Photoproduction of isolated photons, inclusively and with a jet, at HERA

The photoproduction of isolated photons, both inclusive and together with a jet, has been measured with the ZEUS detector at HERA using an integrated luminosity of 374 pb − 1 . Differential cross sections are presented in the isolated-photon transverse-energy and pseudorapidity ranges 6 < E γ T < 15 GeV and − 0 . 7 < η γ < 0 . 9, and for jet transverse-energy and pseudorapidity ranges 4 < E jet T < 35 GeV and − 1 . 5 < η jet < 1 . 8, for exchanged-photon virtualities Q 2 < 1 GeV 2 . Differential cross sections are also presented for inclusive isolated-photon production as functions of the transverse energy and pseudorapidity of the photon. Higher-order theoretical calculations are compared to the results. the


Introduction
Events containing an isolated high-energy photon can provide a direct probe of the underlying partonic process in high-energy collisions involving hadrons, since the emission of such photons is largely unaffected by parton hadronisation. Processes of this kind have been studied in a number of fixed-target and hadroncollider experiments [1]. In ep collisions at HERA, the ZEUS and H1 Collaborations have previously reported the production of isolated photons in photoproduction [2][3][4][5][6][7], in which the exchanged virtual photon is quasi-real, and also in deep inelastic scattering (DIS) [8][9][10][11]. In this Letter, earlier photoproduction measurements by ZEUS are extended by using the full HERA II data set. The statistical precision is much improved owing to the availability of higher integrated luminosity. Measurements are presented of isolated-photon production at high transverse energy with and without an explicit accompanying-jet requirement. The measurement of the jet gives further information on the event dynamics. Fig. 1 gives examples of the lowest-order (LO) diagrams for high-energy photoproduction of photons in quantum chromodynamics (QCD). In "direct" production processes, the entire incoming photon is absorbed by a quark from the incoming proton, while in "resolved" processes, the photon's hadronic structure provides a quark or gluon that interacts with a parton from the proton. Photons that are radiated in the hard scattering process, rather than resulting from meson decay, are commonly called "prompt". 37 Higher-order processes include "fragmentation processes" in which a photon is radiated within a jet, also illustrated in Fig. 1. Such processes are suppressed by requiring that the photon be isolated. Photons radiated at large angles from the incoming or outgoing electron give rise to an observed scattered electron in the detector; such events are excluded from this measurement.
Perturbative QCD predictions are compared to the measurements. The cross sections for isolated-photon production in photoproduction have been calculated to next-to-leading order (NLO) by Fontannaz, Guillet and Heinrich (FGH) [12,13]. Calculations based on the k T -factorisation approach have been made by Lipatov, Malyshev and Zotov (LMZ) [14][15][16].

Experimental set-up
The measurements are based on a data sample corresponding to an integrated luminosity of 374 ± 7 pb −1 , taken during the years 2004 to 2007 with the ZEUS detector at HERA. During this period, HERA ran with an electron or positron beam energy of 27.5 GeV and a proton beam energy of 920 GeV. The sample is a sum of e + p and e − p data. 38 A detailed description of the ZEUS detector can be found elsewhere [17]. Charged particles were measured in the central 32 36 Supported by the Israel Science Foundation. 37 An alternative commonly-used nomenclature is to refer to "prompt" photons as "direct"; thus Figs. 1(a) and 1(b) would be called "direct-direct" and "resolveddirect" diagrams, respectively. 38 Hereafter "electron" refers to both electrons and positrons unless otherwise stated.
tracking detector (CTD) [18] and a silicon micro vertex detector (MVD) [19] which operated in a magnetic field of 1.43 T provided by a thin superconducting solenoid. The high-resolution uraniumscintillator calorimeter (CAL) [20] consisted of three parts: the forward (FCAL), the barrel (BCAL) and the rear (RCAL) calorimeters. The BCAL covered the pseudorapidity range from −0.74 to 1.01 as seen from the nominal interaction point, and the FCAL and RCAL extended the coverage to the range from −3.5 to 4.0. Each part of the CAL was subdivided into elements referred to as cells. The barrel electromagnetic calorimeter (BEMC) cells had a pointing geometry aimed at the nominal interaction point, with a cross section approximately 5 × 20 cm 2 , with the finer granularity in the Z direction 39 and the coarser in the (X, Y ) plane. This fine granularity allows the use of shower-shape distributions to distinguish isolated photons from the products of neutral meson decays such as π 0 → γ γ . The CAL energy resolution, as measured under test-beam conditions, was σ (E)/E = 0.18/ √ E for electrons and 0.35/ √ E for hadrons, where E is in GeV. The luminosity was measured [21] using the Bethe-Heitler reaction ep → eγ p by a luminosity detector which consisted of two independent systems: a lead-scintillator calorimeter [22] and a magnetic spectrometer [23].

Theory
The LO QCD processes relevant to the present measurements are the direct and resolved photoproduction processes (Fig. 1). Higher-order processes include NLO diagrams and fragmentation processes; a box-diagram term also contributes significantly at next-to-next-to-leading order.
Two theoretical predictions are compared to the measurements presented here. In the approach of FGH [12,13], the LO and NLO diagrams and the box-diagram term are calculated explicitly. Fragmentation processes are also calculated in terms of a fragmentation function in which a quark or gluon gives rise to a photon; an experimentally determined non-perturbative parameterisation is used as input to the theoretical calculation [24]. The CTEQ6 [25] and AFG04 [26] parton densities are used for the proton and photon respectively; the use of alternatives altered the results by typically 5%, which was small compared to the other uncertainties on the theory. The authors stress that their NLO calculation must include fragmentation terms to give a well-defined result. Fragmentation and box terms contribute each about 10% to the total cross section. Theoretical uncertainties arise due to the choice of renormalisation, factorisation and fragmentation scales. They were estimated, using a more conservative approach [27] than in the original published paper [12], by varying the renormalisation scale by factors of 0.5 and 2.0, since this gave the largest effect on the cross sections.
The k T -factorisation method used by LMZ [14][15][16] makes use of unintegrated parton densities in the proton, using the KMR formalism [28] based on the MRST08 proton parton densities [29]. Fragmentation terms are not included. The box diagram is included together with 2 → 3 subprocesses to represent the LO direct and resolved photon contributions. Uncertainties were evaluated as provided by LMZ.
All results are presented at the hadron level, and to make use of the predictions, cuts equivalent to the experimental kinematic selections including the photon isolation (see Section 5) were applied at the parton level. Hadronisation corrections were then evaluated (Section 4) and applied to each of the calculations to enable the predictions to be compared to the experimental data.

Monte Carlo event simulation
Monte Carlo (MC) event samples were generated to evaluate the detector acceptance and event-reconstruction efficiency, and to provide signal and background distributions. The program Pythia 6.416 [30] was used to generate the direct and resolved prompt-photon processes, and also 2 → 2 parton-parton scattering processes not involving photons ("dijet events"). For these purposes, CTEQ4 [31] and GRV [32] parton densities were used. The dijet event samples were generated to enable background events to be extracted and used in the analysis. Backgrounds to the isolated photons measured here arise from decays of neutral mesons in hadronic jets where the decay products create an energy cluster in the BCAL that passes the selection criteria for a photon. In Pythia dijet events, a photon can also be radiated from an incoming or outgoing quark. Events in which a high-energy photon was radiated from a quark or lepton ("radiative events") were not included in the final background samples but were defined, in accordance with theory, as a component of the signal.
As a check and to enable systematic uncertainties to be estimated, event samples were also generated using the Herwig 6.510 program [33]. The cluster-based hadronisation scheme of Herwig provides an alternative to the string-based scheme of Pythia.
The generated MC events were passed through the ZEUS detector and trigger simulation programs based on Geant 3.21 [34]. They were then reconstructed and analysed using the same programs as used for the data. The hadronisation corrections to the theory calculations were evaluated using Pythia and Herwig, and lowered the theoretical prediction by typically 10%. Pythia and Herwig are in agreement to a few percent; Pythia was used to provide the numbers for the present analysis. No uncertainties were applied to these corrections. They were calculated by running the same jet algorithm and event selections, including the isolation criterion, on the generated partons and on the hadronised final state in the direct and resolved prompt-photon MC events.

Event selection and reconstruction
A three-level trigger system was used to select events online [17,35,36]. The first-level trigger required a loosely measured track in the CTD and a minimum of energy deposited in the CAL. The event conditions were tightened at the second level, and a highenergy photon candidate was required at the third level. Events were initially selected offline by requiring a high-energy photon candidate of transverse energy > 3.5 GeV recorded in the BCAL. To reduce background from non-ep collisions, events were required to have a reconstructed vertex position, Z vtx , within the range |Z vtx | < 40 cm. No scattered beam electron was permitted in the detector, and photoproduction events were selected by the require- is the energy of the electron beam. Here, E i is the energy of the i-th CAL cell, θ i is its polar angle and the sum runs over all cells [37].
Energy-flow objects (EFOs) [38] were constructed from clusters of calorimeter cells with signals, associated with tracks when appropriate. Tracks not associated with calorimeter clusters were also included. Photon candidates were identified as EFOs with no associated track, and with at least 90% of the reconstructed energy measured in the BEMC. Those EFOs with wider electromagnetic showers than are typical for a single photon were accepted to make possible the evaluation of backgrounds. Each event was required to contain a photon candidate with a reconstructed transverse energy, E γ T , in the range 6 < E γ T < 15 GeV and with pseudorapidity, η γ , in the range −0.7 < η γ < 0.9.
Jet reconstruction was performed, making use of all the EFOs in the event including photon candidates, by means of the k T clustering algorithm [39] in the E-scheme in the longitudinally invariant inclusive mode [40] with the radius parameter set to 1.0. The jets were required to have transverse energy, E jet T , between 4 and 35 GeV and to lie within the pseudorapidity, η jet , range −1.5 < η jet < 1.8. By construction, one of the jets found by this procedure corresponds to or includes the photon candidate. An additional accompanying jet was required in the non-inclusive measurements; if more than one was found, that with the highest E jet T was used. In this kinematic region, the resolution of the jet transverse energy was about 15-20%, estimated using MC simulations.
To reduce the fragmentation contribution and the background from the decay of neutral mesons within jets, the photon candidate was required to be isolated from the reconstructed tracks and other hadronic activity. High-E T photons radiated from beam leptons were also suppressed by requiring no observed scattered lepton in the apparatus. The isolation from tracks was applied to exclude radiating electrons, and was achieved by demanding 2 is the distance to the nearest reconstructed track with momentum greater than 250 MeV in the η-φ plane, where φ is the azimuthal angle. This condition was applied only at the detector level, and not in the hadronor parton-level calculations. Isolation from other hadronic activity was imposed by requiring that the photon-candidate EFO had at least 90% of the total energy of the reconstructed jet of which it formed a part. These selections gave 17441 events with an inclusive-photon candidate and 12450 events with a photon candidate and an accompanying jet.

Extraction of the photon signal
The selected samples contain a large admixture of background events in which one or more neutral mesons, such as π 0 and η, decayed to photons, thereby producing a photon candidate in the BEMC. The photon signal was extracted statistically following the approach used in previous ZEUS analyses [8][9][10][11].
The photon signal was extracted from the background using the energy-weighted width, measured in the Z direction, of the BEMC energy-cluster comprising the photon candidate. This width was Here, Z i is the Z position of the centre of the i-th cell, Z cluster is the energyweighted centroid of the EFO cluster, w cell is the width of the cell in the Z direction, and E i is the energy recorded in the cell. The sum runs over all BEMC cells in the EFO.
The global distribution of δ Z in the data and in the Pythia MC are shown in Fig. 2 for inclusive photon events and those containing an additional jet. The δ Z distribution exhibits a doublepeaked structure with the first peak at ≈ 0.1, associated with the photon signal, and the second peak at ≈ 0.5, dominated by the π 0 → γ γ component of the background.
The number of isolated-photon events in the data is determined by a χ 2 fit to the δ Z distribution in the range 0.05 < δ Z < 0.8, varying the relative fractions of the signal and background components as represented by histogram templates obtained from the MC. This is illustrated in Fig. 2, and a corresponding fit was performed for each measured cross section bin, with χ 2 values of typically 1.1 per degree of freedom (i.e. 31/28). The extracted signals corresponded overall to 8193 ± 156 inclusive-photon events A bin-by-bin correction method was used to determine the production cross section, by means of the relationship where N(γ ) is the number of photons in a bin as extracted from the fit, in events accompanied by a jet if required, and Y is the bin width, L is the total integrated luminosity, and A is the acceptance correction. The acceptance correction was calculated, using MC samples, as the ratio of the number of events that were generated in the given bin to the number that were obtained in the bin after event reconstruction. Its value was typically 1.2. To evaluate the acceptances, allowance must be made for the different acceptances for the direct and the resolved processes, as modelled by Pythia. These components can be substantially distinguished by means of events containing a photon and a jet, in which the quantity is a measure of the fraction of the incoming photon energy given to the final-state photon and jet, at a lowest-order approximation. The energies and longitudinal momentum components of the photon (γ ), the jet and all of the EFOs in the event were combined as indicated. Fig. 3 shows the x meas γ distribution; a peak close to unity is seen, which can be attributed to direct events, and a tail at lower values due to resolved events. A reasonable phenomenological description of the data can be obtained using a MC sample consisting of a 50:40 mixture of Pythia-simulated direct and resolved events, as normalised to the data, with a 10% admixture of radiative events divided equally between direct and resolved. The acceptance factors were calculated using this model. Acceptance factors calculated in this way were applied both to the inclusive and to the jet data. The trigger efficiency was approximately flat above a photon transverse energy of 4.5 GeV, with a value of 87± 2%. This includes a correction of 3.6% which was applied to the trigger acceptance modelled by the MC. The correction was evaluated using DIS samples, in data and MC, in which events with prompt photons were triggered in an independent way.
A correction of typically 2% was applied to subtract a contamination of the sample by DIS events, which was determined using MC-simulated DIS samples [11].

Systematic uncertainties
The most significant sources of systematic uncertainty were evaluated as follows: • to allow for uncertainties in the simulation of the hadronic final state, the cross sections were recalculated using Herwig to model the signal and background events. The ensuing changes in the results correspond to an uncertainty of typically up to 8%, but rising to 18% in the highest bin of x meas γ ; • the energy of the photon candidate was varied by ±2% in the MC at the detector level. This value was obtained from a study of energy-momentum conservation in Deeply Virtual Compton Scattering events measured in the ZEUS detector, in which the final state consisted of a photon and a scattered electron. Independently, the energy of the accompanying jet, when measured, was varied by an amount decreasing from ±4.5% to ±2.5% as E jet T increases from 4 GeV to above 10 GeV. These values were obtained as described in a previous ZEUS publication [11]. Each of these contributions gave variations in the measured cross sections of typically 5%.
Further systematic uncertainties were evaluated as follows: • the uncertainty in the acceptance due to the estimation of the relative fractions of direct and resolved events and radiative events in the MC sample was estimated by varying these fractions by ±15% and ±5% respectively in absolute terms; the changes in the cross sections were typically ±2% in each case; • the dependence of the result on the modelling of the hadronic background by the MC was investigated by varying the upper limit for the δ Z fit in the range [0.6, 1.0]; this gave a ±2% variation.
Other sources of systematic uncertainty were found to be negligible and were ignored. These included the modelling of the track-isolation cut, the track-momentum cut, and the cuts on photon isolation, the electromagnetic fraction of the photon shower, y JB and Z vtx . Except for the uncertainty on the modelling of the hadronic final state, the major uncertainties were treated as symmetric, and all the uncertainties were combined in quadrature. The common uncertainties of 2.0% on the trigger efficiency and 1.9% on the luminosity measurement were not included in the tables and figures.

Results
Differential cross sections were measured for the production of an isolated photon inclusively, and with at least one accompanying jet, in the kinematic region defined by Q 2 < 1 GeV 2 , 0.2 < y < 0.7, −0.7 < η γ < 0.9, 6 < E γ T < 15 GeV, and where relevant 4 < E jet T < 35 GeV and −1.5 < η jet < 1.8. All quantities were evaluated at the hadron level in the laboratory frame. Again, the jets were formed according to the k T clustering algorithm with the radius parameter set to 1.0. Photon isolation was imposed such that at least 90% of the energy of the jet-like object containing the photon originated from the photon. If more than one accompanying jet was found within the designated η jet range in an event, that with highest E jet T was taken. The integrated luminosity was 374 ± 7 pb −1 . Cross sections in E jet T above 15 GeV are omitted from Table 5 and Fig. 6(a) owing to limited statistics, but this kinematic region is included in the other cross-section measurements. The theoretical predictions described in Section 3 are compared to the measure-

Conclusions
The production of inclusive isolated photons and photons with an accompanying jet has been measured in photoproduction with the ZEUS detector at HERA using an integrated luminosity of taining an isolated photon accompanied by a jet, compared to predictions from FGH and LMZ. The kinematic region of the measurement is described in the text. The inner and outer error bars respectively denote statistical uncertainties and statistical uncertainties combined with systematic uncertainties in quadrature. The theoretical uncertainties are shown as hatched and dotted bands. The first two FGH points in (a) have been averaged into a single bin for calculational reasons. the kinematic region is defined in the laboratory frame by: Q 2 < 1 GeV 2 , 0.2 < y < 0.7, −0.7 < η γ < 0.9, 6 < E γ T < 15 GeV and, where a jet is required, 4 < E jet T < 35 GeV and −1.5 < η jet < 1.8.
Photon isolation was imposed such that at least 90% of the energy of the jet-like object containing the photon originated from the photon. The NLO-based predictions of Fontannaz, Guillet and Heinrich reproduce the measured experimental distributions well. The k T -factorisation approach of Lipatov, Malyshev and Zotov describes , for events containing an isolated photon and a jet, compared to predictions from FGH and LMZ. The kinematic region of the measurement is described in the text. The inner and outer error bars respectively denote statistical uncertainties and statistical uncertainties combined with systematic uncertainties in quadrature. The theoretical uncertainties are shown as hatched and dotted bands. the photon distributions well but gives a less good description of the jet-based variables.