Dynamics of isolated-photon plus jet production in pp collisions at sqrt(s)=7 TeV with the ATLAS detector

The dynamics of isolated-photon plus jet production in pp collisions at a centre-of-mass energy of 7 TeV has been studied with the ATLAS detector at the LHC using an integrated luminosity of 37 pb-1. Measurements of isolated-photon plus jet bin-averaged cross sections are presented as functions of photon transverse energy, jet transverse momentum and jet rapidity. In addition, the bin-averaged cross sections as functions of the difference between the azimuthal angles of the photon and the jet, the photon--jet invariant mass and the scattering angle in the photon--jet centre-of-mass frame have been measured. Next-to-leading-order QCD calculations are compared to the measurements and provide a good description of the data, except for the case of the azimuthal opening angle.


Introduction
The production of prompt photons in association with a jet in proton-proton collisions, pp → γ+jet+X, provides a testing ground for perturbative QCD (pQCD) in a cleaner environment than in jet production, since the photon originates directly from the hard interaction. The measurements of angular correlations between the photon and the jet can be used to probe the dynamics of the hard-scattering process. Since the dominant production mechanism in pp collisions at the LHC is through the qg → qγ process, measurements of prompt-photon plus jet production have been used to constrain the gluon density in the proton [1,2]. Furthermore, precise measurements of photon plus jet production are also useful for the tuning of the Monte Carlo (MC) models. In addition, these events constitute the main reducible background in the identification of Higgs bosons decaying to a photon pair.
The dynamics of the underlying processes in 2 → 2 hard collinear scattering can be investigated using the variable θ * , where cos θ * ≡ tanh(∆y/2) and ∆y is the difference between the rapidities 1 of the two final-state particles. The variable θ * coincides with the scattering angle in the centre-of-mass frame, and its distribution is sensitive to the spin of the exchanged particle. For processes dominated by t-channel gluon exchange, such as dijet production in pp collisions shown in Fig. 1(a), the differential cross section behaves as (1 − | cos θ * |) −2 when | cos θ * | → 1. In contrast, processes dominated by t-channel quark exchange, such as W/Z + jet production shown in Fig. 1(b), are expected to have an asymptotic (1 − | cos θ * |) −1 behaviour. This fundamental prediction of QCD can be tested in photon plus jet production at the centre-of-mass energy of the LHC.
At leading order (LO) in pQCD, the process pp → γ + jet + X proceeds via two production mechanisms: direct photons (DP), which originate from the hard process, and fragmentation photons (F), which arise from the fragmentation of a coloured high transverse momentum (p T ) parton [3,4]. The direct-photon contribution, as shown in Fig. 1(c), is expected to exhibit a (1 − | cos θ * |) −1 dependence when | cos θ * | → 1, whereas that of fragmentation processes, as shown in Fig. 1 (d), is predicted to be the same as in dijet production, namely (1−| cos θ * |) −2 . For both processes, there are also s-channel contributions which are, however, non-singular when | cos θ * | → 1. As a result, a measurement of the cross section for prompt-photon plus jet production as a function of | cos θ * | provides a handle on the relative contributions of the direct-photon and fragmentation components as well as the possibility to test the dominance of t-channel quark exchange, such as that shown in Fig. 1(c). Measurements of prompt-photon production in a final state with accompanying hadrons necessitates of an isolation requirement on the photon to avoid the large contribution from neutralhadron decays into photons. The production of inclusive isolated photons in pp collisions has been studied previously by ATLAS [5,6] and CMS [7,8]. Recently, the differential cross sections for isolated photons in association with jets as functions of the photon transverse energy in different regions of rapidity of the highest transverse-momentum (leading) jet were measured by ATLAS [9]. The analysis presented in this paper is based on the same data sample and similar selection criteria as in the previous publication, but extends the study by measuring also cross sections in terms of the leading-jet and photon-plus-jet properties. The goal of the analysis presented here is to study the kinematics and dynamics of the isolated-photon plus jet system by measur-unconverted photon candidates. Clusters matched to pairs of tracks originating from reconstructed conversion vertices in the inner detector or to single tracks with no hit in the innermost layer of the pixel detector were classified as converted photon candidates [17]. The overall reconstruction efficiency for unconverted (converted) photons with transverse energy above 20 GeV and pseudorapidity in the range |η γ | < 2.37, excluding the transition region 1.37 < |η γ | < 1.52 between calorimeter sections, was estimated to be 99. 8 (94.3)% [17]. The final energy measurement, for both converted and unconverted photons, was made using only the calorimeter, with a cluster size depending on the photon classification. In the barrel, a cluster corresponding to 3 × 5 (η × φ) cells in the second layer was used for unconverted photons, while a cluster of 3 × 7 cells was used for converted photon candidates to compensate for the opening angle between the conversion products in the φ direction due to the magnetic field. In the end-cap, a cluster size of 5 × 5 was used for all candidates. A dedicated energy calibration [18] was then applied separately for converted and unconverted photon candidates to account for upstream energy loss and both lateral and longitudinal leakage. Photons reconstructed near regions of the calorimeter affected by readout or high-voltage failures were rejected, eliminating around 5% of the selected candidates.
Events with at least one photon candidate with calibrated E γ T > 45 GeV and |η γ | < 2.37 were selected. The candidate was excluded if 1.37 < |η γ | < 1.52. The same shower-shape and isolation requirements as described in previous publications [5,6,9] were applied to the candidates; these requirements are referred to as "tight" identification criteria. The selection criteria for the showershape variables are independent of the photon-candidate transverse energy, but vary as a function of the photon pseudorapidity, to take into account significant changes in the total thickness of the upstream material and variations in the calorimeter geometry or granularity. They were optimised independently for unconverted and converted photons to account for the different developments of the showers in each case. The application of these selection criteria suppresses background from jets misidentified as photons.
The photon candidate was required to be isolated by restricting the amount of transverse energy around its direction. The transverse energy deposited in the calorimeters inside a cone of radius ∆R = 0.4 centred around the photon direction is denoted by E iso T,det . The contributions from those cells (in any layer) in a window corresponding to 5 × 7 cells of the second layer of the electromagnetic calorimeter around the photon-shower barycentre are not included in the sum. The mean value of the small leakage of the photon energy outside this region, evaluated as a function of the photon transverse energy, was subtracted from the measured value of E iso T,det . The typical size of this correction is a few percent of the photon transverse energy. The measured value of E iso T,det was further corrected by subtracting the estimated contributions from the underlying event and additional inelastic pp interactions. This correction was computed on an event-by-event basis and amounted on average to 900 MeV [6]. After all these corrections, E iso T,det was required to be below 3 GeV for a photon to be considered isolated.
The relative contribution to the total cross section from fragmentation processes decreases after the application of this requirement, though it remains non-negligible especially at low transverse energies. The isolation requirement significantly reduces the main background, which consists of multi-jet events where one jet typically contains a π 0 or η meson that carries most of the jet energy and is misidentified as an isolated photon because it decays into an almost collinear photon pair.
A small fraction of events contain more than one photon candidate passing the selection crite-5 ria. In such events, the highest-E γ T (leading) photon was kept for further study.

Jet selection
Jets were reconstructed from three-dimensional topological clusters built from calorimeter cells, using the anti-k t algorithm with distance parameter R = 0.6. The jet four-momenta were computed from the sum of the topological cluster four-momenta, treating each as a four-vector with zero mass. The jet four-momenta were then recalibrated using a jet energy scale (JES) correction described in Ref. [19]. This calibration procedure corrected the jets for calorimeter instrumental effects, such as inactive material and noncompensation, as well as for the additional energy due to multiple pp interactions within the same bunch crossing. These jets are referred to as detector-level jets. The uncertainty on the JES correction in the central (forward) region, |η| < 0.8 (2.1 < |η| < 2.8), is less than 4.6% (6.5%) for all jets with transverse momentum p T > 20 GeV and less than 2.5% (3%) for jets with 60 < p T < 800 GeV.
Jets reconstructed from calorimeter signals not originating from a pp collision were rejected by applying jet-quality criteria [19]. These criteria suppressed fake jets from electronic noise in the calorimeter, cosmic rays and beam-related backgrounds. Remaining jets were required to have calibrated transverse momenta greater than 40 GeV. Jets overlapping with the candidate photon or with an isolated electron were discarded; if the jet axis lay within a cone of radius ∆R = 1 (0.3) around the leading-photon (isolated-electron) candidate, the jet was discarded. The removal of electrons misidentified as jets suppresses contamination from W/Z plus jet events. In events with multiple jets satisfying the above requirements, the jet with highest p jet T (leading jet) was retained for further study. The leading-jet rapidity was required to be in the region |y jet | < 2.37.

Final photon plus jet sample
The above requirements select approximately 124 000 events. The fraction of events with multiple photons fulfilling the above conditions is 3 · 10 −4 . The average jet multiplicity in the data is 1.19. The signal MC (see Section 4) predictions for the jet multiplicity are 1.21 in Pythia [20] and 1.19 in Herwig [21].
For the measurements of the bin-averaged cross sections as functions of m γj and | cos θ γj |, additional requirements were imposed to remove the bias due to the rapidity and transverse-momentum requirements on the photon and the jet. Specifically, to have a uniform coverage in both cos θ γj and m γj , the restrictions |η γ + y jet | < 2.37, | cos θ γj | < 0.83 and m γj > 161 GeV were applied. The first two requirements restrict the phase space to the inside of the square delineated by the dashed lines, as shown in Fig. 2(a); within this square, slices in cos θ γj have the same length along the η γ + y jet axis. The third requirement avoids the bias induced by the minimal requirement on E γ T , as shown in Fig.2(b); the hatched area represents the largest region in which unbiased measurements of both | cos θ γj | and m γj distributions can be performed. These requirements do not remove the small bias due to the exclusion of the 1.37 < |η γ | < 1.52 region. The number of events selected in the data after these additional requirements is approximately 26 000.
The contamination from jets produced in pile-up events in the selected samples was estimated to be negligible.

Monte Carlo simulations
Samples of simulated events were generated to study the characteristics of signal and background. These MC samples were also used to determine the response of the detector to jets of hadrons and the correction factors necessary to obtain the particle-level cross sections. In addition, they were used to estimate hadronisation corrections to the NLO QCD calculations.
The MC programs Pythia 6.423 [20] and Herwig 6.510 [21] were used to generate the simulated signal events. In both generators, the partonic processes are simulated using leading-order matrix elements, with the inclusion of initial-and final-state parton showers. Fragmentation into hadrons was performed using the Lund string model [22] in the case of Pythia and the cluster model [23] in the case of Herwig. The modified leading-order MRST2007 [24,25] parton distribution functions (PDFs) were used to parameterise the proton structure. Both samples include a simulation of the underlying event, via the multiple-parton interaction model in the case of Pythia and via the Jimmy package [26] in the case of Herwig. The event-generator parameters, including those of the underlying-event modelling, were set according to the AMBT1 [27] and AUET1 [28] tunes for Pythia and Herwig, respectively. All the samples of generated events were passed through the Geant4-based [29] ATLAS detector simulation program [30]. They were reconstructed and analysed by the same program chain as the data.
The Pythia simulation of the signal includes leading-order photon plus jet events from both direct processes (the hard subprocesses qg → qγ and qq → gγ) and photon bremsstrahlung in QCD dijet events, which can be generated simultaneously. On the other hand, the Herwig signal sample was obtained from the cross-section-weighted mixture of samples containing only direct-photon plus jet or only bremsstrahlung-photon plus jet events, since these processes cannot be generated simultaneously.
The multi-jet background was simulated by using all tree-level 2 → 2 QCD processes and removing photon plus jet events from photon bremsstrahlung. The background from diphoton events was estimated using Pythia MC samples by computing the ratio of diphoton to isolatedphoton plus jet events and was found to be negligible [9].
Particle-level jets in the MC simulation were reconstructed using the anti-k t jet algorithm and were built from stable particles, which are defined as those with a rest-frame lifetime longer than 10 ps. The particle-level isolation requirement on the photon was applied to the transverse energy of all stable particles, except for muons and neutrinos, in a cone of radius ∆R = 0.4 around the photon direction after the contribution from the underlying event was subtracted; in this case, the same underlying-event subtraction procedure used on data was applied at the particle level. The isolation transverse energy at particle level is denoted by E iso T,part . The measured bin-averaged cross sections refer to particle-level jets and photons that are isolated by requiring E iso T,part < 4 GeV [5]. For the comparison to the measurements (see Section 9), samples of events were generated at the particle level using the Sherpa 1.3.1 [31] program interfaced with the CTEQ6L1 [32] PDF set. The samples were generated with LO matrix elements for photon plus jet final states with up to three additional partons, supplemented with parton showers. Fragmentation into hadrons was performed using a modified version of the cluster model [33].

Background subtraction and signal-yield estimation
A non-negligible background contribution remains in the selected sample, even after the application of the tight identification and isolation requirements on the photon. This background comes predominantly from multi-jet processes, in which a jet is misidentified as a photon. This jet usually contains a light neutral meson, mostly a π 0 decaying into two collimated photons, which carries most of the jet energy. The very small contributions expected from diphoton and W/Z plus jet events [5,9] are neglected.
The background subtraction does not rely on MC background samples but uses instead a datadriven method based on signal-depleted control regions. The background contamination in the selected sample was estimated using the same two-dimensional sideband technique as in the previous analyses [5,6,9] and then subtracted bin-by-bin from the observed yield. In this method, the photon was classified as: • "non-isolated", if E iso T,det > 5 GeV; • "tight", if it passed the tight photon identification criteria; • "non-tight", if it failed at least one of the tight requirements on the shower-shape variables computed from the energy deposits in the first layer of the electromagnetic calorimeter, but passed all the other tight identification criteria.
In the two-dimensional plane formed by E iso T,det and the photon identification variable, four regions were defined: • A: the "signal" region, containing tight and isolated photon candidates; • B: the "non-isolated" background control region, containing tight and non-isolated photon candidates; • C: the "non-identified" background control region, containing isolated and non-tight photon candidates; • D: the background control region containing non-isolated and non-tight photon candidates.
The signal yield in region A, N sig A , was estimated by using the relation where N K , with K = A, B, C, D, is the number of events observed in region K and is the so-called background correlation and was taken as R bg = 1 for the nominal results; N bg K with K = A, B, C, D is the number of background events in each region. Eq. (1) takes into account the expected number of signal events in the three background control regions (N sig K ) via the signal leakage fractions, ǫ K = N sig K /N sig A with K = B, C, D, which were extracted from MC simulations of the signal. Since the simulation does not accurately describe the electromagnetic shower profiles, a correction factor for each simulated shape variable was applied to better match the data [5,6]. Eq. (1) leads to a second-order polynomial equation in N sig A that has only one physical (N sig This method was tested on a cross section-weighted combination of simulated signal and background samples and found to accurately determine the amount of signal in the mixture. The only hypothesis underlying Eq. (1) is that the isolation and identification variables are uncorrelated in background events, thus R bg = 1. This assumption was verified both in simulated background samples and in data in the background-dominated region defined by E iso T,det > 10 GeV. Deviations from unity were taken as systematic uncertainties (see Section 7).
The signal purity, defined as N sig A /N A , is typically above 0.9 and is similar whether Pythia or Herwig is used to extract the signal leakage fractions. The signal purity increases as E γ T , p jet T and m γj increase, is approximately constant as a function of |y jet | and ∆φ γj and decreases as | cos θ γj | increases.
The signal yield in data and the predictions of the signal MC simulations are compared in Figs. 3-5. Both Pythia and Herwig give an adequate description of the E γ T , |y jet | and m γj data distributions. The measured p jet T distribution is described well for p jet T 100 GeV; for p jet T 100 GeV, the simulation of Pythia (Herwig) has a tendency to be somewhat above (below) the data.

9
The simulation of Pythia provides an adequate description of the ∆φ γj data distribution, whereas that of Herwig is somewhat poorer. The | cos θ γj | data distribution, with or without additional requirements on m γj or |η γ + y jet |, is not well described by either Pythia or Herwig.
For most of these distributions, the shapes of the direct-photon and fragmentation components in the signal MC simulations are somewhat different. Therefore, in each case, the shape of the total MC distribution depends on the relative fraction of the two contributions. To obtain an improved description of the data by the leading-order plus parton-shower MC samples, a fit to each data distribution 2 was performed with the weight of the direct-photon contribution, α, as the free parameter; the weight of the fragmentation contribution was given by 1 − α. In this context, the default admixture used in the MC simulations would be represented by α = 0.5. The fitted values of α were found to be different for each observable and in the range 0.26-0.84. It is emphasized that α does not represent a physical observable and it was used solely for the purpose of improving the description of the data by the LO simulations. Nevertheless, an observable-dependent α may approximate the effects of higher-order terms. 3 After adjusting the fractions of the DP and F components separately for each distribution, a good description of the data was obtained by both the Pythia and Herwig MC simulations for all the observables (see Figs. [6][7][8], though the descriptions of ∆φ γj and p jet T by Herwig are still somewhat poor. The MC simulations using the optimised admixture for each observable were used as the baseline for the determination of the measured cross sections (see Section 6).
To be consistent, the optimisation of the admixture of the two components should be done simultaneously with the background subtraction since the signal leakage fractions ǫ K also depend on the admixture. However, such a procedure would result in an estimated signal yield that would depend on the fitted variable. To obtain a signal yield independent of the observable, except for statistical fluctuations, the background subtraction was performed using the default admixture of the two components and a systematic uncertainty on the background subtraction due to this admixture was included (see Section 7).

Signal efficiency
The total selection efficiency, including trigger, reconstruction, particle identification and event selection, was evaluated from the simulated signal samples described in Section 4. The integrated efficiency was computed as ε = N det,part /N part , where N det,part is the number of MC events that pass all the selection requirements at both the detector and particle levels and N part is the number of MC events that pass the selection requirements at the particle level. The integrated efficiency was found to be 68.5 (67.9)% from the Pythia (Herwig) samples. The bin-to-bin efficiency was computed as is the number of MC events that pass all the selection requirements at both the detector and particle levels and are generated and reconstructed in bin i,  is the number of MC events that pass the selection requirements at the particle level and are located in bin i. The bin-to-bin efficiencies are typically above 60%, except for p jet T and ∆φ γj ( 40%) due to the limited resolution in these steeply falling distributions, and are similar for Pythia and Herwig.
The bin-to-bin reconstruction purity was computed as κ i = N det,part is the number of MC events that pass the selection requirements at the detector level and are located in bin i. The bin-to-bin reconstruction purities are typically above 70%, except for p jet T and ∆φ γj ( 45%) due to the limited resolution in these steeply falling distributions, and are similar for Pythia and Herwig.
The efficiency of the jet-quality criteria (see Section 3.2) applied to the data was estimated using a tag-and-probe method. The leading photon in each event was considered as the tag to probe the leading jet. Additional selection criteria, such as ∆φ γj > 2.6 (probe and tag required to be back-to-back) and |p jet T −E γ T |/p avg T < 0.4, where p avg T = (p jet T +E γ T )/2 (to have well-balanced probe and tag), were applied. The jet-quality criteria were then applied to the leading jet and the fraction of jets accepted was measured as a function of p jet T and |y jet |. The jet-quality selection efficiency is approximately 99%. No correction for this efficiency was applied, but an uncertainty was included in the measurements (see Section 7).

Cross-section measurement procedure
Isolated-photon plus jet cross sections were measured for photons with E γ T > 45 GeV, |η γ | < 2.37 (excluding the region 1.37 < |η γ | < 1.52) and E iso T,part < 4 GeV. The jets were reconstructed using the anti-k t jet algorithm with R = 0.6 and selected with p jet T > 40 GeV, |y jet | < 2.37 and ∆R γj > 1. Bin-averaged cross sections were measured as functions of E γ T , p jet T , |y jet | and ∆φ γj . Binaveraged cross sections as functions of m γj and | cos θ γj | were measured in the kinematic region |η γ + y jet | < 2.37, | cos θ γj | < 0.83 and m γj > 161 GeV. In addition, the bin-averaged cross section as a function of | cos θ γj | was measured without the requirements on m γj or |η γ + y jet |.
The data distributions, after background subtraction, were corrected to the particle level using a bin-by-bin correction procedure. The bin-by-bin correction factors were determined using the MC samples; these correction factors took into account the efficiency of the selection criteria, jet and photon reconstruction as well as migration effects.
For this approach to be valid, the uncorrected distributions of the data must be adequately described by the MC simulations at the detector level. This condition was satisfied by both the Pythia and Herwig MC samples after adjusting the relative fractions of the LO direct-photon and fragmentation components (see Section 5.1). The data distributions were corrected to the particle level via the formula where dσ/dO is the bin-averaged cross section as a function of observable O = E γ T , p jet T , |y jet |, ∆φ γj , m γj or | cos θ γj |, N sig A (i) is the number of background-subtracted data events in bin i, C MC (i) is the correction factor in bin i, L is the integrated luminosity and ∆O(i) is the width of bin i. The bin-by-bin correction factors were computed as where α corresponds to the optimised value obtained from the fit to the data for each observable, as explained in Section 5.1. The final bin-averaged cross sections were obtained from the average of the cross sections when using C MC with MC = Pythia or Herwig. The uncertainties from the parton-shower and hadronisation models used for the corrections were estimated as the deviations from this average when using either Pythia or Herwig to correct the data (see Section 7). The correction factors differ from unity by typically 20% and are similar for Pythia and Herwig.

Systematic uncertainties
The following sources of systematic uncertainty were considered; average values, expressed in percent and shown in parentheses, quantify their effects on the cross section as a function of | cos θ γj | (with the requirements on m γj and |η γ + y jet | applied): • Simulation of the detector geometry. The systematic uncertainties originating from the limited knowledge of the material in the detector were evaluated by repeating the full analysis using a different detector simulation with increased material in front of the calorimeter [15]. This affects in particular the photon-conversion rate and the development of electromagnetic showers (±5%).
• Photon simulation and model and fit dependence. The MC simulation of the signal was used to estimate (i) the signal leakage fractions and (ii) the bin-by-bin correction factors: -For step (i), both the Pythia and Herwig simulations were used with the admixture of the direct-photon and fragmentation components as given by each MC simulation to yield two sets of background-subtracted data distributions. The signal leakage fractions depend on the relative fraction of the two components. The uncertainty related to the simulation of the isolated-photon components in the signal leakage fractions was estimated (conservatively) by performing the background subtraction with only the direct-photon or the fragmentation component (±3%).
-For step (ii), the effects of the parton-shower and hadronisation models in the bin-bybin correction factors were estimated as deviations from the nominal cross sections by using either only Pythia or only Herwig to correct the data (±1%).
-The bin-by-bin correction factors also depend on the relative fractions of the two components; the nominal admixture was taken from the fit to the background-subtracted data distributions. A systematic uncertainty due to the fit was estimated (conservatively) by using the default admixture of the components (±2%).
• Uncertainty on the background correlation in the two-dimensional sideband method. In the background subtraction, R bg = 1 was assumed (see Section 5.1); i.e. the photon isolation and identification variables are uncorrelated for the background. This assumption was verified using both the data and simulated background samples and was found to hold within a 10% uncertainty in the kinematic region of the measurements presented here. The cross sections were recomputed accounting for possible correlations in the background subtraction, and the differences from the nominal results were taken as systematic uncertainties (±0.6%).
• Definition of the background control regions in the two-dimensional sideband method. The estimation of the contamination in the signal region is affected by the choice of the background control regions. The uncertainty due to this choice was estimated by repeating the analysis with different identification criteria and by changing the isolation boundary from the nominal value of 5 GeV to 4 or 6 GeV (±2%).
• Data-driven correction to the photon efficiency. The shower shapes of simulated photons in the calorimeter were corrected to improve the agreement with the data. The uncertainty on the photon-identification efficiency due to the application of these corrections was estimated using different simulated photon samples and a different detector simulation with increased material in front of the calorimeter [15] (±2%).
• Uncertainty on the jet reconstruction efficiency. The MC simulation reproduces the jet reconstruction efficiencies in the data to better than 1% [34] (±1%).
• Jet-quality selection efficiency. The efficiency of the jet-quality criteria was determined to be 99% (+1%).
• Uncertainty arising from the photon-isolation requirement. This uncertainty was evaluated by increasing the value of E iso T,det in the MC simulations by the difference (+500 MeV) between the averages of E iso T,det for electrons in simulation and data control samples [6] (+4%). • Uncertainty on the integrated luminosity. The measurement of the luminosity has a ±3.4% uncertainty [16] (±3.4%).
For dσ/dE γ T , the dominant uncertainties arise from the detector material in the simulation, the isolation requirement, the model dependence in the signal leakage fractions and the photon energy scale, though in some bins the uncertainty from the luminosity measurement provides the largest contribution. The dominant uncertainties for the other bin-averaged cross sections come from the detector simulation, the model dependence in the signal leakage fractions, the isolation requirement and the jet energy scale. All these systematic uncertainties were added in quadrature together with the statistical uncertainty and are shown as error bars in the figures of the measured cross sections (see Section 9).

Next-to-leading-order QCD calculations
The NLO QCD calculations used in this analysis were computed using the program Jetphox [35]. This program includes a full NLO QCD calculation of both the direct-photon and fragmentation contributions to the cross section.
The number of flavours was set to five. The renormalisation (µ R ), factorisation (µ F ) and fragmentation (µ f ) scales were chosen to be µ R = µ F = µ f = E γ T . The calculations were performed using the CTEQ6.6 [36] parameterisations of the proton PDFs and the NLO photon BFG set II photon fragmentation function [37]. The strong coupling constant was calculated at two-loop order with α s (m Z ) = 0.118. Predictions based on the CT10 [38] and MSTW2008nlo [39] proton PDF sets were also computed.
The calculations were performed using a parton-level isolation cut, which required a total transverse energy below 4 GeV from the partons inside a cone of radius ∆R = 0.4 around the photon direction. The anti-k t algorithm was applied to the partons in the events generated by this program to define jets of partons. The NLO QCD predictions were obtained using the photon and these jets of partons in each event.

Hadronisation and underlying-event corrections to the NLO QCD calculations
Since the measurements refer to jets of hadrons with the contribution from the underlying event included, whereas the NLO QCD calculations refer to jets of partons, the predictions were corrected to the particle level using the MC models. The multiplicative correction factor, C NLO , was defined as the ratio of the cross section for jets of hadrons to that for jets of partons and was estimated by using the MC programs described in Section 4; a simulation of the underlying event was only included for the sample of events at particle level. The correction factors from Pythia and Herwig are similar and close to unity, except at high p jet T ; for p jet T > 200 GeV, the value of C NLO is 0.87 (0.82) for Pythia (Herwig). The means of the factors obtained from Pythia and Herwig were applied to the NLO QCD calculations.

Theoretical uncertainties
The following sources of uncertainty in the theoretical predictions were considered; average values, expressed in percent and shown in parentheses, quantify their effects on the cross section as a function of | cos θ γj | (with the requirements on m γj and |η γ + y jet | applied): • The uncertainty on the NLO QCD calculations due to terms beyond NLO was estimated by repeating the calculations using values of µ R , µ F and µ f scaled by the factors 0.5 and 2. The three scales were either varied simultaneously, individually or by fixing one and varying the other two. In all cases, the condition 0.5 ≤ µ A /µ B ≤ 2 was imposed, where A, B = R, F, f and A B. The final uncertainty was taken as the largest deviation from the nominal value among the 14 possible variations (±14%) and is dominated by the µ R variations.
• The uncertainty on the NLO QCD calculations due to those on the proton PDFs was estimated by repeating the calculations using the 44 additional sets from the CTEQ6.6 error analysis (±3.5%).
• The uncertainty on the NLO QCD calculations due to that on the value of α s (m Z ) was estimated by repeating the calculations using two additional sets of proton PDFs, for which different values of α s (m Z ) were assumed in the fits, namely α s (m Z ) = 0.116 and 0.120, following the prescription of Ref. [40] (±2.5%).
• The uncertainty on the NLO QCD calculations due to the modelling of the parton shower, hadronisation and underlying event was estimated by taking the difference of the C NLO factors based on Pythia and Herwig from their average (±0.5%).
For all observables, the dominant theoretical uncertainty is that arising from the terms beyond NLO. The total theoretical uncertainty was obtained by adding in quadrature the individual uncertainties listed above.
The predictions of the NLO QCD calculations from the Jetphox program described in Section 8 and corrected for hadronisation and underlying-event effects are compared to the data in Figs. 9-14. The predictions give a good description of the E γ T and p jet T measured cross sections. The shape and normalisation of the measured cross section as a function of |y jet | is described well by the calculation in the whole range measured. For the maximum three-body final state of the NLO QCD calculations, the photon and the leading jet cannot be in the same hemisphere in the transverse plane, i.e. ∆φ γj is necessarily larger than π/2; as a result, it is not unexpected that they fail to describe the measured ∆φ γj distribution. The leading-logarithm parton-shower predictions of the Pythia, Herwig and Sherpa MC models are also shown in Fig. 12; Pythia and Sherpa give a good description of the data in the whole range measured whereas Herwig fails to do so. The measured cross sections as functions of m γj and | cos θ γj | are described well by the NLO QCD calculations.
The NLO QCD calculations based on the CT10 and MSTW2008nlo proton PDF sets are within the uncertainty band of the CTEQ6.6-based calculations. The shapes of the distributions from the three calculations are similar. The predictions based on the CTEQ6.6 and CT10 PDF sets are very similar in normalisation whereas those based on MSTW2008nlo are approximately 5% higher. All of these comparisons validate the description of the dynamics of isolated-photon plus jet production in pp collisions at O(α em α 2 s ). To gain further insight into the interpretation of the results, LO QCD predictions of the directphoton and fragmentation contributions to the cross section were calculated. Even though at NLO the two components are no longer distinguishable, the LO calculations are useful to identify regions of phase space dominated by the fragmentation contribution and to illustrate the basic differences in the dynamics of the two processes. The ratio LO/NLO does (not) show a strong dependence on p jet T and | cos θ γj | (E γ T , |y jet | and m γj ). The LO and NLO QCD calculations as functions of | cos θ γj | are compared in Fig. 15. The fragmentation contribution is observed to decrease  Figure 9: The measured bin-averaged cross section for isolated-photon plus jet production (dots) as a function of E γ T . The NLO QCD calculations from Jetphox corrected for hadronisation and underlying-event effects (non-perturbative effects, NP) and using the CTEQ6.6 (solid lines), MSTW2008nlo (dashed lines) and CT10 (dotted lines) PDF sets are also shown. The bottom part of the figure shows the ratios of the NLO QCD calculations to the measured cross section. The inner (outer) error bars represent the statistical uncertainties (the statistical and systematic uncertainties added in quadrature) and the shaded band represents the theoretical uncertainty. For most of the points, the inner error bars are smaller than the marker size and, thus, not visible.  as a function of E γ T , p jet T and m γj and is approximately constant as a function of |y jet |. However, it increases as a function of | cos θ γj | from 2% up to 16%. Therefore, the regions at low E γ T , p jet T and m γj as well as large | cos θ γj | are expected to be sensitive to the fragmentation contribution.
The shapes of the bin-averaged cross sections for the direct-photon and fragmentation contributions at LO QCD were compared. The major difference is seen in the bin-averaged cross section as a function of | cos θ γj | (see Fig. 16), with the contribution from fragmentation showing a steeper increase as | cos θ γj | → 1 than that of direct-photon processes. This different behaviour is due to the different spin of the exchanged particle dominating each of the processes: a quark in the case of direct processes and a gluon in the case of fragmentation processes. Therefore, the distribution in | cos θ γj | is particularly useful to study the dynamics underlying the hard process and the relative contributions of direct processes and fragmentation. The fact that the shape of the measured cross section dσ/d| cos θ γj | is much closer to that of the direct-photon processes than that of fragmentation is consistent with the dominance of processes in which the exchanged particle is a quark. Furthermore, the increase of the cross section as | cos θ γj | → 1 observed in the data is milder than that measured in dijet production in pp collisions [41], which is dominated by gluon exchange.
The measurement of the bin-averaged cross section as a function of | cos θ γj | without the requirements on m γj and |η γ + y jet | is presented in Fig. 17 and Table 7. The decrease of the binaveraged cross section as | cos θ γj | increases is due to the non-uniform coverage in | cos θ γj | induced by the requirements on the photon and jet rapidities and transverse momenta. The NLO QCD calculations are compared to the data in the same figure; they give a good description of the measured bin-averaged cross section. The comparison of the data to the predictions of Pythia, Herwig and Sherpa is shown in Fig. 18; in this figure, the MC calculations are normalised to the integrated measured cross section. The shapes of the predictions from Pythia and Herwig are very similar and do not describe the measured cross section. In these predictions, the contributions of directphoton and fragmentation processes were added according to the MC default cross sections. It is possible to improve the description of the measured cross section by adjusting the relative contribution of the subprocesses, as demonstrated in Fig. 8 for the estimated signal yield. In contrast, the prediction of Sherpa gives a good description of the measured cross section, both in shape and magnitude; this may be attributable to the inclusion of higher-order contributions at tree-level in the prediction. The studies summarised in Figs. 17 and 18 give insight into the characteristics of one of the primary backgrounds in the study of the new particle discovered by ATLAS [12] and CMS [13] in the search for the Higgs boson.

Summary and conclusions
Bin-averaged cross sections for isolated photons in association with a jet in 7 TeV protonproton collisions, pp → γ + jet + X, have been presented using an integrated luminosity of 37.1 pb −1 . The jets were reconstructed using the anti-k t jet algorithm with R = 0.6. Isolatedphoton plus jet bin-averaged cross sections were measured as functions of E γ T , p jet T , |y jet |, ∆φ γj , m γj and cos θ γj . The bin-averaged cross sections dσ/dm γj and dσ/d| cos θ γj | were measured with additional selection criteria on |η γ + y jet |, | cos θ γj | and m γj .
Regions of phase space sensitive to the contributions from fragmentation have been identified.   Figure 17: The measured bin-averaged cross section for isolated-photon plus jet production (dots) as a function of | cos θ γj | without the requirements on m γj and |η γ + y jet |. Other details as in the caption to Fig. 9. As a result, these measurements can be used to tune the relative contributions of direct and fragmentation processes in the description of isolated-photon production by the Monte Carlo models.
The NLO QCD calculations, based on various proton PDFs and corrected for hadronisation and underlying-event effects using Pythia and Herwig, have been compared to the measurements. The calculations give a reasonably good description of the measured cross sections both in shape and normalisation, except for ∆φ γj ; this distribution is adequately described by the leading-order plus parton-shower prediction of Pythia or Sherpa. The measured dependence on | cos θ γj | is consistent with the dominance of processes in which a quark is being exchanged.
A measurement of the bin-averaged cross section as a function of | cos θ γj | without the requirements on m γj and |η γ +y jet | was also presented to understand the photon plus jet background relevant for the studies of the spin of the new particle observed by ATLAS and CMS in the search for the Higgs boson. The NLO QCD calculations give a good description of the data.

Acknowledgements
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.
We  The measured bin-averaged cross-section dσ/dE γ T for isolated-photon plus jet production. The statistical (δ stat ) and systematic (δ syst ) uncertainties are shown separately. The corrections for hadronisation and underlyingevent effects to be applied to the parton-level NLO QCD calculations (C NLO ) are shown in the last column. All tables with information on the measured cross sections, their uncertainties and correlations are available in HepData.