Measurement of prompt photon production in $\sqrt{s_\mathrm{NN}} = 8.16$ TeV $p$+Pb collisions with ATLAS

TL;DR

This paper measures isolated prompt photon production in proton-lead collisions at 8.16 TeV using ATLAS, comparing results with QCD predictions and models of parton energy loss to improve understanding of nuclear parton distributions.

Contribution

It provides the first detailed measurement of prompt photon production in p+Pb collisions at this energy, constraining nuclear parton distribution functions and energy loss models.

Findings

Data disfavors large parton energy loss prior to scattering.

Results constrain nuclear parton distribution functions.

Photon production cross-sections agree with NLO QCD predictions without large energy loss.

Abstract

The inclusive production rates of isolated, prompt photons in $p$+Pb collisions at $\sqrt{s_\mathrm{NN}} = 8.16$ TeV are studied with the ATLAS detector at the Large Hadron Collider using a dataset with an integrated luminosity of 165 nb$^{-1}$ recorded in 2016. The cross-section and nuclear modification factor $R_{p\mathrm{Pb}}$ are measured as a function of photon transverse energy from 20 GeV to 550 GeV and in three nucleon-nucleon centre-of-mass pseudorapidity regions, (-2.83,-2.02), (-1.84,0.91), and (1.09,1.90). The cross-section and $R_{p\mathrm{Pb}}$ values are compared with the results of a next-to-leading-order perturbative QCD calculation, with and without nuclear parton distribution function modifications, and with expectations based on a model of the energy loss of partons prior to the hard scattering. The data disfavour a large amount of energy loss and provide new constraints on the parton densities in nuclei.

Equations

$$\frac{\mathrm{d}\sigma }{\mathrm{d}{E}_{\mathrm{T}}^{\gamma }}=\frac{1}{L_{\mathrm{int}}}\frac{1}{\Delta E_{\mathrm{T}}^{\gamma }}\frac{N_{\mathrm{sig}}{P}_{\mathrm{sig}}}{{ϵ}^{\mathrm{sel}}{ϵ}^{\mathrm{trig}}}{C}_{\mathrm{MC}},$$

$$R_{p\mathrm{Pb}}=(\mathrm{d}{\sigma }^{p+\mathrm{Pb}\to \gamma +X}/\mathrm{d}{E}_{\text{T}}^{\gamma })/(A\cdot \mathrm{d}{\sigma }^{pp\to \gamma +X}/\mathrm{d}{E}_{\text{T}}^{\gamma }),$$

Full text

\AtlasTitle

Measurement of prompt photon production in $\sqrt{s_{\mathrm{NN}}}=8.16$ TeV $p$+Pb collisions with ATLAS \AtlasAbstractThe inclusive production rates of isolated, prompt photons in $p$+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=8.16$ TeV are studied with the ATLAS detector at the Large Hadron Collider using a dataset with an integrated luminosity of $165$ nb*-1* recorded in 2016. The cross-section and nuclear modification factor $R_{p\mathrm{Pb}}$ are measured as a function of photon transverse energy from $20$ GeV to $550$ GeV and in three nucleon–nucleon centre-of-mass pseudorapidity regions, $(-2.83,-2.02)$, $(-1.84,0.91)$, and $(1.09,1.90)$. The cross-section and $R_{p\mathrm{Pb}}$ values are compared with the results of a next-to-leading-order perturbative QCD calculation, with and without nuclear parton distribution function modifications, and with expectations based on a model of the energy loss of partons prior to the hard scattering. The data disfavour a large amount of energy loss and provide new constraints on the parton densities in nuclei.

\PreprintIdNumberCERN-EP-2019-002 \arXivId1903.02209 \AtlasJournalRefPhys. Lett. B 796 (2019) 230 \AtlasDOI10.1016/j.physletb.2019.07.031

1 Introduction

Measurements of particle and jet production rates at large transverse energy are a fundamental method of characterising hard-scattering processes in all collision systems. In collisions involving large nuclei, production rates are modified from those measured in proton+proton ($pp$) collisions due to a combination of initial- and final-state effects. The former arise from the dynamics of partons in the nuclei prior to the hard-scattering process, while the latter are attributed to the strong interaction of the emerging partons with the hot nuclear medium formed in nucleus–nucleus collisions. Modification due to the nuclear environment is quantified by the nuclear modification factor, $R_{\mathrm{AA}}$, defined as the ratio of the cross-section measured in A+A to that in $pp$ collisions, scaled by the expected geometric difference between the systems.

Measurements of prompt photon production rates offer a way to isolate the initial-state effects because the final-state photons do not interact strongly. These initial-state effects include the degree to which parton densities are modified in a nuclear environment [1, 2, 3], as well as potential modification due to an energy loss arising through interactions of the partons traversing the nucleus prior to the hard scattering [4, 5]. Constraints on such initial-state effects are particularly important for characterising the observed modifications of strongly interacting final states, such as jet and hadron production [6, 7], since they are sensitive to effects from both initial- and final-state. Due to the significantly simpler underlying-event conditions in proton–nucleus collisions, measurements of photon rates can be performed with better control over systematic uncertainties than in nucleus–nucleus collisions, allowing a more precise constraint on these initial-state effects.

Prompt photon production has been extensively measured in $pp$ collisions at a variety of collision energies [8, 9, 10, 11, 12] at the Large Hadron Collider (LHC). It was also measured in lead–lead (Pb+Pb) collisions at a nucleon–nucleon centre-of-mass energy $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [13, 14] at the LHC, and in gold–gold collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV at the Relativistic Heavy Ion Collider (RHIC) [15], where the data from both colliders indicate that photon production rates are unaffected by the passage of the photons through the hot nuclear medium. At RHIC, photon production rates were measured in deuteron–gold collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV [16, 17] and were found to be in good agreement with perturbative QCD (pQCD) calculations. Additionally, jet production [18, 19] and electroweak boson production [20, 21, 22] were measured in $28$ nb*-1* of proton–lead ($p$+Pb) collision data at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV recorded at the LHC; the former is a strongly interacting final state, while the latter is not. All measurements provided some constraints on initial-state effects.

The data used in this measurement were collected with the ATLAS detector during the $p$+Pb collision running period in 2016, and correspond to an integrated luminosity of $165$ nb*-1*, approximately six times larger than the measurements made in the previous 5.02 TeV data. The proton and lead beams had an energy of $6.5$ TeV and $2.51$ TeV per nucleon respectively, resulting in a nucleon–nucleon centre-of-mass collision energy of $8.16$ TeV and a rapidity boost of this frame by $\pm 0.465$ units relative to the ATLAS laboratory frame, depending on the direction of the Pb beam.111ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the $z$-axis along the beam pipe. The $x$-axis points from the IP to the centre of the LHC ring, and the $y$-axis points upward. Cylindrical coordinates $(r,\phi)$ are used in the transverse plane, $\phi$ being the azimuthal angle around the $z$-axis. The pseudorapidity is defined in terms of the polar angle $\theta$ as $\eta=-\ln\tan(\theta/2)$ and the rapidity of the components of the beam, $y$, are defined in terms of their energy, $E$, and longitudinal momentum, $p_{z}$, as $y=0.5\ln\frac{E+p_{z}}{E-p_{z}}$. By convention, the results are reported as a function of photon pseudorapidity in the nucleon–nucleon collision frame, $\eta^{*}$, with positive $\eta^{*}$ corresponding to the proton beam direction, and negative $\eta^{*}$ corresponding to the Pb beam direction.

At leading order, the process $p+\mathrm{Pb}\to\gamma+X$ has contributions from direct processes, in which the photon is produced in the hard interaction, and from fragmentation processes, in which it is produced in the parton shower. Beyond leading order the direct and fragmentation components are not separable and only their sum is a physical observable.

To reduce contamination from the dominant background of photons mainly from light-meson decays in jets, the measurements presented here require the photons to be isolated from nearby particles. This requirement also acts to reduce the relative contribution of fragmentation photons in the measurement, and thus, the same fiducial requirement must be imposed on theoretical models when comparing with the data. Specifically, as in previous ATLAS measurements [9, 10], the sum of energy transverse to the beam axis within a cone of $\Delta{R}\equiv\sqrt{(\Delta\eta)^{2}+(\Delta\phi)^{2}}=0.4$ around the photon, $E_{\mathrm{T}}^{\mathrm{iso}}$, is required to be smaller than $4.8+4.2\times 10^{-3}E_{\mathrm{T}}^{\gamma}$ [GeV], where $E_{\mathrm{T}}^{\gamma}$ is the transverse energy of the photon. At particle level, $E_{\mathrm{T}}^{\mathrm{iso}}$ is calculated as the sum of transverse energy of all particles with a decay length above 10 mm, excluding muons and neutrinos. This sum is corrected for the ambient contribution from underlying-event particles, consistent with the previous measurements [9, 10].

This letter reports a measurement of the cross-section for prompt, isolated photons in $p$+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=8.16$ TeV. Photons are measured with $E_{\mathrm{T}}^{\gamma}>20$ GeV, the isolation requirement detailed above, and in three nucleon–nucleon centre-of-mass pseudorapidity ($\eta^{*}$) regions, $-2.83<\eta^{*}<-2.02$, $-1.84<\eta^{*}<0.91$, and $1.09<\eta^{*}<1.90$. In addition to the cross-section, the data are compared to a $pp$ reference cross-section derived from a previous measurement of prompt photon production in $pp$ collisions at $\sqrt{s}=8$ TeV that used the identical isolation condition  [9]. The nuclear modification factor $R_{p\mathrm{Pb}}$ is derived in each pseudorapidity region, using an extrapolation for the different collision energy and center-of-mass pseudorapidity selection, and is reported in the region $E_{\mathrm{T}}^{\gamma}>25$ GeVwhere reference data is available. Furthermore, the ratio of $R_{p\mathrm{Pb}}$ in the forward region to that in the backward region is presented. The measurements are compared with next-to-leading-order (NLO) pQCD predictions from Jetphox [23] using parton distribution functions (PDF) extracted from global analyses that include nuclear modification effects analyses [24, 25]. Additionally, the data are compared with predictions from a model including initial-state energy loss [4, 5, 26].

2 Experimental set-up

The ATLAS detector [27] is a multipurpose detector with a forward–backward symmetric cylindrical geometry. For this measurement, its relevant components include an inner tracking detector surrounded by a thin superconducting solenoid, and electromagnetic and hadronic calorimeters. The inner-detector system is immersed in a $2$ T axial magnetic field and provides charged-particle tracking in the pseudorapidity range $\left|\eta^{\mathrm{lab}}\right|<2.5$ in the laboratory frame. In order of closest to furthest from the beam pipe, it consists of a high-granularity silicon pixel detector, a silicon microstrip tracker, and a transition radiation tracker. Additionally, the new insertable B-layer [28] has been operating as the innermost layer of the tracking system since 2015. The calorimeter system covers the range $\left|\eta^{\mathrm{lab}}\right|<4.9$. In the region $\left|\eta^{\mathrm{lab}}\right|<3.2$, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) sampling calorimeters. An additional thin LAr presampler covers $\left|\eta^{\mathrm{lab}}\right|<1.8$ to correct for energy loss in material before the calorimeters. The LAr calorimeters are divided into three layers in radial depth. Hadronic calorimetry is provided by a steel/scintillator-tile calorimeter, segmented into three barrel structures within $\left|\eta^{\mathrm{lab}}\right|<1.7$, and two copper/LAr hadronic endcap calorimeters, which cover the region $1.5<\left|\eta^{\mathrm{lab}}\right|<3.2$. Finally, the forward calorimeter covers $3.2<\left|\eta^{\mathrm{lab}}\right|<4.9$ and is divided into three compartments. The first compartment is a copper/LAr electromagnetic calorimeter, while the remaining two tungsten/LAr calorimeter compartments collect the hadronic energy.

During data-taking, events were initially selected using a level-1 trigger, implemented in custom electronics, based on energy deposition in the electromagnetic calorimeter. The high-level trigger [29] was then used to select events consistent with a high-$E_{\mathrm{T}}^{\gamma}$ photon candidate. The high level trigger was configured with five online $E_{\mathrm{T}}^{\gamma}$ thresholds from $15$ GeV to $35$ GeV. Each trigger is used for an exclusive region of the $E_{\mathrm{T}}^{\gamma}$ spectrum, starting 5 GeV above the trigger threshold because there the trigger is fully efficient. The highest-threshold trigger is used in the measurement over the whole $E_{\mathrm{T}}^{\gamma}$ range above 40 GeV and is unprescaled. The lower-threshold, prescaled, triggers are used to perform the measurement for $E_{\mathrm{T}}^{\gamma}$ in the range of $20-40$ GeV.

Data-taking was divided into two periods with different configurations of the LHC beams. In the first period, the lead ions circulated in beam 1 (clockwise) and protons circulated in beam 2, while in the second period the beams were reversed. These periods corresponded to integrated luminosities of $57$ nb*-1* and $108$ nb*-1* respectively.

3 Photon reconstruction and identification

Photons are reconstructed following a procedure used extensively in previous ATLAS measurements [10], of which only the main features are summarised here.

Photon candidates are reconstructed from clusters of energy deposited in the electromagnetic calorimeter in three regions corresponding to the laboratory-frame ($\eta^{\mathrm{lab}}$) positions of the barrel and forward and backward endcaps $\left|\eta^{\mathrm{lab}}\right|<2.37$. The transition region between the barrel and endcap calorimeters, $1.37<\left|\eta^{\mathrm{lab}}\right|<1.56$, is excluded due to its higher level of inactive material. The measurement of the photon energy is based on the energy collected in calorimeter cells in an area of size $\Delta\eta\times\Delta\phi=0.075\times 0.175$ in the barrel and $\Delta\eta\times\Delta\phi=0.125\times 0.125$ in the endcaps. It is corrected via a dedicated energy calibration [30] which accounts for losses in the material before the calorimeter, both lateral and longitudinal leakage, and for variation of the sampling-fraction with energy and shower depth.

The photons are identified using the tight calorimeter shower shape requirements described in Ref. [31]. The tight requirements select clusters which are compatible with originating from a single photon impacting the calorimeter. The information used includes that from the hadronic calorimeter, the lateral shower shape in the second layer of the electromagnetic calorimeter, and the detailed shower shape in the finely segmented first layer.

The isolation transverse energy, $E_{\mathrm{T}}^{\mathrm{iso}}$, is computed from the sum of $E_{\mathrm{T}}$ values in topological clusters of calorimeter cells [32] inside a cone of size $\Delta R=0.4$ centred on the photon. This cone size is chosen to be compatible with a previous measurement of photon production in $pp$ collisions at $\sqrt{s}=8$ TeV [9], which is used to construct the reference spectrum for the $R_{p\mathrm{Pb}}$ measurement. This estimate excludes an area of $\Delta\eta\times\Delta\phi=0.125\times 0.175$ centred on the photon, and is corrected for the expected leakage of the photon energy from this region into the isolation cone.

4 Simulated event samples

Samples of Monte Carlo (MC) simulated events were generated to study the detector performance for signal photons. Proton–proton generators were used as the source of events containing photons. To include the effects of the $p$+Pb underlying-event environment, these simulated $pp$ events were combined with $p$+Pb events from data before reconstruction. In this way, the simulated events contain the effects of the $p$+Pb underlying-event identical to those observed in data.

The Pythia 8.186 [33] generator was used to generate the nominal set of MC events, with the NNPDF23LO parton distribution function (PDF) set [34] and a set of generator parameters tuned to reproduce minimum-bias $pp$ events with the same collision energy as that in the $p$+Pb data (“A14” tune) [35]. A centre-of-mass boost was applied to the generated events to bring them into the same laboratory frame as the data. The generator simulates the direct photon contribution and, through final-state QED radiation in $2\to 2$ QCD processes, also includes the fragmentation photon contributions; these components are defined to be signal photons. Events were generated in six exclusive $E_{\mathrm{T}}^{\gamma}$ ranges from 17 GeV to 500 GeV.

An additional MC sample was used to assess the sensitivity of the measurement to this choice of generator. The Sherpa 2.2.4 [36] event generator produces fragmentation photons in a different way from Pythia and was thus chosen for the comparison. The NNPDF3.0NNLO PDF set [37] was used, and the events were generated in the same kinematic regions as the Pythia events. These events were generated with leading-order matrix elements for photon-plus-jet final states with up to three additional partons, which were merged with the Sherpa parton shower. The Sherpa sample produced results consistent with Pythia, and, thus, no correction or uncertainty is applied.

The Pythia and Sherpa $pp$ events were passed through a full Geant4 simulation of the ATLAS detector [38, 39]. To model the underlying event effects, each simulated event was combined with a minimum-bias $p$+Pb data event and the two were reconstructed together as a single event, using the same algorithms as used for the data. These events were split between the two beam configurations in a proportion matched to that in data-taking. The underlying event activity levels, as characterized by the sum of the transverse energy in the outgoing-Pb-beam side of the forward calorimeter (3.1 < $|\eta^{\mathrm{lab}}|$ < 4.9), are different in the photon-containing data events from the minimum-bias data events used in the simulation. Thus, the simulated events were weighted on a per-event basis to match the underlying event activity distribution in data. Furthermore, the photon shower shapes and identification efficiency in simulation were adjusted for small differences previously observed between these quantities in data and in Geant4 simulation [31].

5 Data analysis

The differential cross-section is calculated for each $E_{\mathrm{T}}^{\gamma}$ and $\eta^{*}$ bin as

[TABLE]

where $L_{\mathrm{int}}$ is the integrated luminosity, $\Delta E_{\mathrm{T}}^{\gamma}$ is the width of the $E_{\mathrm{T}}^{\gamma}$ bin, $N_{\mathrm{sig}}$ is the yield of photon candidates passing identification and isolation requirements, $P_{\mathrm{sig}}$ is the purity of the signal selection, $\epsilon^{\mathrm{sel}}$ is the combined reconstruction, identification and isolation efficiency for signal photons, $\epsilon^{\mathrm{trig}}$ is the trigger efficiency, and $C_{\mathrm{MC}}$ is a MC derived bin-by-bin correction for the change in the $E_{\mathrm{T}}^{\gamma}$ spectrum from photons migrating between bins in the spectrum due to the width in the energy response. $C_{\mathrm{MC}}$ is determined after all selection criteria at both reconstruction and particle levels are imposed.

Trigger efficiencies $\epsilon^{\mathrm{trig}}$ are studied using events selected with minimum-bias triggers, level-1 triggers without additional requirements, and photon high-level triggers without identification requirements. They are greater than 99.5% for all triggers [29]. In this analysis they are taken as $\epsilon^{\mathrm{trig}}=1$, and any uncertainty is neglected as being sub-dominant to other uncertainties.

The purity $P_{\mathrm{sig}}$ is determined via a double-sideband procedure used extensively in previous measurements of cross-sections for processes with a photon in the final state [9, 10, 40, 41] and summarised here. In the procedure, four regions are defined which categorise photon candidates along two axes: (1) isolation, corresponding to an isolated and an inverted “non-isolated” selection; (2) identification, corresponding to photons that pass the tight identification requirements described in Ref. [31], and those that pass the loose requirements of Ref. [31] but fail certain components of the tight requirements, designed to mostly select background. The majority of signal photons are in the tight, isolated region, defined to be the signal region, while the other three regions are dominated by the background. Photon candidates that comprise the background are assumed to be distributed in a way that is uncorrelated along the two axes. The yields in the three non-signal sidebands are used to estimate the yield of background in the signal region and is combined with the yield in the signal region to extract the purity. The procedure also accounts for the small fraction of signal photons which are reconstructed in the non-signal sidebands; these quantities, known as leakage fractions, are determined from the simulation samples described in Section 4. The purity is typically 45% at $E_{\mathrm{T}}^{\gamma}=20$ GeV, rises to 80% at $E_{\mathrm{T}}^{\gamma}=100$ GeV and reaches 99% at $E_{\mathrm{T}}^{\gamma}=300$ GeV.

Figure 1 shows example $E_{\mathrm{T}}^{\mathrm{iso}}$ distributions for identified and isolated photons, the corresponding distributions for background photons with the normalisation determined by the double-sideband method, and the resulting signal-photon distributions after background subtraction, compared with those for generator-level photons in MC simulation. The figure shows the shape of the background distribution within the signal region, and the correspondence between the background-subtracted data and the signal-only Pythia 8 distributions gives confidence that the simulations accurately represent the data.

The photon selection efficiency is determined from MC simulations. Generated prompt photons are required to be isolated at the generator level, after an estimate of the underlying event has been subtracted from the isolation energy, as described above. Reconstruction efficiency is determined by requiring a photon to have been reconstructed within $\Delta R=0.2$ of the generated photon. Reconstructed photons matching to a generated photon are further required to satisfy tight identification and isolation criteria defined in Section 1. The combined efficiency of signal photons to pass all reconstruction level selections, $\epsilon^{\mathrm{sel}}$, is typically $90$% at all $E_{\mathrm{T}}^{\gamma}$ and $\eta^{*}$, except at $E_{\mathrm{T}}^{\gamma}\approx 20$ GeV where it decreases to about $80$%. Figure 2 summarises the different components of the total selection efficiency. The reconstruction efficiency is 96–99% everywhere, with the lowest values at the lowest $E_{\mathrm{T}}^{\gamma}$. The isolation efficiency is lowest at high $E_{\mathrm{T}}^{\gamma}$, most likely because the associated products of fragmentation photons are, on average, more energetic and collimated when the energy of the photon is higher. The largest inefficiency is due to the identification requirements. This identification efficiency is lowest at 20 GeV and increases with $E_{\mathrm{T}}^{\gamma}$ as higher-energy photons create larger and more identifiable showers in the calorimeter. It peaks around 100 GeV, and decreases with increasing $E_{\mathrm{T}}^{\gamma}$ due to the difficulty of separating conversion electrons at high energy.

In MC events, the $E_{\mathrm{T}}$ response for prompt, isolated photons, defined as the ratio of the reconstructed to generator $E_{\mathrm{T}}$, is found to be within 1% of unity, with a resolution that decreases from $3$% to $2$% over the $E_{\mathrm{T}}^{\gamma}$ range of the measurement. The bin migration correction factors $C_{\mathrm{MC}}$ are determined using the event simulations described in Section 4. They are defined as the bin-by-bin ratio $C_{\mathrm{MC}}=N_{\mathrm{MC}}^{\mathrm{part}}/N_{\mathrm{MC}}^{\mathrm{reco}}$ of the reconstructed, identified, and isolated photon $E_{\mathrm{T}}^{\gamma}$ spectrum, where $N_{\mathrm{MC}}^{\mathrm{part}}$ is the number in a given $E_{\mathrm{T}}^{\gamma}$ bin at the particle level and $N_{\mathrm{MC}}^{\mathrm{reco}}$ is the number in the corresponding bin at the reconstruction level.

The nuclear modification factor $R_{p\mathrm{Pb}}$ can be expressed as a ratio of cross-sections in the following way:

[TABLE]

where the geometric factor $A$ is simply the number of nucleons in the Pb nucleus, 208. The reference $pp$ spectrum is constructed using measurements of $\sqrt{s}=8$ TeV $pp$ data by ATLAS [9] that use the same particle-level isolation requirement. The 8 TeV measurements in the regions $|\eta^{\mathrm{lab}}|<1.37$ and $1.56<|\eta^{\mathrm{lab}}|<2.37$ are used as the reference spectra for the central and the forward and backward rapidity data, after applying a multiplicative correction for the effects of the boost in the 8.16 TeV $p$+Pb system. For each kinematic region, extrapolation factors are determined as the ratio of photon cross sections from Jetphox calculations for $pp$ collisions. The numerator has $\sqrt{s}=8.16$ TeV with a boost of the centre-of-mass corresponding to the $p$+Pb system, and the denominator has energy $\sqrt{s}=8$ TeV with its rest frame corresponding with that of the laboratory reference frame. That is, the cross-sections in the numerator and denominator use the same $\eta^{\mathrm{lab}}$ regions, although in the former case this corresponds to a different center-of-mass pseudorapidity. These factors are shown in Figure 3 and are applied as multiplicative factors to the measured $8$ TeV data. They are dominated by the effect from the boost of the $p$+Pb system, as the effect due to the difference in collision energy alone is less than $1$% for all $E_{\mathrm{T}}^{\gamma}$. For $-1.84<\eta^{*}<0.91$, or $E_{\mathrm{T}}^{\gamma}<100$ GeV at large rapidities, the factors are typically within a few percent of unity. However, at large $E_{\mathrm{T}}^{\gamma}$, where the rapidity distribution becomes steeper, the extrapolation factors become more sensitive to the rapidity shift from the centre-of-mass boost between the frames, and at large pseudorapidity they reach a factor of $2$–$3$. An alternative set of factors, derived from the generator-level predictions of Pythia 8, are also shown in Figure 3; these are used to assess the sensitivity of the extrapolation factors to the rapidity and $E_{\mathrm{T}}^{\gamma}$ dependence of the model cross sections.

6 Systematic uncertainties

The sources of systematic uncertainties affecting the measurement are described in this section, which is broken into two parts discussing the uncertainty in 1) the cross-section and 2) the nuclear modification factor $R_{p\mathrm{Pb}}$, including its ratio between forward and backward pseudorapidity regions.

6.1 Cross-section uncertainty

The major uncertainties in the cross-section can be divided into two main categories: those affecting the purity determination, which are dominant at low $E_{\mathrm{T}}^{\gamma}$ where the sample purity is low, and those affecting the detector performance corrections, which are dominant at high $E_{\mathrm{T}}^{\gamma}$. All other sources tend to be weakly dependent on $E_{\mathrm{T}}^{\gamma}$. A summary is shown in Figure 4. In each category, the uncertainty is the sum in quadrature of the individual components; the combined uncertainty is the sum in quadrature of all contributions, excluding those associated with the luminosity. The total uncertainties range from 15% at low and high $E_{\mathrm{T}}^{\gamma}$, where they are dominated by the purity and detector performance uncertainties respectively, to a minimum of approximately $6$% at $E_{\mathrm{T}}^{\gamma}\approx 100$ GeV, where both of these uncertainties are modest.

To assess the uncertainty in the purity determination, each boundary defining the sidebands used in the calculation is varied independently in order to understand the sensitivity of the measurement to the double sideband binning and correlation assumptions. The dominant uncertainty arises from uncertainty in the level of sideband correlation. This is estimated directly from data by dividing the non-isolated region in two subregions and calculating the ratio of identified to background-enhanced yields in each subregion. These ratios differ at the level of 10% which agrees with estimates from previous studies [10]. This $\pm 10\%$ variation in the sideband correlation yields a 13% uncertainty in the cross-section in the lowest $E_{\mathrm{T}}^{\gamma}$ range, decreasing to less than $1$% for $E_{\mathrm{T}}^{\gamma}>100$ GeV. The inverted photon identification requirement for the background candidates is varied to be less or more restrictive about which shower shapes the background candidates are required to fail. This variation yields an uncertainty that is less than $1$% for all $E_{\mathrm{T}}^{\gamma}$ in the forward and backward rapidity bins, but is significant at mid-rapidity ($-1.84<\eta^{*}<0.91$) where it is 9% in the lowest $E_{\mathrm{T}}^{\gamma}$ bin and decreases to be less than $1$% for $E_{\mathrm{T}}^{\gamma}>100$ GeV. Variations in the isolation energy threshold of $\pm 1$ GeV have been shown to cover any difference between simulations and data [10]. These variations result in a 1–2% effect on the cross-section in the lowest $E_{\mathrm{T}}^{\gamma}$ range and less than $1$% at higher $E_{\mathrm{T}}^{\gamma}$. The uncertainty associated with the inverted shower-shape was smoothed and symmetrised, however, the other uncertainties are derived asymmetrically from the positive and negative variations separately.

Uncertainties associated with detector performance corrections are dominant at high $E_{\mathrm{T}}^{\gamma}$. A detailed description of the several components of the photon energy scale and resolution uncertainties are given in Ref. [10]. The impact of these on the measurement is determined by varying the reconstructed photon $E_{\mathrm{T}}^{\gamma}$ in simulation within the energy scale uncertainties and deriving alternative correction factors for positive and negative variations separately. Of these, the impact of the energy scale variation is dominant, giving a 10–15% contribution at 500 GeV in the forward and backward regions, decreasing to less than $2$% at the lowest $E_{\mathrm{T}}^{\gamma}$. In the mid-rapidity region, the energy scale variation gives a 5% uncertainty at high $E_{\mathrm{T}}^{\gamma}$, decreasing to less than $1$% at low $E_{\mathrm{T}}^{\gamma}$. Additionally, there are uncertainties associated with corrections for small differences in reconstruction, identification and isolation efficiencies observed between data and simulation [31]. These uncertainties are about 5% in the forward regions and low $E_{\mathrm{T}}^{\gamma}$ and less than $2$% elsewhere.

Systematic uncertainties related to modelling in simulation, luminosity, electron contamination, and other sources tend to be lower than those previously discussed. However, their combined effect is dominant in the mid-rapidity region and between 90 GeV and 250 GeV. To test the sensitivity of the measurement to the difference of isolation energy between particle-level and detector level in the simulation, the generator-level isolation definition is changed to better correspond to the reconstruction-level definition. The relative change in the cross-section after this deviation from the nominal is about 2% at low $E_{\mathrm{T}}^{\gamma}$, decreasing to about 1% at high $E_{\mathrm{T}}^{\gamma}$, for each pseudorapidity region, and is taken as a symmetric uncertainty. An uncertainty is assigned to cover the possible contribution of misreconstructed electrons, primarily from the decays of $W^{\pm}$ and $Z$ bosons, to the selected photon yield. Based on simulation studies, and the results of previous measurements [9, 10], this is assigned to be 1.3% for $E_{\mathrm{T}}^{\gamma}<105$ GeV in forward pseudorapidity regions, and 0.5% everywhere else. To test the beam orientation dependence, the cross-section is measured using the data from each beam configuration separately. The two measurements agree at the level of 1%, well above the statistical uncertainty for most $E_{\mathrm{T}}^{\gamma}$ bins. This difference is taken as a global, symmetric uncertainty in the combined results. To test the sensitivity to the relative fractions of direct and fragmentation photons in the MC samples, the simulation is weighted such that the fraction of direct photons is unity, that is, all photons in the sample are direct. This reflects a conservative difference compared with the default estimate of this fraction of about $50-80$% from the MC samples. This variation gives a relative change in the cross-section of approximately 1% for all kinematic regions, which is taken as a systematic uncertainty. The uncertainty in the integrated luminosity of the combined data sample is $2.4$% It is derived, following a methodology similar to that detailed in Ref. [42], and using the LUCID-2 detector for the baseline luminosity measurements [43], from calibration of the luminosity scale using x-y beam-separation scans.

6.2 $R_{p\mathrm{Pb}}$ uncertainty

The nuclear modification factor $R_{p\mathrm{Pb}}$ is affected by systematic uncertainties associated with the $p$+Pb and $pp$ measurements. The uncertainties in the differential cross-section of the $pp$ reference data are obtained directly from Ref. [9]. Due to differences in photon reconstruction, energy calibration, isolation and identification procedures between the $pp$ and $p$+Pb datasets, the uncertainties are treated as uncorrelated and added in quadrature.

The uncertainty in the extrapolation of the $pp$ $E_{\mathrm{T}}^{\gamma}$ spectrum at $8$ TeV is determined by using an alternative method to derive the multiplicative extrapolation factors. Instead of Jetphox, photon cross-sections for the $8$ TeV and rapidity-boosted $\sqrt{s}=8.16$ TeV kinematics are determined from Pythia 8. The extrapolation factors from both Jetphox and Pythia 8 are shown in Figure 3. Additionally, Jetphox is run with an alternative PDF set to quantify the impact of a given PDF choice. The differences between the extrapolation factors from these two variations, which are at most a few percent in the kinematic region of the measurement and subdominant with respect to the other uncertainties in the cross-sections, are added in quadrature and used as an estimate of the uncertainty in the extrapolation procedure.

For the measurement of the ratio of $R_{p\mathrm{Pb}}$ values (Eq. (1)) between the forward and backward pseudorapidity regions, each systematic variation affecting the purity and detector performance corrections is applied to the numerator and denominator in a coherent way, allowing them to partially cancel out in the ratio. All uncertainties in the other categories, except those from electron contamination and the beam direction difference, are treated as correlated. For this reason, they cancel out; notably the $p$+Pb luminosity and $pp$ cross-section uncertainties cancel out completely. The extrapolation uncertainties are treated as independent and are added in quadrature to the other uncertainties in $R_{p{\mathrm{P}b}}$.

The resulting uncertainty ranges from about 5% at the lowest $E_{\mathrm{T}}^{\gamma}$, where it is dominated by the uncertainty in the purity, to about 3% at mid-$E_{\mathrm{T}}^{\gamma}$, and again about 5% at high $E_{\mathrm{T}}^{\gamma}$, where it is dominated by uncertainty in the energy scale. A summary of the uncertainties in the forward-to-backward ratio is shown in Figure 5.

7 Results

Photon production cross-sections are shown in Figure 6 for photons with $E_{\mathrm{T}}^{\gamma}>20$ GeV in three pseudorapidity regions. The measured $\mathrm{d}\sigma/\mathrm{d}E_{\mathrm{T}}^{\gamma}$ values decrease by five orders of magnitude over the complete $E_{\mathrm{T}}^{\gamma}$ range, which extends out to $E_{\mathrm{T}}^{\gamma}\approx 500$ GeV for photons at mid-rapidity. In Pythia 8, photons in this range typically arise from parton configurations in which the parton in the nucleus has Bjorken scale variable, $x_{\mathrm{A}}$, in the range $3\times 10^{-3}\lesssim x_{\mathrm{A}}\lesssim 4\times 10^{-1}$. In the nuclear modified PDF (nPDF) picture, this range probes the so-called shadowing (suppression for $x_{\mathrm{A}}\lesssim 0.1$), anti-shadowing (enhancement for $0.1\lesssim x_{\mathrm{A}}\lesssim 0.3$), and EMC (suppression for $0.3\lesssim x_{\mathrm{A}}\lesssim 0.7$) regions [24].

The data are compared with an NLO pQCD calculation similar to that used in Ref. [3], where the data is similarly underestimated at low ET, but using the updated CT14 [44] PDF set for the free-nucleon parton densities. Jetphox [23] is used to perform a full NLO pQCD calculation of the direct and fragmentation contributions to the cross-section. The BFG set II [45] of parton-to-photon fragmentation functions are used, the number of massless quark flavours is set to five, and the renormalisation, factorisation and fragmentation scales are chosen to be $E_{\text{T}}^{\gamma}$. In addition to the calculation with the free-nucleon PDFs, separate calculations are performed with the EPPS16 [24] and nCTEQ15 [25] nPDF sets. The EPPS16 calculation uses the same free-proton PDF set, CT14, as the free-nucleon baseline to which the modifications are applied. The prediction is systematically lower than the data by up to 20% at low $E_{\mathrm{T}}^{\gamma}$ but is closer to the data at higher $E_{\mathrm{T}}^{\gamma}$, consistent with the results of such comparisons in $pp$ collisions at LHC energies [9, 10]. A recent calculation of isolated photon production at NNLO found that the predicted cross-sections were systematically larger at low $E_{\mathrm{T}}^{\gamma}$ than the NLO prediction [46], and thus may provide a better description of the data in this and previous measurements.

Uncertainties associated with these calculations are assessed in a number of ways. Factorisation, renormalisation, and fragmentation scales are varied, up and down, by a factor of two as in Ref [9]. The uncertainty is taken as the envelope formed by the minimum and maximum of each variation in every kinematic region and is dominant in most regions. PDF uncertainties are calculated via the standard CT14 error sets and correspond to a 68% confidence interval. Again following Ref [9] the sensitivity to the choice of $\alpha_{\text{S}}$ is evaluated by varying $\alpha_{\text{S}}$ by $\pm 0.002$ around the central value of 0.118 in the calculation and PDF. Uncertainties from nPDFs are calculated from the error sets which correspond to 90% confidence intervals, as described in Ref. [24]. These are converted into uncertainty bands which correspond to a 68% confidence interval. A summary of each variation is shown in Figure 7.

Figure 8 shows the nuclear modification factor $R_{p\mathrm{Pb}}$ as a function of $E_{\mathrm{T}}^{\gamma}$ in different $\eta^{*}$ regions. At forward rapidities ($1.09<\eta^{*}<1.90$), the $R_{p\mathrm{Pb}}$ value is consistent with unity, indicating that nuclear effects are small. In Pythia 8, photons in this region typically arise from configurations with gluon partons from the Pb nucleus with $x_{\mathrm{A}}\approx 10^{-2}$. Nuclear modification pulls the pQCD calculation down slightly for $E_{\mathrm{T}}^{\gamma}<100$ GeV, above which the modification reverses, indicating a crossover between shadowing and anti-shadowing regions. At mid-rapidity, nuclear effects are similarly small and consistent with unity at low $E_{\mathrm{T}}^{\gamma}$, but at higher $E_{\mathrm{T}}^{\gamma}$, there is a hint that $R_{p\mathrm{Pb}}$ is lower. This feature primarily reflects the different up- and down-quark composition of the nucleus relative to the proton and is more important at larger parton $x$. In this case, the larger relative down-quark density decreases the photon yield. This effect is evident in the Jetphox theory curve in blue dash-dotted line, which includes the proton–neutron asymmetry and the free-nucleon PDF set CT14. This effect is most pronounced at backward pseudorapidity where, in Pythia 8, the nuclear parton composition is typically a quark with $x_{\mathrm{A}}\approx 0.2$. Here, nPDF modification moves $R_{p\mathrm{Pb}}$ above the free-nucleon PDF calculation at low $E_{\mathrm{T}}^{\gamma}$ but below at high $E_{\mathrm{T}}^{\gamma}$, indicating the crossover from the anti-shadowing to the EMC region.

The $R_{p\mathrm{Pb}}$ calculations including nPDFs consider only the nPDF uncertainty, since previous calculations have shown that the scale and PDF uncertainties cancel out almost completely in the kinematic region of the measurement [3], and no non-perturbative corrections are applied. Within the present uncertainties, the data are consistent with both the free-proton PDFs and with the small effects expected from a nuclear modification of the parton densities.

The $R_{p\mathrm{Pb}}$ measurements are also compared with an initial-state energy-loss prediction that is calculated within the framework described in Refs. [4, 5, 26]. In this model, the energetic partons undergo multiple scattering in the cold nuclear medium, and thus lose energy due to this medium-induced gluon bremsstrahlung, before the hard collision. The calculation is performed with a parton–gluon momentum transfer $\mu=0.35$ GeV and mean free path for quarks $\lambda_{q}=1.5$ fm. Alternative calculations with a shorter path length ($\lambda_{q}=1$ fm), and a control version with no initial-state energy loss, are also considered. The data disfavour a large suppression of the cross-section from initial-state energy-loss effects.

The ratio of the $R_{p\mathrm{Pb}}$ values between forward and backward pseudorapidity, shown in Figure 9, is studied as a way to reduce the effect of common systematic uncertainties and better isolate the magnitude of nuclear effects [47]. The remaining systematic uncertainty, discussed in Sec. 6.2, is dominated by the reference extrapolation and treated as uncorrelated between points. Below $E_{\mathrm{T}}^{\gamma}\approx 100$ GeV, this corresponds roughly to the ratio of $R_{p\mathrm{Pb}}$ from photons from gluon nuclear parton configurations in the shadowing $x_{\mathrm{A}}$ region to that from quark partons in the anti-shadowing region. This can be seen in the top two panels of Figure 9, where the nuclear modification (red/purple bands) brings the Jetphox calculation below that of the free-nucleon PDF (blue curve), though the effect from EPPS16 is less significant. In contrast, the behaviour is reversed at higher $E_{\mathrm{T}}^{\gamma}$ where the numerator probes the shadowing/anti-shadowing crossover region and the denominator moves deeper into the EMC region [24]. The data are consistent with the pQCD calculation before incorporating nuclear effects, except possibly in the region $E_{\mathrm{T}}^{\gamma}<55$ GeV, which is sensitive to the effects from gluon shadowing. At low $E_{\mathrm{T}}^{\gamma}$, the data are systematically higher than the calculations which incorporate nPDF effects, but approximately within their theoretical uncertainty. Additionally, in the lower plot of Figure 9, the forward-to-backward ratios are compared with predictions from a model incorporating initial-state energy loss. The data show a preference for no or only a limited amount of energy loss.

8 Conclusion

This letter presents a measurement of the inclusive prompt, isolated photon cross-section in $p$+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=8.16$ TeV, using a dataset corresponding to an integrated luminosity of $165$ nb*-1* recorded by the ATLAS experiment at the LHC. The differential cross-section as a function of the photon transverse energy is reported in three pseudorapidity regions in the nucleon–nucleon collision frame, and covers photon transverse energies from 20 GeV to 550 GeV. The data are compared with a next-to-leading-order calculation which incorporates nuclear PDF effects. A measurement of the nuclear modification factor is reported in the region above 25 GeV using a NLO pQCD-based extrapolation of previously published $pp$ data at $\sqrt{s}=8$ TeV. The data are compatible with the expectation that the PDFs are modestly modified in nuclei in this kinematic region and may help to place an upper limit on the possible amount of energy lost by partons in the initial stages of nuclear collisions.

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 acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, CRC and Compute Canada, Canada; COST, ERC, ERDF, Horizon 2020, and Marie Skłodowska-Curie Actions, European Union; Investissements d’ Avenir Labex and Idex, ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya, Spain; The Royal Society and Leverhulme Trust, United Kingdom.

The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, 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), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [48].