ATLAS NOTEATLAS-CONF-2011-053

March 30, 2011

Light-quark and Gluon Jets in ATLAS:Calorimeter Response, Jet Energy Scale Systematics, and Sample

Characterization

The ATLAS Collaboration

Abstract

The energy response of the ATLAS calorimeter to a jet depends on the observableproperties of a jet, including, for example, the momentum spectra and number of chargedhadrons. The fragmentation differences between jets initiated by a quark and jets initiatedby a gluon lead to a flavor dependence in the jet energy scale. Because the flavor content ofsamples varies, this difference results in an additional flavor-dependent term in the jet energyscale uncertainty. This uncertainty term is derived for a general sample of jets and can beup to ∼6% in cases where the flavor composition of a sample of events is poorly known. Atemplate-fit method for determining the flavor composition of a sample of jets is presented.The templates, based on jet properties sensitive to the partonic origin of the jet, allow thedetermination of flavor composition with a precision of about 10%. The flavor-dependentterm of the jet energy scale systematic uncertainty is correspondingly reduced.

1 Introduction

The precise determination of the jet energy and an optimal jet energy resolution are the two major tasksof the ATLAS jet calibration program. In order for this work to be useful for all physics analyses, the jetenergy scale, resolution, and uncertainty should be universally applicable to all event topologies. The jetenergy calibration used currently in ATLAS, denoted EM+JES [1, 2], corrects the average jet transversemomentum response based only on the pseudo-rapidity and uncalibrated transverse momentum of thejet. While this is sufficient to achieve an average response near unity, the response of a jet calibrated inthis way depends on the details of the jet fragmentation and showering properties, which are correlated tothe flavor of the parton initiating that jet (e.g. see [3]). This dependence results in an inflated jet energyresolution and an additional term in the jet energy scale systematic uncertainty for any measurementusing an event selection different from the one with which the jet energy scale was derived. If thisproblem can be addressed, then all of the ATLAS analyses will have the benefit of the smaller jet energyscale systematic derived for the measurement of the inclusive jet cross-section [4].

This note presents a detailed analysis of the jet energy scale systematic uncertainty due to the dif-ference in response between gluon-initiated and light-quark-initiated jets (henceforth gluon-jets and LQ-jets). This issue can be alleviated by measuring the flavor composition of a sample of jets using templatefits to certain properties of the jets that are sensitive to changes in fragmentation. Although these jetproperties may not have sufficient discrimination power to determine the partonic origin of a specifc jet,it is possible to determine the average flavor composition of a sufficiently large sample of jets. The tem-plates are constructed in di-jet events, which are expected to comprise mostly gluon-jets at low transversemomentum (pT ) and central rapidities. They are then applied to events with a high-pT photon balancinga high-pT jet (γ-jet events), which are expected to comprise mostly LQ-jets balancing the photon. Theapplication of this technique is further demonstrated with a sample of multi-jet events, wherein the jetsare initiated mostly by gluons from radiation.

This document is organized as follows. The event selection and data used for all the studies in thisnote are described in Section 2. Section 3 details the difference in calorimeter response between gluon-and LQ-jets. The systematic uncertainty on the jet energy scale due to this difference in response isexplained in Section 4. In Section 5, the template-fit approach is described and templates for use inMonte Carlo simulation and data are derived. The templates are extracted from di-jet events, validatedin γ-jet events, and tested using γ-jet and multi-jet events.

2 Data Sample and Event Selection

Three different event selections are used. The first is based on [4] and selects QCD di-jet events (di-jetsample). The second is based on [5] and selects jets with a high-pT photon back-to-back with a jet (γ-jetsample). The third is based on [6] and selects QCD multi-jet events (multi-jet sample). For the purposesof the multi-jet sample, the number of jets with pT > 60 GeV and |η| < 2.8 dictates the jet-multiplicitybin for the event.

Only data for which the calorimeter and inner detector were fully operational and the solenoid wason are used [7]. Total integrated luminosities of 2.43±0.08 pb−1 for the di-jet and multi-jet samples and37.1±1.3 pb−1 for the γ-jet sample are selected based on these criteria [8]. The data were collected fromJune to October 2010.

2.1 Trigger and Event Selection

Different triggers are used to select each sample, in order to be maximally efficient over the entire jet pT

range of interest. The di-jet sample is selected using the hardware-based calorimeter jet triggers [9, 10],

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which are fully efficient for jets with pT > 60 GeV. The γ-jet sample is selected using a photon trigger thatis fully efficient for photons passing offline selections with pT > 45 GeV and was not pre-scaled duringthe data taking period. The multi-jet sample uses a hardware-based calorimeter jet trigger that requires atleast two jets with uncalibrated pT > 10 GeV for the inclusive two-jet bin. For higher multiplicity bins,the trigger with three or more jets with the same uncalibrated pT threshold is used. These triggers arefully efficient for jets with calibrated pT > 80 GeV.

Offline, a vertex with at least five tracks with ptrackT > 150 MeV is required, with the longitudinal

position well within the tracking acceptance (|z| <10 cm). This requirement significantly reduces cosmicray and beam backgrounds. Two additional event-level criteria are applied to the γ-jet sample. Thephoton and leading jet are required to be back-to-back (∆φ > π−0.2 radians). In order to ensure balance,the second-leading jet in the event is required to have pT below 10% of the pT of the leading jet.

2.2 Monte Carlo Simulation

The data are compared to Monte Carlo (MC) events generated using PYTHIA [11] with the ATLASAMBT1 (MC10) tune [12] and passed through a full detector simulation [13, 14]. The same trigger,event, jet, and track selection criteria are used in the MC simulation as in the data. The MC simulationsamples all have exactly one proton-proton interaction per event.

To assess systematic uncertainties in Section 5, two additional MC samples are used. The first usesPYTHIA with the Perugia2010 [15] tune. This tune is expected to differ significantly from AMBT1 inits underlying event characteristics. The second sample uses HERWIG++ [16] for event generation. Themulti-jet sample is generated using ALPGEN [17].

2.3 Photon Selection

In the γ-jet sample, photons with pT > 45 GeV are selected in the barrel calorimeter (with pseudo-rapidity |η| < 1.37). Only the leading photon in the event is considered. The photons are required to passpre-selection and “tight” photon cuts as described in [18]. The photons are additionally required to be ina region of the calorimeter where a precise energy measurement can be made (i.e. away from calorimeterdefects). In order to remove photons that convert prior to reaching the front face of the calorimeter,photons are required not to match any reconstructed tracks.

2.4 Jet Reconstruction, Selection, Calibration, and Flavor Tagging

Calorimeter jets with uncalibrated pT > 7 GeV and |η| < 2.8 are reconstructed using the anti-kt jetalgorithm [19, 20] with a four-momentum recombination scheme. Jet-finding distance parameters ofboth R = 0.4 and R = 0.6 are analyzed. Jets are constructed with uncalibrated topological clusters andcalibrated with the EM+JES scheme [1, 4]. This scheme is designed to bring the calorimeter jet energyto the energy of the “true” particle jets on average. Particle jets are reconstructed using the same anti-kt

algorithm with stable, interacting1 particles as input to the jet algorithm. In all cases, jet finding is donein y − φ coordinates and jet calibration is done in ηjet − φ jet coordinates2.

The jet transverse momentum response, R ≡ precoT /ptrue

T (henceforth simply “jet response”), is cal-culated by matching reconstructed calorimeter jets to “true” particle jets with a matching radius ∆R =√

(∆φ)2 + (∆η)2 ≤ 0.3. The reconstructed jets are additionally required to pass several selection criteria,

1 A particle is considered stable and interacting if its lifetime is longer than 10 ps and it is not either a muon or a neutrino.2 In the right-handed ATLAS coordinate system, the pseudo-rapidity η is defined as η ≡ − ln [tan (θ/2)], where the polar

angle θ is measured with respect to the LHC beam-line. The azimuthal angle φ is measured with respect to the x-axis, whichpoints towards the center of the LHC ring. The z-axis is parallel to the anti-clockwise beam, as viewed from above. The rapidityis defined as y = 0.5 × ln[(E + pz)/(E − pz)], where E denotes the energy and pz is the component of the momentum along thebeam direction. Transverse momentum and energy are defined as pT = p × sin (θ) and ET = E × sin (θ), respectively.

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which are each designed to mitigate the impact of specific non-collision backgrounds [4, 7]. In the caseof the γ-jet sample, if the opening angle, ∆R < 0.2, between a photon passing all selection criteria anda jet, the jet was rejected. Jets are considered isolated if there is no other jet with pT > 7 GeV within acone of ∆R = 1.5.

Jets in the MC are additionally identified as LQ-jets or gluon-jets using the partons in the generatorevent record. The highest energy parton that points to the jet (i.e. with ∆R < 0.6 for jets with R = 0.6and ∆R < 0.4 for jets with R = 0.4) determines the flavor of the jet. Using this method, only a smallfraction of the jets (<1% at low-pT and less at high-pT ) are not assigned a partonic flavor. Jets identifiedas originating from c- and b-quarks (HQ-jets) are considered separately from LQ-jets. This definition issufficient to study the dependence of the flavor-dependence of jet response. Any theoretical ambiguitiesof jet flavor assignment are not relevant in this context.

3 Calorimeter Response to Light-quark and Gluon Jets

Jet identified in the MC simulation as LQ-jets have significantly different response from those identifiedas gluon-jets. This is in part a result of the differences in particle-level properties of the two types of jets.The jets identified as gluon-jets tend to have more particles, and those particles tend to be softer than inthe case of LQ-jets. Additionally, the gluon-jets tend to be wider (i.e. with lower energy density in thecore of the jet) before interacting with the detector. The magnetic field of the inner detector amplifiesthe broadness of gluon-jets, since their low-pT charged particles tend to bend more than the higher-pT particles in LQ-jets. The harder particles in LQ-jets additionally tend to penetrate further into thecalorimeter.

The difference in calorimeter response between gluon-jets and LQ-jets is shown in Fig. 1, separatelyfor jets with R = 0.4 and R = 0.6 and separately for jets in the barrel (|η| < 0.8) and end-cap (2.1 ≤ |η| <2.8) calorimeters. In all cases, the difference is large at low-pT (up to 6%) and falls to several percentat high-pT . The smaller difference in response in the end-cap results from the differences being largestat small momentum, while the jet response is shown here as a function of transverse momentum. Theeffect is somewhat reduced for R = 0.6, because the larger jet area diminishes the effect of the broaderjet. The non-closure of the inclusive sample (i.e. the difference of the response from unity) is discussedin [1, 2].

The difference in response is correlated with differences in the properties of the calorimeter jet.Therefore, more complex jet calibration schemes that are able to account for jet shower properties areable to partially compensate for the flavor-dependence. Fig. 2 shows the flavor dependence of the jetresponse for R = 0.6 jets calibrated with the EM+JES, global sequential3 (GS), global cell weighting(GCW), and local cluster weighting (LCW) calibrations [21]. The difference in response between LQ-jets and gluon jets is reduced by almost a factor of two in some cases, but the difference persists across theentire pT spectrum. Thus, even these more advanced calibration techniques are insufficient to completelyalleviate the issue. In fact, a fraction of the improvement in jet energy resolution achieved by the GS andGCW calibrations come as a result of reducing the difference in response between LQ- and gluon-jets.Further improvements in energy resolution might be possible if this difference can be minimized withoutintroducing significant non-Gaussian tails in the jet response.

As two jets approach one-another, the flavor assignment becomes more ambiguous. These effects canbecome particularly problematic when one particle jet is matched to two reconstructed calorimeter jets(“splitting”) or two particle jets are matched to one reconstructed calorimeter jet (“merging”). Severaldifferent classes of close-by jets are examined for changes in the flavor-dependence of the jet response.

3 The global sequential calibration applies post-hoc corrections to the jet energy scale based on several reconstructed jetproperties. In the central calorimeter, for example, jet width and the fraction of jet energy in the pre-sampler, back electromag-netic calorimeter layer, and first layer of the hadronic calorimeter are used for corrections.

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(a) (b)

(c) (d)

Figure 1: Response as a function of particle jet pT (ptrueT ) for all jets in the di-jet sample (black solid

circles), gluon-jets (red open squares), and LQ-jets (blue open circles) falling in the barrel (a,c) and in theend-cap (b,d) in MC simulation. Jets are reconstructed with the anti-kt algorithm with distance parameterR = 0.4 (a,b) and R = 0.6 (c,d) and calibrated with the EM+JES calibration scheme.

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Figure 2: Difference in response of gluon- and LQ-jets as a function of the particle jet pT for anti-kt

jets with R = 0.6 falling in the barrel (left) and the end-cap (right) in MC simulation. Four differentcalibration schemes are shown: the EM+JES calibration (black solid circles), the GS calibration (greenopen circles), the LCW calibration (blue open pluses), and the GCW calibration (red solid triangles).

No significant deviation from isolated jets is found. Therefore, the issues can be treated separately. Thejet energy scale uncertainty deriving from close-by jets is examined further in [22].

4 Systematic Uncertainties Due to Differences in Jet Response

All of the ATLAS jet energy calibration schemes achieve (to better than 2%) unity in the average jetresponse. However, sub-samples of jets are not perfectly calibrated, as in the case of LQ-jets and gluon-jets. The divergence from unity is flavor-dependent and may be different in Monte Carlo simulation anddata, particularly if the flavor content is not well-described by the MC simulation. This results in anadditional term in the systematic uncertainty for any study using an event- or jet-selection different fromthat of the sample in which the jet energy scale was derived.

For example, the multi-jet cross-section measurement [6] uses an event selection essentially identicalto that used to derive the jet energy scale. However, the sample is sub-divided into bins of jet multiplicity.The flavor composition of a given multiplicity bin is not well-known, and therefore, an additional termin the jet energy scale uncertainty must be added.

In order to test the response of exclusive samples of gluon- and LQ-jets, the various MC samplesconsidered in [1] are investigated. The ratio of the response of gluon-jets to that of the inclusive jets isnot found to vary in any sample, and therefore the additional uncertainty on the response of gluon-jetsis neglected. Similarly, the ratio of the response of quark-jets to that of the inclusive jets is consistentacross the samples, and the additional uncertainty is neglected. These conclusions are in good agreementwith [23]. Some variation in jet response may result from differences in color connection and color flowwhen, for example, the jets arise from color-neutral objects. The MC simulation samples that were testedhave varying degrees of color connection, and so give some confidence in the stability of LQ- and gluon-jet response against such issues. With more data, a variety of final states may be tested in order to buildfurther confidence in the color-flow modeling of the MC simulation.

The flavor-dependent uncertainty term depends on both the average flavor content of the sample (e.g.

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the uncertainty on a sample of gluon-jets is different from the uncertainty on an even mixture of LQ- andgluon-jets) and on how well the flavor content is known (e.g. the uncertainty for a generic “new physics”search with an unknown jet flavor composition is different from the uncertainty on a new physics modelin which only LQ-jets are produced). The response of any sample of jets, Rs, can be written as:

Rs = fg × Rg + fq × Rq + fb × Rb + fc × Rc

= 1 + fg ×(Rg − 1

)+ fq ×

(Rq − 1

)+ fb × (Rb − 1) + fc × (Rc − 1) , (1)

where Rx is the response and fx is the fraction of jets for x = g (gluon-jets), q (LQ-jets), b (b-quark-jets),and c (c-quark-jets) and fg + fq + fb + fc = 1. For simplicity, the fraction of HQ-jets is taken to beknown. This approximation will be dealt with in the systematic uncertainty analysis of Section 5. Theuncertainty on the response can then be expressed as:

∆Rs = ∆ fg ×(Rg − 1

)+ ∆ fq ×

(Rq − 1

)+ fg × ∆Rg + fq × ∆Rq + fb × ∆Rb + fc × ∆Rc, (2)

where ∆ denotes the uncertainty on the individual variables. Since fb and fc are known (i.e. withoutuncertainty), ∆ fg = −∆ fq. Also, the uncertainties on the response of the exclusive flavor samples (LQ,gluon, b, and c) are approximately the same as the inclusive jet response uncertainty (∆R j). The expres-sion can therefore be simplified:

∆Rs ≈ −∆ fq ×(Rg − 1

)+ ∆ fq ×

(Rq − 1

)+ fg × ∆R j + fq × ∆R j + fb × ∆R j + fc × ∆R j

= ∆ fq ×(Rq − Rg

)+

(fg + fq + fb + fc

)× ∆R j

= ∆ fq ×(Rq − Rg

)+ ∆R j (3)

The second term is the inclusive jet energy scale systematic uncertainty, and the first term is theadditional flavor-dependent contribution. As a fractional uncertainty, this first term can be re-written as:

∆Rs

Rs= ∆ fq ×

(Rq − Rg

Rs

). (4)

The uncertainty on the flavor content (∆ fq) and the inclusive response of the sample (Rs) are left asanalysis-dependent constants. The difference in response between LQ- and gluon-jets depends only onthe calibration used, as discussed in Section 3.

5 Use of Jet Properties to Estimate the Flavor Composition of Samples

The total jet energy scale uncertainty may be significantly inflated by the flavor-dependent term describedin Section 4. One way of investigating the flavor composition of a sample is to use different MC gener-ators that cover a reasonable range of flavor compositions. However, these different samples may sufferfrom under- or over-coverage of the uncertainty or from changes in other sample characteristics (e.g. jet-pT spectra), which may result in a poor estimate of the true uncertainty. Another approach, pursued inthis section, is to estimate the flavor composition of the samples by using experimental observables thatare sensitive to different jet flavors. As described in Section 3, gluon-jets tend to have a wider transverseprofile and have more particles than LQ-jets. The jet width and number of tracks associated to the jet(ntrk) are thus expected to be sensitive to the difference between LQ-jets and gluon-jets.

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Figure 3: Distribution of number of tracks associated to the jet, ntrk, left, and jet width, right, for isolatedanti-kt jets with R = 0.6 tagged as LQ-jets (black solid circles) and gluon-jets (open red squares) in theMC simulation with the PYTHIA AMBT1 tune. Jets with |η| < 0.8 and 80 ≤ pT < 110 GeV are shown.The distributions are normalized to a unit area.

Templates are built from the di-jet MC sample for the jet width and ntrk of LQ- and gluon-jets sep-arately4, using the flavor tagging algorithm of Section 2. The templates are constructed in bins of jetpT , η, and isolation (∆R to the nearest jet, ∆Rmin). Fits to the data are performed with these templates toextract the flavor composition. The width of a jet, W, is defined as the pT -weighted sum of the openingangle between the jet constituents and the jet axis:

W =1

pjetT

×∑

i∈Constituents

pT,i × ∆Ri, (5)

where the sum is over constituents, pT,i is the pT of constituent i, and ∆Ri is the opening angle betweenthe constituent and the jet axis. Because the width may have contributions from pile-up interactions,in the following discussion only events with exactly one reconstructed primary vertex enter the widthdistributions5. The number of tracks associated to a jet is defined by counting the tracks with pT > 1 GeVcoming from the primary vertex with an opening angle between the jet and the track momentum direction∆R < 0.6. Fig. 3 shows the jet width and ntrk distributions for isolated LQ- and gluon-jets with |η| < 0.8and 80 < pT < 110 GeV in the di-jet MC sample. The gluon-jets are broader and have more tracks thanLQ-jets, as expected.

Comparisons of the inclusive jet width and ntrk distributions in MC simulation and data are shown inFig. 4 for isolated jets with R = 0.6. The jet width in MC simulation is narrower than in the data for thePYTHIA samples, in agreement with other ATLAS analyses [21, 25]. The inclusive ntrk and jet widthMC simulation distributions are re-weighted bin-by-bin to account for the difference observed betweenthe data and MC simulation. The same re-weighting is applied to the LQ-jet and gluon-jet distributions.The re-weighted ntrk and width distributions for the various MC samples are shown in Fig. 5.

After re-weighting, the flavor composition of the di-jet sample extracted from the data is consistent

4 For this note, the ntrk and width templates are dealt with independently, and the results of their estimates of flavor fractionare not combined.

5 Techniques to correct for these additional interactions are being developed and are discussed elsewhere [24].

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Figure 4: Distribution of number of tracks associated to the jet, ntrk, left, and jet width, right, forisolated anti-kt jets with R = 0.6 in data (black solid circles) and MC. The PYTHIA AMBT1 tune(red hollow circles), PYTHIA Perugia2010 tune (green hollow triangles), and HERWIG++ (blue hollowsquares) distributions are shown for jets with |η| < 0.8 and 80 ≤ pT < 110 GeV. The distributions are allnormalized to unity.

Figure 5: Distribution of number of tracks associated to the jet, ntrk (left), and jet width (right) for isolatedanti-kt jets with R = 0.6 in data (solid circles) and MC (bands). LQ-jets are shown in blue, gluon-jetsare shown in red, and the width of the band represents the maximum variation among the PYTHIAAMBT1 and Perugia2010 tunes and the HERWIG++ MC simulation samples. Jets with |η| < 0.8 and80 ≤ pT < 110 GeV are included. The inclusive distributions are all normalized to unity. The inclusiveMonte Carlo distributions, including the HQ-jet contributions (not shown), are re-weighted to exactlymatch the inclusive distribution of the data.

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with that of the MC simulation. The values for two representative jet bins are shown in Table 1. Thisresult is an important closure test and provides some validation of the templates.

5.1 Systematic Uncertainties on Extracted Flavor Composition

Uncertainties on the MC-based templates used in fits to the data result in a systematic uncertainty on theextracted flavor composition. Here the following four systematics effects are considered:

1. MC modeling of jet width and ntrk distributions is considered. MC generated with PYTHIA andthe Perugia2010 tune and HERWIG++ both show reasonable agreement with data (c.f. Fig. 5).Therefore, two separate fits with templates obtained from these alternate MC samples are per-formed. Re-weighting of these alternate samples is performed in the same manner as for the mainMC sample. The larger of the differences in the flavor fractions with respect to the nominal fits istaken as the uncertainty due to MC modeling.

2. The fraction of HQ-jets in the data is assumed to be the same as that predicted by the PYTHIAMC simulation in the template fits. The uncertainty associated with this assumption is estimatedby increasing and decreasing this MC-based fraction of HQ-jets by a factor of two and repeatingthe fits with the LQ- and gluon-jet templates. The factor of two is taken in order to be conservativein the γ-jet and multi-jet samples, due to the lack of knowledge of gluon-splitting rates. For somestudies, like tt̄-production, a factor of two would yield too large an uncertainty.

3. The jet energy scale uncertainty and finite detector resolution, combined with the rapidly fallingjet-pT spectrum, lead to pT -bin migrations that affect the templates. Therefore, the templatesare re-built with all jet momenta scaled up and down according to the inclusive jet energy scalesystematic uncertainty for isolated jets. The difference in the flavor content estimated with themodified templates is taken as a systematic uncertainty.

4. In the process of re-weighting the inclusive MC simulation distributions to match those of the data,there is an implicit assumption that the flavor composition of the MC simulation is correct. ThePYTHIA MC simulation was produced using modified LO parton distribution functions (PDFs),which may not accurately reproduce the true QCD flavor composition. Particularly in the moreforward pseudo-rapidity bins, this could produce some inherent biases in the fits. In order toestimate this uncertainty, the LQ- and gluon-jet templates from the standard MC sample are com-bined according to the flavor content of a di-jet sample generated using ALPGEN [17]. The newcombination is then re-weighted to match the inclusive distribution in data, and the re-weightedtemplates are used to extract the flavor composition of the samples. The difference between theflavor composition derived in this manner and the flavor composition derived using only PYTHIAMC is taken as a systematic uncertainty. When sufficient data are available in 2011, this issuecan be straightforwardly remedied by performing a fully data-driven template fit, using the γ-jetsample and multi-jet sample to derive LQ- and gluon-jet templates.

No one uncertainty is consistently dominant. Therefore, each must be individually considered whenattempting to extract the flavor composition of a sample of jets.

5.2 Flavor Composition in a Photon-jet Sample

The validity of the MC-based templates and fitting method is tested by applying the method to the γ-jetdata sample and comparing the extracted flavor compositions with the γ-jet MC predictions. This sampleshould contain a considerably higher fraction of LQ-jets than the inclusive di-jet sample. Fig. 6 shows

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Figure 6: The jet width template fit performed on the γ-jet data sample using templates derived in adi-jet MC sample created using the PYTHIA AMBT1 tune. Jets with |η| < 0.8 and 60 ≤ pT < 80 GeVare shown. The fraction of HQ-jets is taken directly from the MC simulation.

the fit on the jet width to the γ-jet data for jets with |η| < 0.8 and 60 < pT < 80 GeV. The HQ-jet fractionsare fixed to those obtained from the γ-jet MC simulation. The extracted LQ- and gluon-jet fractions areconsistent with the true fractions in MC simulation, though with large uncertainties, as shown in Table 1.

5.3 Flavor Composition in a Multi-jet Sample

The template-fit method is also useful in dealing with QCD multi-jet events, which are separated byjet multiplicity. These events contain additional jets that mainly result from gluon radiation and henceinclude a larger fraction of gluon-jets than does the γ-jet sample. Moreover, the uncertainty on theinclusive multi-jet production cross sections may be significantly reduced by constraining the flavorcomponent of the total jet energy scale systematic uncertainty.

For this particular analysis, the templates built from the inclusive jet sample are used to determine theflavor of the n-jet bin. However, the pT spectrum of the sub-leading jets is more steeply falling than theleading-jet pT . Bin migrations due to the finite detector resolution exaggerate the difference. Therefore,there is an additional systematic uncertainty applied to account for the difference in pT -spectra shapes.In order to be conservative, the uncertainty is calculated by re-deriving templates built with a flat pT -distribution and a significantly steeper pT -distribution than that of the di-jet sample. The slope of thesteeply-falling distribution is taken from the pT of the sixth leading jet in Monte Carlo events with sixjets, generated using ALPGEN [17]. The fits are repeated with these modified templates, and the largerof the differences is assigned as a pT -spectrum shape systematic uncertainty.

Fig. 7 compares the fractions of LQ- and gluon-jets obtained with a fit on the jet width and ntrk in

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Figure 7: Fitted values of the LQ- and gluon-jet fraction in events with three or more jets, as a functionof jet pT, calculated using jet width templates (left) and ntrk templates (right). Non-isolated jets (0.8 ≤∆Rmin < 1.0) with |η| < 0.8 are shown. The fraction of HQ-jets has been fixed to that of the MCsimulation. The fitted fractions are shown with solid markers, while the values obtained from the MCsimulation are shown with empty markers. The error bars indicate the uncertainty on the fit only. Beloweach figure, the impact of the different systematic effects is shown with magenta markers. The combinedsystematic uncertainty is shown at the bottom as a grey band.

three-jet events in data and MC simulation as a function of jet pT for non-isolated (0.8 < ∆Rmin < 1.0)jets with |η| < 0.8. The higher gluon-jet fractions predicted by the MC simulation are reproduced by thefit, and the data and MC simulation are consistent. The total systematic uncertainty on the measurementis below 10% over the measured pT range.

The fit fractions obtained using the jet width and ntrk distributions in four-jet events are shown inFig. 8. In both cases, the extracted fractions are consistent with the MC predictions, and the total sys-tematic uncertainty is similar to the one for the three-jet bin.

The extracted LQ- and gluon-jet fractions, with the total systematic uncertainty from the width andntrk fits, are summarized in Fig. 9 as a function of inclusive jet multiplicity. The fractions are consistentbetween the data and the MC simulation, and the total systematic uncertainty is around 10% for eachmultiplicity bin. Thus, for the four-jet bin, the flavor-dependent jet energy scale systematic uncertaintycan be reduced by a factor of ∼10, from ∼6% to <1%. The fit results are summarized in Table 1.

6 Conclusions

The flavor-dependence of jet response has been demonstrated, and an additional term to the jet energyscale systematic uncertainty was presented. A generic template fit method was derived to reduce thisuncertainty significantly for any given sample of events. Templates derived in QCD di-jet events wereapplied to both γ-jet and multi-jet events, demonstrating the potential of the method to reduce the system-atic uncertainty. A summary of the flavor fit results using the width templates for the different samplesis provided in Table 1.

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Figure 8: Fitted values of the LQ- and gluon-jet fraction in events with four or more jets as a functionof jet pT for isolated jets with |η| < 0.8. The fraction of HQ-jets has been fixed from the MC simulation.The jet width (left) or ntrk distributions (right) are used in the fits. The fitted fractions are shown withsolid markers, while the values obtained from the MC simulation are shown with empty markers. Thecombined systematic uncertainty is shown below each figure as a grey band.

Figure 9: Fitted values of the LQ- and gluon-jet fraction as a function of inclusive jet multiplicity,with total uncertainties on the fit as obtained using the width (left) and the ntrk (right) distributions. Thefraction of HQ-jets has been fixed from the MC simulation. The fitted fractions are shown with solidmarkers, while the values obtained from the MC simulation are shown with empty markers. The errorbars indicate the uncertainty on the fit only. Below each figure, the impact of the different systematiceffects is shown with magenta markers. The combined systematic uncertainty is shown at the bottom asa grey band.

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Table 1: The results of flavor fits using jet width templates in three data samples: di-jet events, γ-jetevents, and multi-jet events. The MC simulation flavor predictions are taken from ALPGEN for the di-jet and multi-jet samples and PYTHIA for the γ-jet sample. The first uncertainty listed is statistical andthe second uncertainty is systematic, and both apply to the measured gluon- and LQ-jet fractions. TheHQ-fractions in the data are constrained to be the same as those in the MC simulation.

Gluon- / LQ- / HQ-jet FractionSample Bin Data MC

Di-jet 80 ≤ pT < 110 GeV, |η| < 0.8, 73 / 22 / 5% 72 / 23 / 5%1.0 ≤ ∆Rmin < 1.5 ±2(stat.) ± 9(syst.)%

Di-jet 80 ≤ pT < 110 GeV, 2.1 ≤ |η| < 2.8, 45 / 52 / 3% 39 / 58 / 3%1.0 ≤ ∆Rmin < 1.5 ±3(stat.) ± 12(syst.)%

γ-jet 60 ≤ pT < 80 GeV, |η| < 0.8, 16 / 65 / 19% 6 / 74 / 19%Isolated ±10(stat.) ± 19(syst.)%

Multi-jet 3-jet, 80 ≤ pT < 110 GeV, |η| < 0.8, 83 / 13 / 4% 84 / 12 / 4%0.8 ≤ ∆Rmin < 1.0 ±2(stat.) ± 7(syst.)%

Multi-jet 4-jet, 80 ≤ pT < 110 GeV, |η| < 0.8, 89 / 3 / 8% 81 / 11 / 8%1.0 ≤ ∆Rmin < 1.5 ±6(stat.) ± 8(syst.)%

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