Measurement of the inclusive isolated prompt photon cross section in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector using 4.6 fb-1

A measurement of the cross section for the production of isolated prompt photons in pp collisions at a center-of-mass energy sqrt(s) = 7 TeV is presented. The results are based on an integrated luminosity of 4.6 fb-1 collected with the ATLAS detector at the LHC. The cross section is measured as a function of photon pseudorapidity and transverse energy in the kinematic range between 100 GeV and 1000 GeV and in the regions of pseudorapidity less than 1.37 and between 1.52 and 2.37. The results are compared to leading-order parton-shower Monte Carlo models and next-to-leading-order perturbative QCD calculations. Next-to-leading-order perturbative QCD calculations agree well with the measured cross sections as a function of transverse energy and pseudorapidity.


I. INTRODUCTION
Prompt photon production at hadron colliders allows tests of perturbative QCD predictions [1].The measurement is sensitive to the gluon content of the proton through the qg → qγ process, which dominates the prompt photon production cross section at the LHC, and can be used to constrain parton distribution functions (PDFs) [2].
Recent measurements of the production cross section of isolated prompt photons have been performed by AT-LAS [3,4] and CMS [5,6] using pp collision data at √ s = 7 TeV at the LHC.Earlier measurements were made by CDF and D0 using pp collisions collected at √ s = 1.8 TeV and √ s = 1.96TeV at the Tevatron collider [7][8][9][10].Also, similar measurements were made at the SppS collider [11,12].
In this paper, the production cross section of isolated prompt photons is measured in the transverse energy (E γ T ) range between 100 GeV and 1 TeV, extending the result of the previous ATLAS measurement, which covered the range between 45 GeV and 400 GeV [4].The differential cross section as a function of E γ T is measured in the pseudorapidity [13] range |η γ | < 1.37 (the barrel region) and 1.52 ≤ |η γ | < 2.37 (the end-cap region).Photon reconstruction in these pseudorapidity regions has a high efficiency and a low background rate.The differential cross section is also studied as a function of η γ for E γ T > 100 GeV.The data sample corresponds to an integrated luminosity of 4.64 ± 0.08 fb −1 [14]; thus this analysis uses a data set more than two orders of magnitude larger than that used in the previous measurement [4].
In the following, all photons produced in pp collisions and that are not secondaries to hadron decays are considered as "prompt".They include "direct" photons, which originate from the hard processes calculable in perturbative QCD, and "fragmentation" photons, which are the result of the fragmentation of a colored high-p T parton [15,16].Photons are considered "isolated" if the transverse energy (E iso T ) within a cone of radius ∆R = (∆η) 2 + (∆φ) 2 = 0.4 centered around the photon in the pseudorapidity and azimuthal angle (φ) is smaller than 7 GeV.In next-to-leading-order (NLO) parton-level theoretical calculations, E iso T is calculated from all partons within the cone, while in the leading-order (LO) parton-shower Monte Carlo (MC) simulations, E iso T is calculated from all the generated particles (except muons and neutrinos) inside the cone.Experimentally, E iso T is calculated from the energy deposited in the calorimeters in a ∆R = 0.4 cone around the photon candidate, corrected for effects associated with the energy of the photon candidate itself, the underlying event, and the additional pp interactions in the same bunch crossing (pileup) [17].The main background for the prompt photons consists of photons from decays of light neutral mesons such as the π 0 or η.

II. THE ATLAS DETECTOR
ATLAS [18] is a multi-purpose detector with a forwardbackward symmetric cylindrical geometry and nearly 4π coverage in solid angle.The most relevant subdetectors for the present analysis are the inner tracking detector (ID) and the calorimeters.
The ID consists of a silicon pixel detector and a silicon microstrip detector covering the pseudorapidity range |η| < 2.5, and a straw-tube transition radiation tracker covering |η| < 2.0.It is immersed in a 2 T magnetic field provided by a superconducting solenoid.The ID allows efficient reconstruction of converted photons if the conversion occurs at a radius of less than 0.80 m.
The electromagnetic calorimeter (ECAL) is a lead/liquid-argon (LAr) sampling calorimeter providing coverage for |η| < 3.2.It consists of a barrel section (|η| < 1.475) and two end-caps (1.375 < |η| < 3.2).The central region (|η| < 2.5) is segmented into three layers in shower depth.The first (inner) layer, covering |η| < 1.4 in the barrel and 1.5 < |η| < 2.4 in the end-caps, has a high η granularity (between 0.003 and 0.006 depending on η), which can be used to provide event-by-event discrimination between single-photon showers and two overlapping showers such as may be produced by π 0 decay.The second layer, which collects most of the energy deposited in the calorimeter by the photon shower, has a cell granularity of 0.025×0.025 in η × φ.The third layer is used to correct high-energy showers for leakage.In front of the ECAL a thin presampler layer, covering the pseudorapidity interval |η| < 1.8, is used to correct for energy loss before the ECAL.
A three-level trigger system is used to select events containing photon candidates.The first level (level-1) is implemented in hardware and is based on towers with a coarser granularity (0.1 × 0.1 in η × φ) than that of the ECAL.They are used to search for electromagnetic deposits in η × φ regions of 2 × 1 and 1 × 2 towers, within a fixed window of size 2 × 2 and with an E γ T above a programmable threshold.The algorithms of the second and third level triggers (collectively referred to as the highlevel trigger) are implemented in software.The high-level trigger exploits the full granularity and precision of the calorimeter to refine the level-1 trigger selection, based on improved energy resolution and detailed information on energy deposition in the calorimeter cells.

A. Collision Data selection
The measurement presented here is based on protonproton collision data collected at a center-of-mass energy of √ s = 7 TeV with the ATLAS detector at the LHC in 2011.Only events where both the calorimeter and the ID are fully operational and that have good data quality are used.Events are triggered using a high-level photon trigger, with a nominal E γ T threshold of 80 GeV.The trigger selection criteria for the fraction and profile of the energy measured in the various layers of the calorimeters are looser than the photon identification criteria applied in this analysis; as described in Sec.IV C. For 2011, the average number of pp interactions in the same bunch crossing is nine.Events are required to have a reconstructed primary vertex (PV) [19] consistent with the average beam-spot position and with at least three associated tracks.

B. Simulated events
To study the characteristics of signal and background events, MC samples are generated using PYTHIA 6.4 [20], a LO parton-shower MC generator, with the modified LO MRST2007 [21] PDFs.The event generator parameters are set according to the ATLAS AMBT2 tune [22].The ATLAS detector response is simulated using the GEANT4 program [23].In order to have a realistic description of the experimental conditions under which the data are taken, pileup interactions are included in the simulation.These samples are then reconstructed with the same algorithms used for data.More details of the event generation and simulation infrastructure of the ATLAS experiment are provided in Ref. [24].
For the study of systematic uncertainties and for comparisons with the final cross sections, events are generated with the HERWIG 6.5 [25] model using the ATLAS AUET2 tune [26] and the same PDFs as used for the PYTHIA event generation.HERWIG and PYTHIA use different parton-shower and hadronization models.
Signal MC samples include hard-scattering photons from the LO processes qg → qγ and q q → gγ, and photons from QED radiation from quarks produced in QCD 2 → 2 processes.
To study background processes, MC samples enriched in photons from meson decays with an E γ T > 100 GeV are used.The samples are generated using all tree-level 2→2 QCD processes, while events with photons originating from quarks were removed.

IV. PHOTON SELECTION
The reconstruction of photons in the ATLAS detector is described in detail elsewhere [3,27].The selection of photons is discussed in the following three sections: kinematic preselection, isolation selection and shape identification.

A. Photon kinematic preselection
As already stated in Sec.III, photon candidates are first required to have passed an 80 GeV trigger.From these, only those with calibrated transverse energies above 100 GeV are retained for the subsequent analysis.The calibration includes an in situ technique based on the Z boson mass peak [28].In order to benefit from the fine segmentation of the first layer of the ECAL for identification of genuine photons, the photon candidates are required to be within the barrel or the end-cap pseudorapidity regions.After the selection, approximately 2.6×10 6 photon candidates remain in the data sample.

B. Photon isolation selection
Isolation is an important observable for prompt photon studies.The prompt photon signal is expected to be more isolated from hadronic activity than the background.Also, because of the mixture of hard-scattering and fragmentation contributions in the prompt photon signal, it is important to have a well modeled isolation variable that can be linked to the parton-level isolation cut used in NLO QCD computations.A robust isolation prescription helps limit the non-perturbative fragmentation contribution, which is poorly understood in theory, while retaining the signal produced from direct processes.
This study uses the same definition of the cone isolation variable, E iso T , as for the previous ATLAS measurement [4].It is computed using calorimeter cells from both the ECAL and HCAL, in a cone of radius ∆R = 0.4 around the photon candidate.The contributions from the 5 × 7 second layer ECAL cells in the η × φ space around the photon shower barycenter are not included in the calculation.The expected small value of the leakage from the photon shower into the cone outside this small central region, evaluated as a function of the E γ T in simulated samples of single photons, is then subtracted from the isolation variable.The contribution to the photon isolation energy from the underlying event and pileup is subtracted using the procedure proposed in Refs.[29,30], and implemented as described in Ref. [3].After these corrections, the transverse isolation energy of simulated prompt photons is independent of E γ T .A residual mild dependence on the amount of in-time pileup (from collisions of protons in the same bunches as the hard pp scattering from which the photon originates) is observed for this isolation variable.This dependence can be traced back to the fact that E iso T is calculated from cells without noise suppression whereas the pileup correction is computed from noise-suppressed topological clusters [31].The pileup dependence of E iso T is well modeled in the simulation and found to be robust against systematic uncertainties discussed later.
In the following, all photon candidates having reconstructed isolation energies E iso T ≤ 7 GeV are considered "isolated", while candidates with E iso T > 7 GeV are considered "non-isolated".These definitions are applied to the data and to the MC calculations at both parton and particle level.An ambient energy algorithm correction, which is used to correct for the activity of the underlying event, is also applied for the particle level MC isolation.The isolation requirement E iso T ≤ 7 GeV is looser than that used in the previous analysis [4] and is chosen in order to optimize the signal purity and the photon reconstruction efficiency at high E γ T .

C. Photon shower-shape identification
Shape variables computed from the lateral and longitudinal energy profiles of the shower in the ECAL are used to further discriminate the signal from the background.The selection criteria do not depend on the photon candidate's E γ T , but vary as a function of the photon's reconstructed η γ to take into account significant changes in the total thickness of the upstream material and variations in the calorimeter geometry or granularity.The same "tight" selection criteria as used in the measurement of the isolated photon-pair production cross sec-tion [17] are applied.After the photon identification requirements, 1.3×10 6 (6.2×10 5 ) photon candidates remain in the barrel (end-cap) η γ region.The fraction of converted photons, i.e. photons that pair produce in the presence of material and are identified by their tracks are considered converted photons, is 32% (45%) in the barrel (end-cap) η γ region.Converted photons are identified by there tracks.There are 19 photon candidates with E γ T between 800 GeV and 1 TeV.The total number of events with more than one good photon candidate is 1240.

V. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION
The main background for prompt photons is due to hadronic jets containing π 0 mesons that carry most of the jet energy and that decay to photon pairs.Such background photons are expected to be less isolated than prompt photons due to activity from the other particles in the jet.The isolation energy, E iso T , therefore provides a discrimination between prompt photons and photons from jets and meson decays.To avoid relying on the simulation to accurately model the energy flow inside jets and the fragmentation to π 0 mesons, a data-driven technique is used for the reconstruction of the background isolation distribution.
Among the shower-shape variables used in the photon selection, some measured in the first ECAL layer are fairly uncorrelated with the E iso T .A backgroundenhanced sample is provided by requiring the photon candidates to fail the "tight" identification criteria for at least one of four variables computed from the finely segmented first layer of the calorimeter, and to satisfy all the other criteria [3].From now on, such photons are called "non-tight candidates", while the photon candidates satisfying the "tight" selection are called "tight candidates".
The residual background contamination in the tight candidates event sample is estimated using the "twodimensional side bands" method [3].It is based on the definition of a "tight-isolated" signal region A and three background control regions B, C, D: "tightnon-isolated", "non-tight-isolated" and "non-tight-nonisolated", respectively.The basic method assumes that the control regions have negligible signal contamination and that the isolation energy distribution of background events is the same for tight and non-tight candidates.In that case the signal yield in region A, N A S , can be obtained from the number N k of events observed in data, in each of the four regions k = A, B, C, and D, as The method can easily be extended to account for deviations from the previous hypotheses, requiring only a limited knowledge of the signal and background proper-ties.In that case, the equation to solve is where c k = N k S /N A S are the fractions of signal events expected in each of the three control regions, relative to the signal region A, and BKG characterizes the correlation between the isolation and identification variables in background events (R BKG = 1 when the correlations are negligible).Figure 1(a) shows the distribution of E iso T for tight and non-tight candidates.The latter is normalized to the former in the background-dominated region E iso T > 15 GeV.The excess of tight candidates over normalized non-tight candidates in the region E iso T < 15 GeV shows a clear peak for signal prompt photons.Fig. 1(b) and 1(c) show the isolation profile of photon candidates after subtracting the distribution of non-tight candidates (with the same normalization as applied in Fig. 1(a)), for different ranges of the photon candidate transverse energy in the two different η γ regions.The distributions of these signal-enriched samples are largely independent of the E γ T range, according to the simulation.In the following, Eq. ( 2) is used to estimate the prompt photon yield in the selected sample, with R BKG fixed to one as observed (within uncertainties) in simulated background events.Results obtained neglecting signal leakage in the control regions, as in Eq. ( 1), or with R BKG = 1 are used to evaluate systematic uncertainties.In the endcap region there are too few events in the 500 to 600 GeV bin; therefore, the signal purity from the preceding bin is used instead.
The largest contribution to the impurity arises from background photons that come from the meson decays.Figure 2 shows the signal purity for prompt photons in region A as a function of E γ T for the barrel and end-cap regions.The signal purity is estimated from the data using the two-dimensional side band approach shown in Eq. ( 2).The shaded bands indicate statistical uncertainties.The measured signal purity is larger than 93% and increases with E γ T .The purity has also been determined using Eq. ( 2) and the result agrees with the default method to within 3% and has a similar E γ T -dependence.

VI. RESIDUAL BACKGROUND
A possible residual background could arise from electrons that fake photons; primarily high-p T isolated electrons from W or Z boson decays that tend to be misidentified as converted photons.The corresponding misidentification probability is measured by studying the invariant mass spectrum of e ± γ combinations in the Z boson mass range.It was found that the background from prompt electrons is ≈ 0.5% for E γ T < 400 GeV [4].To understand the background from electrons for higher E γ T , a MC study was performed using a sample of high-p T electrons.The current analysis neglects T estimated from the data using the two-dimensional side band approach shown in Eq. ( 2).The shaded bands indicate statistical uncertainties.
contributions from high-p T isolated electrons, since the MC study indicates that the rate of misidentified photons with E γ T above 400 GeV originating from electrons is well below 0.5%.

VII. CROSS-SECTION MEASUREMENT
The differential cross section for the production of isolated prompt photons in a given phase-space bin i is , where N i is the number of photons in a bin i after the background subtraction, C i (γ) is a correction factor, ∆ i is the width of bin i and Ldt is the integrated luminosity.The correction factor, C i (γ), is evaluated from the bin-by-bin ratio of the number of reconstructed prompt photons to the number of particlelevel prompt photons in the signal simulation.The photon reconstruction efficiency in the MC simulation was tuned using data-driven techniques [32].The correction factor C i (γ) accounts for acceptance and smearing effects, photon reconstruction efficiency and selection efficiency, as well as the event selection efficiency.The various components of the correction are discussed.
• Acceptance and smearing correction, is defined as the efficiency for a particle-level photon, in the acceptance of the differential cross section, to be reconstructed as a photon passing all the selection criteria outlined in Sec.VI.The largest contributing factor to this efficiency is the selection requirement E iso T ≤ 7 GeV.The shower-shape corrections for the MC simulation are determined from the comparison of data with the simulation in the control samples of photons selected in the same kinematic regions as used in this measurement.The average value of this efficiency in the barrel region was found to be 95%, while it is 87% in the end-cap region.
• Identification efficiency, which is defined as the efficiency for reconstructed prompt photons after the isolation requirement to pass the tight photon identification criteria described in Sec.V.This efficiency was estimated by using simulated signal events after correcting the simulated showershapes in the calorimeter to match those observed in data [3].This efficiency in the barrel and end-cap region was found to be above 93%.
• Trigger efficiency, which is defined as the efficiency for an event to be accepted by a photon trigger with an energy threshold of 80 GeV.The trigger efficiency is determined using a data-driven technique based on high level triggers with low-E γ T threshold, and it is estimated to be close to 100% for E γ T > 100 GeV [33].
In addition to the efficiencies quoted above, the correction factor also accounts for the bin-by-bin migration due to the finite bin sizes.The MC simulations indicate that the RMS of the E γ T resolution for photons in the range 100 < E γ T < 600 GeV is close to 3% in the central region and 4% in the end-cap region.The widths of the bins for the differential cross-section measurement are chosen to be substantially larger than the resolution in order to minimize migration between neighboring bins.
The average value of the C i (γ) estimated using PYTHIA is about 94% in the barrel region and 86% in the end-cap region.It increases with E γ T by approximately 4% in the range of E γ T explored in this measurement.This correction factor is shown in Fig. 3, where the shaded bands represent the systematic and statistical uncertainties discussed in Sec.VIII.

VIII. SYSTEMATIC UNCERTAINTIES
The systematic uncertainties on the measured differential cross sections are determined by repeating the analysis with some of the selection or analysis procedures changed.The systematic variations affect the C i (γ) correction factors and signal purity, thus an overall change in the cross section.The largest uncertainties are described below.
• A shift between the true and reconstructed isolation energy in the MC simulation was found to be less than 700 MeV for E iso T 7 GeV.This difference does not depend on the E γ T , and is similar in PYTHIA and HERWIG signal and background MC samples.This difference is also similar to that observed between the data and MC simulation.In the previous publication [4], this difference estimated using electrons was found to be 500 MeV.T for the barrel and end-cap regions.The correction factor is evaluated from the bin-by-bin ratio, using the PYTHIA simulation, of reconstructed prompt photons to particle-level prompt photons in the signal simulation.The shaded bands indicate statistical and systematic uncertainties discussed in Sec.VIII.
MC samples with an additional amount of material in front of the calorimeter show a small effect on the isolation distribution.For this MC, the shift between the true and reconstructed levels for the isolation is smaller than 700 MeV.The correction factors C i (γ) calculated using such MC showed a negligible effect on the cross section.
The systematic uncertainty on the cross section due to the isolation cut was evaluated by changing the requirement by ±700 MeV in the simulation and recalculating the correction factors C i (γ).This systematic variation leads to a typical uncertainty of less than 1% for all E γ T explored in this measurement.
• The uncertainty on the cross section due to insufficient knowledge of the photon identification efficiency is estimated by using different techniques for the photon identification as described in Ref. [32].Such uncertainties also account for the amount of material upstream of the calorimeter.An effect of 2% or less is observed for all E γ T explored in this measurement.
• The uncertainty due to the photon energy measurement is calculated by varying the photon energy scale within the expected uncertainty in the MC simulation.This uncertainty mostly affects the C i (γ) correction factor.The effect of such a variation leads to an uncertainty between 2% at low E γ T and 6% at large E γ T .• The systematic uncertainty on the cross section due to the photon energy resolution is calculated by smearing the central value and then varying the reconstructed energy in the MC simulations as described in Ref. [3] and then recomputing the C i (γ) factor.This uncertainty is typically 2% for all E γ T explored in this measurement.
• The stability on the C i (γ) factors due to the choice of MC generator is computed by considering HERWIG for the bin-by-bin correction instead of PYTHIA.The stability affects photon reconstruction and identification.It also probes the uncertainty on the signal reconstruction due to an alternative fragmentation mechanism.The uncertainty on the cross section due to this contribution ranges from 2% at low E γ T to 4% at E γ T > 800 GeV.• The uncertainty on the background subtraction is estimated using alternative background subtraction techniques discussed in Sec.V. Equation ( 2) is modified to either neglect signal leakage or include a modified R BKG .The background is subtracted by either neglecting correlations between the signal and background regions, or using the central values of the correlations estimated from simulated background events.The uncertainty on the cross section due to the background subtraction technique varies between 2% and 3% for all E γ T explored in this measurement.
• The uncertainty arising from the definition of the background control regions is estimated by repeating the measurement using an alternative definition of the non-isolated region.The isolation requirement was increased from 7 GeV to 10 GeV.Such a redefinition affects both the signal purity and the C i (γ) factors.An effect of 1% or less for all E γ T explored in this measurement is observed, which is compatible with the statistical uncertainty.
• The systematic uncertainty on the fraction of photons from fragmentation was estimated using the PYTHIA signal sample with 50% fewer photons from fragmentation.Alternatively, weights of events with photons from fragmentation were scaled by a factor of two.The effect from such changes on the final cross sections is compatible with the statistical uncertainty (< 0.5%).
• The relative systematic uncertainty on the cross section due to the uncertainty of the luminosity measurement is 1.8%.It is fully correlated among all E T and η bins of the differential cross sections.
The sources of systematic uncertainty are assumed uncorrelated and thus the total systematic uncertainty is estimated by summing in quadrature all the contributions.The final systematic uncertainty on the differential and total cross sections in the barrel (end-cap) region is below 6(7)%.
As a cross-check, the measurement is repeated using an alternative definition of the photon transverse isolation energy, based on three-dimensional topological clusters [31] of energy deposits in the calorimeters, affecting mostly the photon reconstruction efficiency.The same calorimeter cells are used for both the calculation of the photon isolation and for the subtraction of the contribution from the underlying event and pileup, thus providing a quantity that is less dependent on the amount of pileup.A difference smaller than 3% is found between the alternative and the nominal results.In addition, in order to verify the reliability of the pileup removal technique, differential cross sections were calculated separately for low pileup and high-pileup runs.These two cross sections were found to be consistent.

IX. THEORETICAL PREDICTIONS
The expected prompt-photon production cross section was estimated using the JETPHOX 1.3 Monte Carlo program [15,16], which implements a full NLO QCD calculation of both the direct and fragmentation contributions to the total cross section.The parton-level isolation, defined as the total E T from the partons produced with the photon inside a cone of radius ∆R = 0.4 in η × φ around the photon direction, is required to be smaller than 7 GeV.The fragmentation contribution in the JETPHOX calculation decreases with increasing E γ T and becomes negligible for E γ T > 500 GeV.Further details of the JETPHOX calculation can be found in Ref. [34].The calculation uses the NLO photon fragmentation function of BFG set II [35].The CT10 [36] and MSTW2008NLO [37] PDFs for the proton are provided by the LHAPDF package [38].The nominal renormalization (µ R ), factorization (µ F ) and fragmentation (µ f ) scales were set to the photon transverse energy (µ R = µ F = µ f = E γ T ).Systematic uncertainties on the QCD cross sections are estimated and listed below.
• The scale uncertainty is evaluated by varying the three scales following the constraints and are added in quadrature [34]: This leads to a change of between 12% and 20% in the predicted cross section.
• The uncertainty on the differential cross section due to insufficient knowledge of the PDFs was obtained by repeating the JETPHOX calculation for 52 eigenvector sets of the CT10 PDF and applying a scaling factor in order to obtain the uncertainty for the 68% confidence-level (CL) interval [34].The corresponding uncertainty on the cross section increases with E γ T and varies between a 5% at E γ T 100 GeV and 15% at E γ T 900 GeV.
• The effect of the uncertainty on the value of the strong coupling constant, α s , is evaluated following the recommendation in Ref. [36].This was done using different CT10 PDF sets with α s values varied by ±0.002 around the central value, α s = 0.118.Then, a scaling factor was applied in order to obtain the uncertainty for the 68% CL interval.The average α s uncertainty on the cross section is 4.5%, with a small dependence on E γ T .In the following, the total uncertainty includes the three sources above added in quadrature.In addition the uncertainty arising from the scale variations, which is the largest of these three contributions, will be shown separately.
In order to perform a proper comparison with the JETPHOX calculation, the effects of hadronization, pileup and the underlying event have to be understood because the isolation energy is directly sensitive to these effects.The ambient-energy-density correction used for the E iso T reconstruction reduces the effects from the underlying event and pileup, but this effect may not be completely taken into account.Using PYTHIA and HERWIG with different tunes, the combined effect from hadronization and the underlying event is estimated to be about ±1%.This correction is small compared to the full uncertainty from other sources and is not included in the total theoretical uncertainty.
The measured cross sections are also compared to those from the LO parton-shower generators, PYTHIA and HERWIG.These models are described in Sec.III B. Both simulate the fragmentation components through the emission of photons in the parton shower.

X. RESULTS
The differential cross section for the production of isolated prompt photons is obtained from the number of signal events as discussed in Sec.VII.The measured E γ Tdifferential cross sections together with the theoretical predictions are shown in Figs. 4 and 5 for the barrel and end-cap η γ regions, respectively.Tables I and II list the values of the differential cross sections shown in these figures.Figure 6 and Table III show the cross section as a function of η γ for E γ T > 100 GeV.The full error bars on the data points represent the combination of statistical and systematic uncertainties.The inner error bars show statistical uncertainties.The shaded bands on the NLO predictions show the theoretical uncertainties as discussed in Sec.IX.The theoretical uncertainties due to the choice of factorization and renormalization scales as well as the fragmentation scale are shown as an inner band.
The NLO calculations agree with the data up to the highest E γ T considered.The data are somewhat higher

than the central NLO calculation for low E γ
T , but agree within the theoretical uncertainty of the NLO calculation.This trend is also visible throughout η γ as it is dominated by the low E γ T range of the measurement.At low E γ T , the observed difference between the NLO predictions based CT10 PDF and MSTW2008NLO PDF are larger than the PDF uncertainty estimated using CT10.The difference between CT10 and MSTW2008NLO predictions is smaller than the CT10 PDF uncertainty for E γ T > 600 GeV.The predictions of the LO parton-shower MC generators, PYTHIA and HERWIG, are also shown in Figs.4-6.The PYTHIA model describes the data fairly well, while HERWIG falls below the data by 10%-20%.The shapes of the cross sections are well described by both models.
The data are also compared to MC predictions that include only direct photons from qg → qγ and q q → gγ processes calculated at LO QCD. Figure 7 shows that these MC generators predict a cross section at low E γ T that is 20% lower than the data which includes all the higher-order fragmentation processes.This difference is reduced at high E γ T , where the contribution from photons originating from fragmentation becomes small.This shows that the higher order fragmentation processes contribute significatly to the shape of the predicted E γ T cross section.Theory/Data FIG. 7. Same data as in Fig. 4, but the comparison is made with MC predictions that include only direct photons from the hard processes.
The total inclusive cross section of direct photons calculated in the kinematic region PYTHIA predicts that this cross section is 224 pb while HERWIG predicts 187 pb.The cross section was calculated from the total number of signal events in the given kinematic region.The NLO calculations with the CT10 and MSTW2008NLO PDFs predict 203 ± 25 (theory) pb and 212 ± 24 (theory) pb, respectively, where the theory uncertainty is symmetrized and includes the scale, PDF and α s uncertainties.The total inclusive cross section for direct photons within the kinematic range E γ T > 100 GeV, 1.52 ≤ |η γ | < 2.37 and E iso T ≤ 7 GeV is which can be compared to predictions of 118 pb (PYTHIA) and 99 pb (HERWIG).The NLO calculations based on CT10 and MSTW2008NLO PDFs predict 105 ± 15 (theory) pb and 109 ± 15 (theory) pb, respectively.

XI. CONCLUSION
A measurement of the differential cross sections for the inclusive production of isolated prompt photons in pp collisions at a center-of-mass energy of √ s = 7 TeV was presented using 4.6 fb −1 of collision data collected with the ATLAS detector at the LHC.The cross sections were measured as a function of photon transverse energy E γ T and pseudorapidity η γ .The E γ T kinematic range of this measurement spans from 100 GeV to 1 TeV, thus significantly extending the measured kinematic range previously published [4] by ATLAS.The measured differential cross section falls by more than five orders of magnitude in this kinematic range.Both PYTHIA and HERWIG describe the shapes of the differential cross sections.The HERWIG generator predicts a smaller cross section compared to PYTHIA and the data.The MC studies presented in this paper indicate that fragmentation contributions are needed for a good description of the data.
The data agree with the NLO predictions based on the CT10 and MSTW2008 PDF up to the highest measured E γ T 1 TeV.In this kinematic regime, the theoretical uncertainties due to the PDFs of the proton become significant.Thus the presented cross sections have the potential to provide additional constraints on the proton PDFs.The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide.

FIG. 1 .FIG. 2 .
FIG. 1. (a): Distributions of tight photon transverse energy E iso T (dots) and non-tight (shaded gray region) photon candidates in data, for photon transverse energy E γ T > 100 GeV in the central η γ region.The latter is normalized to the former for E iso T > 15 GeV.Distributions of tight E iso T photons in the barrel (b) and end-cap (c) regions after subtracting the normalized non-tight distribution.For both (b) and (c) a comparison of two representative E γT regions with different η γ is shown.The vertical lines show the requirement of E iso T ≤ 7 GeV used to define the final cross sections.These distributions are normalized to one.

FIG. 3 .
FIG.3.The correction factor, Ci(γ), as a function of photon transverse energy E γ T for the barrel and end-cap regions.The correction factor is evaluated from the bin-by-bin ratio, using the PYTHIA simulation, of reconstructed prompt photons to particle-level prompt photons in the signal simulation.The shaded bands indicate statistical and systematic uncertainties discussed in Sec.VIII.

FIG. 4 .
FIG.4.Measured (dots with error bars) and expected inclusive prompt photon cross section as a function of the photon transverse energy, E γ T , in the barrel η γ region.The inner error bars on the data points show statistical uncertainties, while the full error bars show statistical and systematic uncertainties added in quadrature.The NLO theory prediction is shown with the shaded bands that indicate the scale uncertainty (the inner yellow band) and the total uncertainty (the outer green band), which also includes the PDF and αs uncertainties.The LO parton-shower MC generators are shown as lines.The bottom panel shows the corresponding theory/data ratio, in which the data points are centered at one.

FIG. 5 .FIG. 6 .
FIG. 5. Measured (dots with error bars) and expected inclusive prompt photon cross section in the end-cap region.The inner error bars on the data points show statistical uncertainties, while the full error bars show statistical and systematic uncertainties added in quadrature.The NLO theory prediction is shown with the shaded bands that indicate the scale uncertainty (the inner yellow band) and the total uncertainty (the outer green band), which also includes the PDF and αs uncertainties.The LO parton-shower MC generators are shown as lines.

TABLE I .
Measured inclusive prompt photon production cross section in the pseudorapidity range |η γ | < 1.37 as a function of E γ T with statistical and systematic uncertainties.