Measurement of the differential jet and dijet cross sections
In this section the reconstruction of the jet transverse momentum and dijet mass spectra from
the different samples is presented. Then the unfolding procedure, which translates the recon-
structed spectra into true spectra, is described. Finally, the experimental uncertainties related
tothemeasurementsaredescribedanddiscussed.
4 5 Measurementofthedifferentialjetanddijetcrosssections
s 106 s
ent CMS Leading jet pT > 510 GeV ent CMS |y|max < 0.5, Mjj > 910 GeV
Ev 105 s = 7 TeV Data ( 5.0 fb-1 ) Ev 104 s = 7 TeV Data ( 5.0 fb-1 )
QCD Simulation QCD Simulation
104 EmTiss/S ET < 0.3 103
103
102
102
10
10
1 1
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
Emiss/S E Emiss/S E
T T T T
Figure 2: Distribution of Emiss/ΣE for data events (black points) and simulated QCD events
T T
(continuousline)withatleastonejetwith p > 510GeV(left)andfordijeteventswith|y| <
T max
2.5 and M > 910GeV (right), collected with the 370GeV single-jet trigger. The distribution
jj
from the inclusive-jet selection is shown before the offline selection Emiss/ΣE < 0.3. The
T T
larger tail in the data is caused by other processes with true Emiss (such as Z+jet(s), where the
T
Zbosondecaystoneutrinos,andW+jet(s),wheretheWbosondecaystoleptons).
5.1 Determination of transverse momentum and dijet mass spectra
GeV 110078 sC = M7 STeV GeV 106 sC = M7 STeV
ale / 105 anLti -=k T5 .R0 =fb 0-1.7 ale / 105 anLti -=k T5 .R0 =fb 0-1.7
c c
es es 103
Pr 103 Pr

·Jets 10 |y| <J 0e.t560 ·ents 10 |y|maJx e<t 600.5
Jet110 v Jet110
Jet190 E Jet190
10-1 Jet240 10-1 Jet240
Jet370 Jet370
10-3 10-3
200 300 400 1000 2000 200 300 400 1000 2000 3000
Jet p (GeV) M (GeV)
T jj
Figure3: Spectrumconstructionfromindividualtriggerpaths. Left: inclusivejet p spectrum
T
for |y| < 0.5. Right: dijet mass spectrum for |y| < 0.5. The different markers indicate
max
differenttriggerpaths.
Thejet p (dijetinvariantmass)spectrumisobtainedbypopulatingeachbinwiththenumber
T
ofjets(events)collectedusingthehighestthresholdtriggerwhichgivesmorethan99%trigger
efficiency. Then, the yields from each trigger path are scaled according to the corresponding
prescale value for this path (effective luminosity), as shown in Table 1. Figure 3 shows the
reconstructed spectra for inclusive jets (left) and dijets (right), in the central rapidity bin, de-
composedintothefivecontributingtriggerpaths.
Theobservedinclusivejetyieldsaretransformedintodouble-differentialcrosssectionsasfol-
lows:
d2σ 1 Njets
= , (1)
dp dy (cid:101)·L ∆p (2·∆|y|)
T eff T
where N isthenumberofjetsinthebin,L istheintegratedluminosityofthedatasample
jets eff
fromwhichtheeventsaretaken,(cid:101)istheproductofthetriggerandeventselectionefficiencies,
bothofwhicharegreaterthan99%,and∆p and∆|y|arethetransversemomentumandrapid-
T
ity bin widths, respectively. The width of the p bins is proportional to the p resolution and
T T
so increases with p . The statistical uncertainty assigned to each p bin takes into account the
T T
number of independent events that contribute at least one jet in the bin. The largest fraction
(more than 90%) of the observed jets in each p bin originate from different events, however
T
5.2 Unfolding 5
a smallfraction of events contribute morethan one jet. Such events aretypically back-to-back
dijetevents,socloselybalancedin p thatbothjetsendupinthesame|y|and p bin.
T T
(cid:112) (cid:112)
The statistical uncertainty in the number of jets in a bin is e = (4−3f)/(2− f)· N ,
stat jets
where f = N /N isthefractionofeventsthatcontributeonejetinthegivenbin. Theformula
1 ev
is valid under the assumption that the number of events that contribute more than two jets in
eachbinisnegligible,whichhasbeenverifiedforthecurrentmeasurement.
Theobserveddijetyieldsaretransformedintodouble-differentialcrosssectionsasfollows:
d2σ 1 N
= · , (2)
dM dy (cid:101)·L ∆M (2·∆|y| )
jj max eff jj max
where∆M and∆|y| arethemassandrapiditybinwidths,respectively. Thesizeofthedijet
jj max
mass bins isapproximately equalto orlarger thanthe massresolution atthe bincenter, while
the bins at the edge of the spectrum have been merged to assure a minimal number of events
ineachbin.
5.2 Unfolding
Because of the detector resolution and the steeply falling spectra, the measured differential
cross sections are smeared with respect to the particle-level cross sections. Each p and mass
T
bin contains events that have migrated in from neighboring bins and is missing events that
have migrated out. For a steeply falling spectrum more events migrate into a bin than out.
In order to allow for a direct comparison of experimental measurements with corresponding
results from other experiments and with QCD predictions, the spectra are unfolded in order
to correct for detector effects. The response matrix is obtained from the detector simulation
andcorrectedforthemeasureddifferencesintheresolutionbetweendataandsimulation[10].
Figure4showstheresponsematricesforthejet p (left)andthedijetmass(right)inthecentral
T
rapidity bins. The unfolding is done with the RooUnfold package [14] using the D’Agostini
method[15].
) 2000 ) 4000
V CMS Simulation V CMS Simulation
Ge |y| < 0.5 0.7 Ge 3000 |y|max < 0.5 0.9
(et pT1000 antsi- k=T 7R T =e V0.7 0.6 (e Mjj2000 antsi- k=T 7R T =e V0.7 00..78
e J 0.5 Tru 0.6
u 1000
r 0.4 0.5
T
0.4
0.3
0.3
0.2
200 0.2
0.1
0.1
0 200 0
200 300 1000 2000 200 300 1000 2000
Measured Jet p (GeV) Measured M (GeV)
T jj
Figure4: Responsematricesfortheinclusivejet p spectrum(left)andthedijetmassspectrum
T
(right)inthecentralrapiditybins.
6 5 Measurementofthedifferentialjetanddijetcrosssections
5.3 Experimental uncertainties
Thedominantexperimentaluncertaintiesarerelatedtothejetenergyscale(JES),theluminos-
ity, and the jet p resolution. Other sources of systematic uncertainty, such as the jet angular
T
resolution,arenegligible. Theagreementoftheresultsforpositiveandnegativerapiditieshas
alsobeenconfirmed. Figure5showstheeffectsoftheexperimentaluncertaintiesinallrapidity
bins for the cross section measurements. For rapidities up to |y| = 1.5 the total uncertainty of
both cross sections ranges from 5% at low p or M to 20% at high p or M , respectively. For
T jj T jj
higherrapiditiesthe totaluncertaintyincreasesto10–30% inbothcases, with the exceptionof
the highest dijet mass bin in the outer rapidity region of 2.0 < |y| < 2.5, where the uncer-
max
tainty is substantially larger. A discussion of the individual contributions to the uncertainty
follows.
5.3.1 Jet energy scale (JES) uncertainty
Thejetenergyscaleisthedominantsourceofsystematicuncertainty. Becauseofthesteepslope
ofthe p spectrum,asmalluncertaintyinthe p scaletranslatesintoalargeuncertaintyinthe
T T
crosssectionforagivenvalueof p . Thejetenergyscaleuncertaintyisdependenton p andη
T T
and has been estimated to be 2.0–2.5% [11]. The individual, uncorrelated contributions to the
JESuncertaintyhavebeenestimatedandarediscussedbelow.
The JES uncertainty sources account for the p and η dependence of the JES within the total
T
uncertainty. Forthephasespaceofjetsconsideredhere,16mutuallyuncorrelatedsourcescon-
tribute to the total uncertainty, where each such source represents a signed 1σ variation from
agivensystematiceffectforeachpointin (p ,η). Summingupseparatelythepositiveorneg-
T
ative variations of the sources in quadrature will reproduce the total upward and downward
JESuncertaintiesateachpoint. Theuncertaintiesfromall16independentsourcesareincluded
in the supplemental material [URL will be inserted by publisher] submitted with this paper
and in the HEPDATA record for this paper; the cross section measurements and other details
arealsotabulatedtherein.
Theuncertaintysourcesaredividedintofourbroadcategories: pileupeffects,relativecalibra-
tionofjetenergyscaleversusη,absoluteenergyscaleincludingp dependence,anddifferences
T
in quark- and gluon-initiated jets. The first category, containing pileup effects, has relatively
littleimpactontheanalysespresentedinthispaper.
Thesecondcategory,containingη-dependenteffects,parameterizesthepossiblerelativevaria-
tionsinJES,whichforthedijetandinclusivejetanalysesleadtocorrelationsbetweenrapidity
bins. In principle these effects could also have a p dependence, but systematic studies on
T
data and Monte Carlo (MC) events indicate that the p and η dependence of the uncertainties
T
factorizetoagoodapproximation.
The third category deals with the uncertainty in the absolute energy scale and its p depen-
T
dence and is the most relevant one for these analyses. The photon+jet and Z+jet events only
constrain the JES directly in a limited jet p range of about 30–600GeV, and the response at
T
higher (and lower) p is estimated by MC simulation. The p -dependent uncertainty arising
T T
from modeling of the underlying event and jet fragmentation is obtained by comparing pre-
dictionsfromPYTHIA6andHERWIG++. Moststudiesshowthatbothgeneratorsagreewiththe
datawithdifferencescomparabletothoseseenbetweendataandMC. Theuncertaintyarising
fromthecalorimeterresponsetosinglehadronsisestimatedbyvaryingtheresponseparame-
terizationby±3%aroundthecentralvalue. Thefinaluncertaintyarisesfromdifferencesinthe
JESforquark-andgluon-initiatedjetsandisdeterminedfromMCstudies.
5.3 Experimentaluncertainties 7
ncertainty 000...234 |y| < 0.TJU5EontSfaollding anLtsi -=C k= T5 M 7.R0 ST =feb V0-1.7 ncertainty 00..23 |y|max <TJU Eo0ntS.fa5ollding anLtsi -=C k= T5 M 7.R0 ST =feb V0-1.7
u Luminosity u Luminosity
ction 0.1 ction 0.1
e e
s s 0 s s 0
s s
Cro -0.1 Cro
-0.1
-0.2
-0.3 -0.2
200 300 400 1000 2000 200 300 400 1000 2000 3000
Jet p (GeV) M (GeV)
T jj
ncertainty 000...234 0.5 < |yTJU|Eon <tSfao 1lld.0ing anLtsi -=C k= T5 M 7.R0 ST =feb V0-1.7 ncertainty 00..23 0.5 < |yTJU|EomntSafaoxl l<d in1g.0 anLtsi -=C k= T5 M 7.R0 ST =feb V0-1.7
u Luminosity u Luminosity
ction 0.1 ction 0.1
e e
s s 0 s s 0
s s
Cro -0.1 Cro
-0.1
-0.2
-0.3 -0.2
200 300 400 1000 300 400500 1000 2000 3000
Jet p (GeV) M (GeV)
T jj
ncertainty 000...234 1.0 < |yTJU|Eon <tSfao 1lld.5ing anLtsi -=C k= T5 M 7.R0 ST =feb V0-1.7 ncertainty 00..23 1.0 < |yTJU|EomntSafaoxl l<d in1g.5 anLtsi -=C k= T5 M 7.R0 ST =feb V0-1.7
u Luminosity u Luminosity
ction 0.1 ction 0.1
e e
s s 0 s s 0
s s
Cro -0.1 Cro
-0.1
-0.2
-0.3 -0.2
200 300 400500 1000 500 1000 2000 3000 4000
Jet p (GeV) M (GeV)
T jj
ainty 0.6 1.5 < |yT|o <ta 2l.0 sC = M7 STeV ainty 0.6 1.5 < |yT|omtaaxl < 2.0 sC = M7 STeV
ncert 0.4 JUEnSfolding anLti -=k T5 .R0 =fb 0-1.7 ncert 0.4 JUEnSfolding anLti -=k T5 .R0 =fb 0-1.7
u Luminosity u Luminosity
on 0.2 on 0.2
cti cti
e e
s s
s 0 s 0
s s
o o
Cr Cr
-0.2 -0.2
-0.4 -0.4
200 300 400 500 1000 600 1000 2000 3000 4000
Jet p (GeV) M (GeV)
T jj
ainty 0.81 2.0 < |yT|o <ta 2l.5 sC = M7 STeV ainty 0.81 2.0 < |yT|omtaaxl < 2.5 sC = M7 STeV
ncert 0.6 JUEnSfolding anLti -=k T5 .R0 =fb 0-1.7 ncert 0.6 JUEnSfolding anLti -=k T5 .R0 =fb 0-1.7
u Luminosity u Luminosity
n 0.4 n 0.4
o o
ecti 0.2 ecti 0.2
s s
ss 0 ss 0
o o
Cr -0.2 Cr -0.2
-0.4 -0.4
-0.6 -0.6
200 300 400 500 600 2000 3000 4000 5000
Jet p (GeV) M (GeV)
T jj
Figure5: Effectoftherelativeexperimentaluncertaintiesfortheinclusivejet(leftcolumn)and
dijet(rightcolumn)crosssectionmeasurements,andforallfive|y|and|y| bins,respectively.
max
Theupwardanddownwarduncertaintiesareestimatedseparately.
8 6 Theoreticalpredictions
5.3.2 Luminosity uncertainty
Theluminosityuncertaintyisestimatedtobe2.2%[16],whichcanbedirectlytranslatedintoa
2.2%uncertaintyonthecrosssectionnormalization. Itisfullycorrelatedacrossall p andmass
T
bins.
5.3.3 Unfolding uncertainty
Theunfoldingcorrectioniscloselyrelatedtothedependenceonthe p and M resolutionand
T jj
thespectrumslope. Fortheinclusivejet p spectrumitvariesbetween5%and10%, whilefor
T
the dijet mass spectrum it ranges between 2% and 5%. The shape of the unfolding correction
and uncertainty as displayed in Fig. 5 is understood as follows: the resolution in the observ-
able, p or M , improves when going from low to high values. As a consequence the effect of
T jj
smearingismorepronouncedinthelower p or M region. Ontheotherhandthe p and M
T jj T jj
spectrabecomesteeperwhenapproachingthekinematiclimitathigh p or M ,leadingagain
T jj
toalargersmearingeffectthanobservedatmediumvalues.
Theuncertaintyintroducedbytheunfoldingiscausedbythemodelingofthejet p (dijetmass)
T
resolutionandthejet p (dijetmass)spectruminthesimulation. Inordertoestimatethesensi-
T
tivityofthecorrectiontotheseinputs,thejet p resolutionisvariedby±10%andthejet(dijet
T
mass) spectrum slope by ±5%. The former is motivated by the observed difference between
data and simulation in the jet energy resolution [10], and the latter is a conservative estimate
based on comparisons of the theoretical and measured spectrum shapes. An additional con-
stant 2% uncertainty is assigned to the dependence on the unfolding method. Overall, the
unfolding uncertainty is of the order of 3–4%, and is fully correlated across the p and mass
T
bins.
5.3.4 Other uncertainty sources
The contributions from small trigger and jet identification inefficiencies, time dependence of
the jet p resolution, and uncertainty on the trigger prescale factor have been shown to be
T
muchsmallerthan1%. Toaccountfortheseresidualeffectsaconservativeuncertaintyof1%is
assignedtoeachjet p anddijetmassbin,uncorrelatedacrossthebins.
T
6 Theoretical predictions
The theoretical predictions for the jet cross sections consist of a next-to-leading-order (NLO)
QCDcalculationandanonperturbative(NP)correctiontoaccountforthemultipartoninterac-
tions(MPI)andhadronizationeffects.
6.1 NLO calculations
The NLO calculations are performed using the NLOJet++ program (v2.0.1) [17] within the
framework of the fastNLO package (v1.4) [18]. The renormalization and factorization scales
(µ and µ ) for the inclusive and dijet measurements are identified with the jet p and the
R F T
average transverse momentum pave of the two jets, respectively. The NLO calculation is per-
T
formed using five different PDF sets: CT10 [19], MSTW2008NLO [20], NNPDF2.1 [21], HER-
APDF1.5 [22], and ABKM09 [23] at the corresponding default values of the strong coupling
constantα (M ) = 0.1180,0.120,0.119,0.1176,and0.1179,respectively.
S Z