Measurement of forward photon production cross-section in proton-proton collisions at $\sqrt{s}$ = 13 TeV with the LHCf detector

In this paper, we report the production cross-section of forward photons in the pseudorapidity regions of $\eta\,>\,10.94$ and $8.99\,>\,\eta\,>\,8.81$, measured by the LHCf experiment with proton--proton collisions at $\sqrt{s}$ = 13 TeV. The results from the analysis of 0.191 $\mathrm{nb^{-1}}$ of data obtained in June 2015 are compared to the predictions of several hadronic interaction models that are used in air-shower simulations for ultra-high-energy cosmic rays. Although none of the models agree perfectly with the data, EPOS-LHC shows the best agreement with the experimental data among the models.


Introduction
Hadronic interaction models play an important role in ultra-high energy cosmic-ray (UHECR) observations. They are used in Monte Carlo (MC) simulations of air-shower developments induced by UHECRs, which are one of the key tools used for reconstructing information about primary cosmic rays from observables measured by ground-based detectors. Currently, the Pierre Auger Observatory [1] and Telescope Array [2] are taking data for UHECRs. Although the experiments have published the results of the measured observables which are sensitive to the chemical composition of UHECRs, they have not yet reached any clear conclusions, because of the uncertainty related to the choice of hadronic interaction model [3,4,5]. Since it began operation in 2009, the Large Hadron Collider (LHC), the world's largest hadron collider, has provided unique opportunities for testing hadronic interaction models with collision energies exceeding 10 15 eV in a fixed target frame ( [6] for review of early results).
The major models used in air-shower simulations for UHECRs were re-tuned and updated by taking into account several experimental results obtained from proton-proton collisions with center-of-momentum collision energies of 0.9 and 7 TeV. These models, QGSJET II-04 [7], EPOS-LHC [8], and SIBYLL 2.3 [9], are called the post-LHC models. However, even with these post-LHC models, inconsistencies between the observed data and MC simulations were reported [10].
The LHC forward (LHCf) experiment [11], one of the LHC experiments designed to test hadronic interaction models, was running during the early phase of the LHC operation with proton-proton collisions at √ s = 13 TeV in 2015.
In this paper, we report the results of photon analyses performed on the taken data. The production cross-section of photons, of which 90% are decay products of π 0 mesons produced in collisions, is analyzed in two pseudorapidity ranges.
The results of the photon analyses for the lower-energy collisions of √ s = 0.9 and 7 TeV have been published in Ref. [12,13]. Because of a collision energy nearly a factor of two higher than 7 TeV, the collision energy in the fixed target frame, 0.9 × 10 17 eV, was about a factor of four higher and the coverage of the transverse momentum p T of the measurement was a factor of two wider than that at √ s = 7 TeV.
The LHCf possesses two sampling and imaging calorimeter detectors which are installed on both sides of the LHC interaction point IP1 [14]. towers cover a pseudorapidity (η) range above 10, including the zero-degree collision angle. The larger towers are located above the smaller towers oriented 0 • (Arm1) and 45 • (Arm2) in the clockwise direction from the vertical. They cover the slightly off-center region where 8.5 < η < 9.5. Before operation in 2015, the detectors were upgraded to improve their radiation hardness by replacing the plastic scintillators with Gd 2 SiO 5 (GSO) scintillators [15]. Four pairs of X-Y scintillating-fibre hodoscopes used in the Arm1 imaging sensor were also replaced with X-Y GSO bar-bundle hodoscopes [16]. In addition, four X-Y pairs of silicon detectors inserted in the Arm2 detector were upgraded to optimise the linearity. The performance of the upgraded detectors was studied in two beam tests at CERN-SPS before and after operation at the LHC. We confirmed that the energy and position resolutions for electromagnetic showers were better than the requirements of < 5% and < 200 µm, respectively [17].
In this paper, we present the forward photon production cross-section in two regions of photon pseudorapidity (η > 10.94 and 8.81 < η < 8.99) measured by the LHCf detectors. All photons with energies above 200 GeV produced directly in collisions or from subsequent decays of directly produced short-lifetime particles (i.e. particles with c · τ < 1 cm, where c is the speed of light and τ is the mean lifetime of the particle) are considered.

Data
The experimental data used in this analysis were obtained by a dedicated

MC Simulation
A full MC simulation was performed to obtain some parameters and correction factors used in this analysis and to validate the analysis method. The simulation consisted of the following three parts: 1) event generation of p-p inelastic collisions at IP1; 2) particle transportation from IP1 to the front of the detector; and 3) detector response. All three parts were implemented with MC simulation packages Cosmos 7.633 [19] and EPICS 9.15 [20]. In the first part of the simulation, either QGSJET II-04 or EPOS-LHC was used as an event generator and the DPMJET 3.04 [21] model was used as a hadronic interaction model in the detector simulation of the third part. We generated 10 8 inelastic collisions with the QGJSET II-04 model. The dataset was used as a template sample for particle identification (PID) correction and a training sample for the unfolding method described in Sec. 4.2. Another full MC simulation dataset of 5 × 10 7 inelastic collisions was generated with EPOS-LHC and used to validate the analysis method and estimate systematic uncertainties.
In addition, we generated 10 8 events of inelastic p-p collisions with each hadronic interaction model, EPOS-LHC, QGSJET II-04, DPMJET 3.06, SIBYLL 2.3, and PYTHIA 8.212 [22], using either the PYTHIA dedicated generator or CRMC 1.6.0, an interface tool of event generators [23]. The decay of shortlifetime particles with c · τ less than 1 cm was treated in these generators.
These event sets were used only in Sec. 6 to compare the photon production cross-section of the data and model predictions. The total inelastic cross-section predicted by each model was used to express the results as the differential crosssection (dσ/dE). The cross-sections used for each model are listed in Table 1.

Event Reconstruction
In this analysis, we used an event reconstruction algorithm resembling that employed in Ref. [13,24]. The detector upgrades warranted a revaluation of the calibration parameters by beam tests [16,17]. Then, the criteria in this analysis were re-optimised by MC simulation studies. We selected the events that met the criteria of PID for photons and the rejection of multi-hit events in which two or more particles hit a calorimeter tower.
The reconstructed energy of each event was rescaled by the factor obtained from a study of π 0 events, in which photon pairs were detected by the two calorimeter towers of each detector. The invariant mass of a photon pair was calculated using both the measured photon energies and hit positions, assuming the decay vertex coincides with IP1. The distribution of the reconstructed mass had a peak corresponding to the π 0 mass. We compared the peak masses from the data and the MC simulations and obtained energy rescale factors of +3.5% and +1.6% for Arm1 and Arm2, respectively. The factors were consistent with the systematic uncertainty of energy-scale calibrations discussed in Sec. 5.1.

Corrections
• Beam-related background The contribution of background events is due to interactions between the circulating beams and residual gas in the beam pipe. The background was estimated using the events associated with non-crossing bunches at IP1.
These events were generated purely from the beam-gas interactions, while the events associated with the colliding bunches were related to both the signal and background. The estimated background-to-signal ratio was less than 1%; this ratio was subtracted from the measured cross-section. The difference in bunch intensity between colliding and non-colliding bunches was considered in the calculation. Because of the limited statistics of the non-colliding bunch data, the correction was applied as an energyindependent factor; nonetheless, the shape of the background spectrum is consistent with the shape of the signal.
• PID correction Corrections related to the PID selection, the inefficiency of photon selection and the contamination of hadrons, were performed using the templatefit method of the distribution of the PID estimator, L 90% , defined as the longitudinal depth, in units of radiation length (X 0 ), at which the integral of the energy deposition in a calorimeter reached 90% of the total.
As a criterion of the selection of the photon component, we set an energydependent criterion L 90%,thr , which defines the L 90% value to maintain a 90% efficiency of photon selection in the MC simulations. Figure 1 presents the L 90% distribution of Arm1-Region A for the reconstructed energy range between 1.1 and 1.2 TeV. The red and blue lines in Fig. 1, obtained from the MC simulation dataset of QGSJET II-04, indicate the template distributions for the pure photon and pure hadron samples, respectively.
These distributions were produced with normalization obtained from the template-fit result. According to the template-fit results, the hadron contamination, typically 10%, can be estimated as a function of energy and it is corrected together with the 90% efficiency in the analysis.
• Multi-hit correction Because the mis-reconstruction of multi-hit events as single-hit events makes the measured spectra more complex, multi-hit events were rejected from the analysis. In order to identify multi-hit events, a lateral shower profile measured by the position-sensitive layers was fitted by an empirical function. The difference in the goodness-of-fit between the single and double peak assumptions, the distance between two peaks, and the ratio between two peak heights were used to identify multi-hit events.
These criteria were adjusted to achieve a high efficiency of multi-hit detection while maintaining a reasonably low incidence of single-hit-event mis-reconstructions as multi-hit events.
The consistency of the multi-hit identification efficiencies exhibited by the data and MC simulation was tested using 'artificial' multi-hit event sets.
These artificial multi-hit events were created by merging two independent single-hit events. The combinations of single-hit events were selected to represent the distributions of photon-pair energies and hit-position distances in the true multi-hit events of QGSJET II-04. The same procedure was performed for the MC simulation also. The multi-hit detection efficiency exceeds 85% across the full energy range and reaches nearly 100% above 2 TeV, while inconsistencies between the data and MC are less than approximately 5% and 10% for Arm1 and Arm2, respectively. In the highenergy range, most of the multi-hit events are caused by photon pairs from π 0 decay. In these events, the separation between photons is kinematically limited above 5.8 mm. This makes the identification of multi-hits simpler.
About 4% of the total triggered events were identified as multi-hit events.
Two corrections were applied to the measured cross-section: 1. 'Multi-hit performance' correction: The contamination of multi-hit events misidentified as single-hits and the loss of single-hit events misidentified as multi-hits are corrected with an energy-dependent factor based on the MC dataset of QGSJET II-04. This correction factor depends mostly on the detector performance, while it depends weakly on the model chosen to generate the dataset.
2. 'Multi-hit cut' correction: As the single-photon cross-section is measured by the detector, another correction factor based on the same MC dataset was applied to correct for the multi-hit cut and recover the inclusive production cross-section. This correction factor ranged within ±50%, which was the largest contribution among the corrections and was strongly dependent on the choice of event-generation model in the MC simulation. This is because the multi-hit rate is related to the cross-section of high-energy π 0 production, as discussed above.
Both multi-hit corrections were performed inside the unfolding algorithm, which is described below.
• Unfolding: We corrected for detector biases (as energy resolution and multi-hit effects) in the obtained cross-section by performing an unfolding technique based on the iterative Bayesian method [25] provided by the RooUnfold package [26]. The MC simulation dataset with 10 8 inelastic collisions generated by the QGSJET II-04 model was used as a training sample.
• Decay correction: The photons detected by the LHCf experiment mainly come from the decay of short-lifetime particles such as π 0 and η mesons, which decay near the interaction point. Particles with a longer lifetime (such as K 0 , K ± and Λ) can decay along the beam pipe between the interaction point and detector and can contribute to the photon yield. In order to remove the contribution of long-lifetime particles, an energy-dependent correction was estimated with MC simulations by comparing the photon production cross-section at the interaction point with that after transportation along the beam pipe to the detector (i.e. after step '2' described in Sec. 3). The correction reaches a maximum of about 15% in the lowest-energy bin and becomes less than 1% above 2 TeV.

Systematic Uncertainties
We considered the following contributions as systematic uncertainties of the measured production cross-section. Figure 2 shows the estimated systematic uncertainties for each detector and each region as a function of photon energy.

Energy scale
Energy scale errors are attributable to a) the absolute gain calibration of each sampling layer, b) uniformity, c) relative gain calibration of the photomultiplier tubes (PMTs) used for the readout of scintillator lights, and d) the Landau-Pomeranchuk-Migdal (LPM) effect [27,28]. The first two contributions were studied in beam tests and are described in Ref. [17]. The third source of errors is related to the differences in the high-voltage configurations of PMTs between the beam tests and operation. The error was about 1.9%. The contribution to the error from the LPM effect was estimated as 0.7% by comparing the detector responses upon activation and inactivation of the LPM effect in the detector simulation. The total energy-scale error, estimated from the quadratic summation of all contributions, was ±3.4% for Arm1 and ±2.7% for Arm2. The systematic uncertainty of the cross-section was estimated by shifting the energy scale within the errors.

Beam-center stability
The beam center, an important parameter for defining analysis regions, was calculated from the measured hit-map distribution of the hadronic shower events, which were selected such that L 90% > L 90%,thr . The fluctuations between subsequent data subsets were found to be of the order of 0.3 mm, which is greater than the statistical uncertainty of the mean beam-center measurements that used all the data in the Fill. The systematic uncertainty associated with the beam-center determination was estimated by artificially moving the beam-center position by ±0.3 mm on the x-and y-axes. The measured crosssection with the shifted beam-center positions was compared to the original cross-section and the variation was deemed to be the systematic uncertainty.

PID
The contribution from the uncertainty on the fit of the L 90% distributions was negligible with respect to the statistical error of the cross-section. The systematic uncertainty associated with the PID correction was estimated instead by changing the criterion for the choice of L 90%,thr to discriminate between photons and hadrons, as discussed above. Instead of choosing L 90%,thr to obtain a 90% photon selection efficiency, PID selection and correction were also performed using the threshold values that produced photon-selection efficiencies of 85% and 95%. The 85%-95% limits were chosen in order to maintain the 'efficiency × purity' product above 75% in the full energy range. We compared the measured cross-section after correction and determined the systematic uncertainty from the relative deviation from the original cross-section.

Multi-hit identification efficiency
The correction factors attributable to the 'multi-hit performance' were obtained from the MC simulation. Thus, we tested the consistency of the multi-hit identification efficiencies exhibited by the data and the MC simulation by using the artificial multi-hit event sets, as previously described in Sec. 4.2. The systematic uncertainty on the production cross-section was calculated by multiplying the relative error of the multi-hit identification efficiency (i.e. the discrepancy between the data and MC simulation) by the ratio of multi-hit events to single-hit events.

Unfolding
It was discovered that the interaction model dependency of the 'multi-hit cut' correction factors, computed from the training sample, was the main source of systematic uncertainty in the cross-section unfolding process. EPOS-LHC predicted a higher multiplicity of photons than QGSJET II-04. Thus, a larger correction factor was expected in EPOS-LHC than in QGSJET II-04. We performed cross-section unfolding with a training sample of 5 × 10 7 inelastic collisions generated by EPOS-LHC. The relative difference between the QGSJET II-04 and EPOS-LHC results was chosen as the systematic uncertainty associated with the unfolding.

Decay correction
The systematic uncertainty related to the correction for the decay of longlifetime particles was estimated as the maximum relative fluctuation between the corrections predicted by the EPOS-LHC, QGSJET II-04, DPMJET 3.06, SIBYLL 2.3, and PYTHIA 8.212 models. Figure 3 presents the photon production cross-section measured by the Arm1 and Arm2 detectors. The error bars and hatched areas indicate the statistical and systematic uncertainties, respectively. In this comparison of the results of the two detectors, the detector-correlated systematic uncertainties due to the luminosity, unfolding, and decay correction were not considered. We found a general agreement, within the given uncertainties, between the results of the two detectors.

Results
We combined the results using the same method as the analysis presented in Ref. [29]. This approach assumed that the systematic uncertainties of the energy scale, PID correction, performance of multi-hit identification, and beam posi-  to these models and differences in collision energy do not produce significant changes in the forward photon production cross-section in the QGSJET II and EPOS models. Thus, the detailed differences in the results from √ s = 7 TeV and √ s = 13 TeV may correspond to the differences between the p T coverages.

Summary
The LHCf experiment measured the production cross-section of forward pho- by-event information measured by ATLAS will help us better understand the production of photons in the forward region [30].