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Measurement of the triple-differential cross section for photon + jets production in proton-proton collisions at sqrt(s) = 7 TeV

A measurement of the triple-differential cross section (sigma as a function of the photon pt and eta and the jet eta) in photon + jets final states using a data sample from proton-proton collisions at sqrt(s) = 7 TeV is presented. This sample corresponds to an integrated luminosity of 2.14 inverse femtobarns collected by the CMS detector at the LHC. Photons and jets are reconstructed within a pseudorapidity range of abs(eta)<2.5, and are required to have transverse momenta in the range 4030 GeV, respectively. The measurements are compared to theoretical predictions from the SHERPA leading-order QCD Monte Carlo event generator and the next-to-leading-order perturbative QCD calculation from JETPHOX. The predictions are found to be consistent with the data over most of the examined kinematic region.

Events selected for this analysis are recorded using a two-level trigger system. A level-1 trigger requires a cluster of energy deposited in the ECAL with transverse energy E T > 20 GeV. The CMS high-level trigger (HLT) applies a more sophisticated energy clustering algorithm to events passing the level-1 threshold and further requires E T trigger thresholds from 30 to 135 GeV. These thresholds are raised with increased instantaneous luminosity to prevent saturation of the readout. In addition to these trigger requirements, an offline requirement is imposed to ensure that events have at least one well reconstructed primary vertex within 24 cm in z of the nominal center of the detector.
Photons deposit most of their energy through electromagnetic showers in the ECAL. They are reconstructed by clustering energy deposits in neighboring crystals according to criteria that are optimized for different regions of pseudorapidity. Each clustering algorithm begins from a seed crystal with large transverse energy. In the barrel region, clusters are formed by summing energies across 5 (35) crystals in the η (φ) direction. Clusters in the endcap are formed by combining contiguous 5 × 5 arrays of crystals and including the corresponding energy in the preshower detector. The full details of these algorithms can be found in ref. [26]. We apply the same selection criteria used in the measurement of the inclusive photon cross section [27] and provide a summary here. A photon reaching the ECAL without undergoing conversion to an e + e − pair deposits most of its energy in a 3 × 3 crystal matrix. Only a very small fraction of the energy from the resulting shower leaks into the HCAL, hence the ratio of the energy of the photon candidate in the HCAL to the energy in the ECAL, H/E, within a cone of radius R = (∆η) 2 + (∆φ) 2 = 0.15 around the seed crystal can be used to separate photon showers from electromagnetic components of hadron-initiated showers. For this analysis, a requirement of H/E < 5% is applied to the photon candidates. To reject electrons, we require that there be no hits in the first two inner layers of the silicon pixel detector that are consistent with an electron track matching the location and energy of the photon candidate in the calorimeter (pixel detector veto). To further improve the purity of the photon candidate sample, an additional requirement is applied based on the second moment of the electromagnetic shower in η, calculated using a 5 × 5 matrix of crystals around the highest energy crystal in the cluster, where the sum runs over all elements of the 5 × 5 matrix, and η i = 0.0174η i , withη i denoting the η index of the ith crystal; the individual weights w i are given by w i = -3 -

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max (0, 4.7 + ln(E i /E 5×5 )) and E i is the energy of the ith crystal;η = η i w i / w i is the energy-weighted average pseudorapidity. The requirement σ ηη < 0.01 (0.028) in the barrel (endcaps) further suppresses background from neutral mesons (π 0 , η, etc.) that may satisfy the isolation requirements described below as a result of fluctuations in the fragmentation of partons. The combined H/E and shower shape requirements along with the pixel detector veto comprise the photon identification criteria. If multiple photons are reconstructed within the fiducial range of this analysis, only the photon with highest p γ T , leading photon, is considered.
Jets are reconstructed using the anti-k T [28] clustering algorithm with distance parameter of 0.5. Inputs for the jet clustering are defined by the particle-flow [29] algorithm, which is a full-event reconstruction technique that aims to reconstruct and identify all stable particles produced in an event through the combination of information from all subdetectors. Jets with p T > 30 GeV are selected for this analysis, and are required to pass data quality requirements designed to remove spurious jets resulting from noise [30]. Inefficiencies due to these criteria are negligible. Since energetic photons are also reconstructed as jets by the anti-k T algorithm, any jet that overlaps with the leading photon within a cone of R < 0.5 is removed from consideration.
Even after the photon identification criteria are applied, a significant background remains, mostly from neutral mesons that decay to photons that overlap in the ECAL. Templates constructed from signal and background distributions are fitted to data to determine the purity of the selected photon sample. The method exploits the distribution of energy in the vicinity of the photon using the variable Iso γ = Iso TRK + Iso ECAL + Iso HCAL , where Iso TRK is the sum of the p T of tracks consistent with the reconstructed vertex in a hollow cone, 0.04 < R < 0.40, centered around the candidate photon momentum vector extending from the primary vertex to the ECAL cluster. Similarly, Iso ECAL is the transverse energy deposited in the ECAL in 0.06 < R < 0.40, and Iso HCAL is the transverse energy deposited in the HCAL in 0.15 < R < 0.40. For the Iso TRK (Iso ECAL ) distributions, we do not include energy in a rectangular strip of ∆η × ∆φ = 0.015 (0.040) × 0.040 to exclude energy associated with the photon in case of conversion [31]. The method takes advantage of differences in the Iso γ distributions between signal and background. The main contribution to Iso γ for genuine photons comes from the underlying event and multiple pp interactions in the same bunch crossing (pile-up collisions). The average number of pile-up collisions for data used in this analysis is ∼6. In contrast, Iso γ for misidentified photons includes additional contributions of energy from jet fragmentation. Hence, the Iso γ distribution for the background tends to be broader than for signal.
The signal template is modeled using Monte Carlo (MC) events generated with pythia 6.424 [32] and parameterized by the convolution of an exponential function with a Gaussian, where x = Iso γ , (µ, σ) = p and α describe the peak and tail of the signal template, respectively, and C S normalizes the distribution to unit area. The background template is obtained from data using a background-enriched sample collected from a sideband region, obtained by inverting the shower shape selection requirement and requiring σ ηη > 0.011 (0.030) in the barrel (endcap) regions. The background distribution is parameterized using an inverse ARGUS function [33], where x = Iso γ , z describes the shape of the background template in the signal-dominated region, q 1 (q 2 , q 3 ) describe the starting point of the background template (or its shape in the background-dominated region), and C B normalizes the distribution to unit area. The signal purity is determined by fitting the signal and background template functional forms to data, N S · Iso γ S + N B · Iso γ B , and minimizing an extended χ 2 defined as where N S and N B are the numbers of signal and background events, n is the number of bins in the templates, N i the observed number of events for the ith bin with uncertainty σ N i , S i and B i are the per-bin integrals of the corresponding signal and background templates, and z central (σ z ) is the value (uncertainty) of the parameter z determined by the fitting of the background template. The parameters can be categorized into those that most directly model the signal-dominated (µ, σ, z, and q 1 ) and background-dominated (α, q 2 , and q 3 ) regions. The parameter that describes the peak in the signal template is allowed to vary in the fit to correct for differences between data and MC in the region of low isolation energy. This procedure is validated with data using a photon sample collected from Z → µ + µ − γ events. The parameter that describes the tail of the signal template in the high isolation energy region is shifted by 5% to account for differences observed between data and MC simulation, and to estimate the uncertainty from the contributions of nonprompt photons, which originate from jet fragmentation. In the low Iso γ region, the background distribution is constrained by the sideband data, allowing the parameter z to vary based on the value z central with an uncertainty σ z . An example of the resulting templates is shown in figure 1. The purity is determined independently in bins of γ and jet pseudorapidity and as a function of p γ T . The signal purity is defined as the ratio of prompt photons to the total number of selected photons. This is shown as a function of p γ T in figure 2 for two ranges of η γ ; it increases with the transverse momentum of the photons. The variation of the measured photon purity across kinematic regions is consistent with expectations for signal and background, which correspond to different admixtures of initial partonic states. The main contribution to the systematic uncertainty in the photon signal purity is due to the modeling the shape of the background template, which is dominated by statistical uncertainty in the sideband samples. This uncertainty is evaluated by performing pseudo-experiments based on simulated QCD samples to examine variations in the measurement of the purity due to statistical fluctuations in the template models. The upper limit of p γ T < 300 GeV in this analysis is determined by the availability of data that allows us to independently model background templates for each bin in the triple differential cross section. We also consider a contribution to the systematic uncertainty related to the modeling of the signal template. The systematic uncertainty is evaluated independently for each bin and increases with decreasing photon transverse momentum from 1% to 30%.
The selection efficiency for photons can be factorized into four terms, which are measured independently: total = trigger · RECO · ID · PMV . The first factor, trigger , is the trigger selection efficiency, and is measured in data using electrons from the decay of Z bosons following a 'tag-and-probe' method [34]. The tag electron is required to match an object reconstructed as an HLT electron, while the probe requirement is relaxed to pass the offline photon selection requirements and a photon HLT path. This efficiency factor is found to be consistent with 100% within its systematic uncertainty. The reconstruction ef-  Total efficiency for photon selection as a function of photon transverse momentum (p γ T ) in four different photon pseudorapidity (η γ ) ranges. The error bars include both statistical and systematic uncertainties and are dominated by the latter. For clarity, points corresponding to the second and third η γ bins are shifted to the right by 5 and 10 GeV, respectively. ficiency, RECO , is measured using simulated events in a photon+jets sample generated with pythia. The same sample is used to determine ID , the efficiency of the photon identification criteria apart from the pixel detector veto. The systematic uncertainty in the photon identification efficiency is determined from the differences between MC simulation and data by applying the nominal photon selection criteria to electrons in a Z-boson-enriched data sample. The photon pixel veto efficiency, PMV , is estimated from data by employing the tag-and-probe technique with final-state-radiation photons in Z → µ + µ − γ events and is independent of p T . The total photon efficiency as a function of photon transverse momentum in the four photon pseudorapidity ranges is shown in figure 3. The variation of total efficiency values in the photon pseudorapidity regions is mainly caused by the pixel veto efficiency contribution. Figures 4 and 5 show the measurement of the triple-differential cross section d 3 σ/(dp γ T dη γ dη jet ) for |η jet | < 1.5 and 1.5 < |η jet | < 2.5. The measurements are corrected for detector acceptance, efficiency and resolution by unfolding the spectra using an iterative method [35]. The cross section is calculated using where N γ signal is the number of photon candidates corrected for purity in bins of ∆p γ T , ∆η γ , and ∆η jet with integrated luminosity L; U and are the unfolding and efficiency corrections, respectively.
The systematic uncertainty due to the unfolding procedure is estimated by varying the parameterization of signal model and photon energy resolution according to differences between the data and MC distributions. The effect of uncertainties in the photon energy scale varies from 1.1%-1.5% (2.2%-3%) for measurements with photons in the barrel (endcap),while those due to the jet energy scale are negligible. The contributions to the  systematic uncertainty in the differential cross section from the determination of photon reconstruction efficiency, unfolding, photon energy scale and the photon purity determination are given in table 1. The table also shows the total systematic uncertainty obtained by adding all the contributions in quadrature. At low p γ T the systematic uncertainty is dominated by the purity determination. This is also the region where the uncertainty is the highest. At high p γ T the most significant contribution usually comes from the determination of the reconstruction efficiency.
The measured cross sections are compared to theoretical predictions based on perturbative QCD using the leading order (LO) MC event generator sherpa (v1.3.1) [36] and the full next-to-leading order (NLO) calculation implemented in jetphox (v1.2.2) [37]. The SHERPA MC program incorporates higher-order tree level matrix elements (ME) and parton shower (PS) modeling using the ME-PS matching algorithm described in ref. [38]. A similar technique is also applied to processes involving prompt photons [39], combining the photon and QCD parton multiplicity tree-level matrix elements with a QCD+QED parton shower using the formalism given in ref. [38], thus treating photons and jets on an equal footing [39]. This treatment also includes contributions from the photon fragmentation component, permitting a direct comparison with experimental measurements. The predictions from sherpa agree well with earlier photon measurements from the Tevatron [21]. The photon+jets final states are generated with up to three additional jets using sherpa and the CTEQ6 [40] parton distribution functions (PDFs). Calculations are performed using default choices for renormalization (µ R ) and factorization (µ F ) scales equal to p γ T . The jetphox calculation at NLO in perturbative QCD includes a model of fragmentation functions of partons to photons [41] and uses the CT10 [42] NLO PDFs with µ R = µ F = µ f = p γ T /2, where µ f defines the fragmentation scale. To model the effect of experimental selection requirements for these processes, the energy around the photon within the R < 0.4 cone is required to be less than 5 GeV. The effect due to the choice of theory scales is obtained by independently varying µ R , µ F , µ f by the factors 0.5 and 2.0. The uncertainty in the predictions due to the choice of PDF is determined from the 40 (52) component error sets of CTEQ6M (CT10) and evaluated using the master equations as given by the 'modified tolerance method' recommended in ref. [43]. The effects of contributions from the parton-to-hadron fragmentation and the underlying event are examined by comparing cross sections determined using our default tune in pythia at hadron level with and without multiple parton interactions (MPI) and hadronization processes included. We find these contributions to produce small fluctuations around the parton-level cross section with little dependence on kinematic variables and conclude that an uncertainty of 1% added to the jetphox predictions in each (η γ , η jet ) region covers their effects. Figure 6 shows the ratios of the measured triple-differential cross section to theoretical predictions. The determination of the photon signal purity contributes the main systematic uncertainty affecting this measurement. The central values of the cross section, the statistical uncertainty, and the total systematic uncertainty are summarized in tables 2 and 3. The predictions from sherpa and jetphox are consistent with data, -9 -JHEP06(2014)009 |η γ | < 1.44 p γ T (GeV) efficiency (%) unfolding (%) photon energy (%) purity (%) total (%) 40 Table 1. Contributions to the relative systematic uncertainty (in percent) in the cross section measurement from efficiency, unfolding, photon energy scale, and purity calculations. The total systematic uncertainty is obtained by adding all the contributions in quadrature, a 2.2% uncertainty due to the integrated luminosity measurement is not included. The numbers in the table represent the ranges of uncertainties obtained in different η γ and η jet bins. except for cases of photons measured in the largest η and p T regions. Figure 7 shows the ratios of cross sections with different angular orientations between the photon and the leading jet. An earlier study performed by the D0 experiment at the Tevatron [21] restricted the photon to |η γ | < 1.0, while allowing the jet to be either in the central (|η jet | < 0.8) or forward (1.5 < |η jet | < 2.5) region. In this study, we consider |η γ | < 0.9 and |η jet | < 1.5 or 1.5 < |η jet | < 2.5. The advantage of measuring the ratios of cross sections is that uncertainties in the integrated luminosity and reconstruction efficiencies largely cancel.
In conclusion, events with at least one photon and one jet have been studied with a data sample corresponding to an integrated luminosity of 2.14 fb −1 collected in proton-proton collisions at √ s = 7 TeV. The cross section is measured as a function of the transverse momentum of the photon for various configurations of the leading photon and the leading jet. These measurements are used to determine eight ratios of the triple-differential cross section d 3 σ/(dp γ T dη γ dη jet ). They provide measures of the relative cross sections for photon+jets production in different pseudorapidity regions and, thus, over a wide range  Figure 6. The ratios of the measured triple-differential cross sections to the NLO QCD prediction using jetphox with the CT10 PDF set and scales µ R,F,f = 1 2 p γ T . The vertical lines on the points show the statistical and systematic uncertainties added in quadrature. The two dotted lines represent the effect of varying the theoretical scales as described in the text. The shaded bands correspond to the CT10 PDF uncertainty. The dash-dotted lines show the ratios of the sherpa predictions to jetphox.
-11 -JHEP06(2014)009 |η γ | < 0.9 and |η jet | <  Table 2. The triple-differential cross sections d 3 σ/(dp γ T dη γ dη jet ) for photons located in the central region with statistical and systematic uncertainties, compared to predictions from jetphox and sherpa. A 2.2% luminosity uncertainty is included in the systematic uncertainty [44]. The final two columns show the ratio of CMS data to jetphox (D/J) and sherpa (D/S), respectively.
-12 -JHEP06(2014)009  Table 3. The triple-differential cross sections d 3 σ/(dp γ T dη γ dη jet ) for photons located in forward region with statistical and systematic uncertainties, compared to predictions from jetphox and sherpa. A 2.2% luminosity uncertainty is included in the systematic uncertainty. The final two columns show the ratio of CMS data to jetphox (D/J) and sherpa (D/S), respectively.  Figure 7. Ratios of the triple-differential cross sections for the various jet orientations with respect to the photon. The error bars on the theoretical predictions correspond to statistical, scale and PDF uncetainties. of parton momentum fraction. Comparisons of the data to theoretical predictions from sherpa and jetphox are also presented. Although predictions from sherpa are observed to be lower than those from jetphox, the measured cross sections are found to be consistent with both MC predictions within systematic uncertainties over most of the measured kinematic regions. The NLO predictions in QCD and tree-level predictions of sherpa both fail to describe the data for photons in the highest η and p T regions within expected variances of either theoretical scale or parton distribution functions.
We congratulate our colleagues in the CERN accelerator departments for the excellent -14 -

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performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWF and FWF ( Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.