Measurement of differential cross sections for inclusive isolated-photon and photon+jet production in proton-proton collisions at $\sqrt{s} =$ 13 TeV

Measurements of inclusive isolated-photon and photon+jet production in proton-proton collisions at $\sqrt{s} =$ 13 TeV are presented. The analysis uses data collected by the CMS experiment in 2015, corresponding to an integrated luminosity of 2.26 fb$^{-1}$. The cross section for inclusive isolated photon production is measured as a function of the photon transverse energy in a fiducial region. The cross section for photon+jet production is measured as a function of the photon transverse energy in the same fiducial region with identical photon requirements and with the highest transverse momentum jet. All measurements are in agreement with predictions from next-to-leading-order perturbative QCD.


Introduction
The measurement of inclusive isolated-photon and photon+jets production cross sections can directly probe quantum chromodynamics (QCD).The dominant production processes in protonproton (pp) collisions at the energies of the CERN LHC are quark-gluon Compton scattering qg → qγ, together with contributions from quark-antiquark annihilation qq → gγ, and parton fragmentation qq(gg) → X + γ.Both the CMS and ATLAS Collaborations have reported measurements of the differential cross sections for isolated prompt photon production [1][2][3][4][5] and for the production of a photon in association with jets [6][7][8] using data with center-of-mass energies of 2.76, 7, and 8 TeV.The ATLAS Collaboration has also reported the same measurements at a center-of-mass energy of 13 TeV [9,10].
The published measurements show agreement with the results of next-to-leading-order (NLO) perturbative QCD calculations [11,12].Although these LHC measurements are not currently included in the global parton distribution functions (PDF) fits [13][14][15], they are sensitive, in particular to the gluon density function g(x, Q 2 ) over a wide range of parton momentum fraction x and energy scale Q 2 [16][17][18].An improved understanding of all PDFs is key to reducing the associated theoretical uncertainties in the calculation of many relevant cross sections, including Higgs boson production and new physics searches.
In this paper, measurements of the inclusive isolated-photon and the photon+jets production cross sections are reported using data collected by the CMS Collaboration in 2015 during 13 TeV proton-proton collisions, corresponding to an integrated luminosity of 2.26 fb −1 [19].The significant increase of center-of-mass energy, compared to the previous CMS measurements [1,2], opens a large additional region of phase space.
The dominant background for the photon+jets process is QCD multijet production with an isolated electromagnetic (EM) deposit from decays of neutral hadrons, mostly from π 0 mesons.A multivariate analysis method is used to identify prompt photons using a boosted decision tree (BDT) algorithm, implemented using the TMVA v4.1.2toolkit [20].Photon yields are extracted using the shape of the BDT distributions, and the measured cross sections are compared to the results of NLO QCD calculations.

The CMS detector
CMS is a general-purpose detector built to explore physics at the TeV scale.The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and a strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections.Forward calorimeters extend the pseudorapidity η coverage provided by the barrel and endcap detectors.Muons are measured in gas-ionization detectors embedded in the steel flux return yoke outside the solenoid.A more detailed description of the CMS detector, together with the definition of the coordinate system and the relevant kinematic variables, is given in Ref. [21].
The ECAL consists of 75 848 lead tungstate crystals, which provide coverage up to |η| = 1.479 in the barrel region (EB) and 1.479 < |η| < 3.0 in two endcap regions (EE).A preshower detector consisting of two planes of silicon sensors interleaved with a total of 3 radiation lengths of lead is located in front of the EE.
The global event reconstruction (also called particle-flow event reconstruction) [23] reconstructs and identifies each particle candidate with an optimized combination of all subdetector information.
Photons are identified as energy clusters in the ECAL that are not consistent with an electron track in the tracker.The clustering algorithm allows an almost complete collection of the energy of the photons, even for those converting in the material upstream of the calorimeter.First, cluster "seeds" are identified as local energy maxima above a given threshold.Second, clusters are grown from the seeds by aggregating crystals with at least one side in common with a clustered crystal and with an energy in excess of a given threshold.This threshold represents about two standard deviations of the electronic noise, which has an |η| dependence in the ECAL.The energy in an individual crystal can be shared between clusters under the assumption that each seed corresponds to a single EM particle.Finally, clusters are merged into "superclusters", to allow good energy containment, accounting for geometrical variations of the detector along η, and optimizing robustness against additional pp collisions in the same or adjacent bunch crossings (pileup).The clustering excludes 1.44 < |η| < 1.56, which corresponds to the transition region between the EB and EE.The fiducial region terminates at |η| = 2.5 where the tracker coverage ends.
The energy of photons is computed from the sum of the energy of the clustered crystals, calibrated and corrected for degradation in the crystal response over time [24].The preshower energy is added to that of the superclusters in the region covered by this detector.To optimize the resolution, the photon energy is corrected using a multivariate technique for the containment of the electromagnetic shower in the superclusters and the energy losses from converted photons [25].In the EB, an energy resolution of about 1% is achieved for unconverted photons in the tens of GeV energy range.The remaining EB photons have a resolution of about 1.3% up to |η| = 1.0, rising to about 2.5% at |η| = 1.4.In the EE, the resolution of unconverted or late-converting photons is about 2.5%, while the remaining EE photons have a resolution between 3 and 4%.
Electrons are identified as a primary charged track consistent with potentially multiple ECAL energy clusters from both the electron and from potential bremsstrahlung photons produced in the tracker material.Muons are identified as a track in the central tracker consistent with either a track or several hits in the muon system, associated with a minimum ionization signature in the calorimeters.Charged hadrons are charged-particle tracks not identified as electrons or muons.Finally, neutral hadrons are identified as HCAL energy clusters not linked to any charged-hadron track, or as ECAL and HCAL energy excesses with respect to the expected charged-hadron energy deposit.
Jets are clustered from all particle candidates reconstructed by the global event reconstruction with the infrared-and collinear-safe anti-k T algorithm [26,27] using a distance parameter R of 0.4.Jet energy corrections are derived from simulation, and are confirmed with in situ measurements exploiting the energy balance of dijet or photon+jet events [28].The jet energy resolution amounts typically to 15 (8)% at 10 (100) GeV.

Simulation samples
Simulated event samples for photon+jets and multijet final states are generated at leading order (LO) with PYTHIA 8 (v8.212) [29].The photon+jets sample contains direct photon pro-duction originating from quark-gluon Compton scattering and quark-antiquark annihilation.A filter is used to reject generated events that do not contain an isolated-photon, where the isolation requires that the sum of the p T of all stable particles within a cone of size ∆R = √ (∆φ) 2 + (∆η) 2 = 0.4 around the photon direction is less than 5 GeV.For the multijet sample, final states with quark and gluon jets dominate, and the photon+jets processes are explicitly removed.The MADGRAPH (v5.2.2.2) [30,31] LO generator, interfaced with PYTHIA 8, is used to generate an additional sample of photon+jet events containing up to 4 jets that is used to estimate systematic uncertainties.Samples of Z/γ * +jets events are generated at NLO with MADGRAPH5 aMC@NLO (v5.2.2.2) [30,32] and are used for calibration and validation studies described later.The CUETP8M1 tune [33] is used in PYTHIA 8.The NNPDF2.3 LO PDF [34] and the NNPDF3.0NLO PDF [13] are used to generate simulation samples, where the former is used with PYTHIA 8.
The simulated processes include the effect of pileup.The pileup contribution is simulated with additional minimum bias events superimposed on the primary event using the measured distribution of the number of reconstructed interaction vertices, an average of 14 vertices per bunch crossing.A detailed detector simulation based on the GEANT4 (v9.4p03) [35] package is applied to all the generated signal and background samples.

Data samples and event selection criteria
Events containing high energy photon candidates are selected using the two-level CMS trigger system [36].At the first level, events are accepted if they have an ECAL trigger tower, which has a segmentation corresponding to 5 × 5 ECAL crystals, with total transverse energy E T , defined as the magnitude of the photon transverse momentum, greater than 40 GeV.The second level of the trigger system uses the same reconstruction algorithm as the offline photon reconstruction [25].An event is accepted online if it contains at least one ECAL cluster with E T greater than 175 GeV, and if the "H/E", defined as the ratio of energy deposited in the HCAL to that in the ECAL, is less than 0.15 (0.10) in the EB (EE) region.
All events are required to have at least one well-reconstructed primary vertex [22].The reconstructed vertex with the largest value of summed physics-object p 2 T is the primary pp interaction vertex.The physics objects are the jets, clustered using the jet finding algorithm [26,27] with the tracks assigned to the vertex as inputs, and the associated missing transverse momentum p miss T [37], taken as the negative vector sum of the p T of those jets.In addition, photon+jets events are required to be balanced in p T , and hence the magnitude of missing transverse momentum, defined as the magnitude of negative vector sum of the momenta of all reconstructed particle-flow objects projected onto the plane perpendicular to the beam axis in an event, is required to be less than 70% of the highest photon E T .Photon candidates are selected as described below.An electron veto is imposed by requiring the absence of hits in the innermost layer of the silicon pixel detector that could be ascribed to an electron track consistent with the energy and position of the photon ECAL cluster.Criteria on the energy measured in HCAL (H), isolation, and shower shape variables are applied to reject photons arising from electromagnetic decays of particles in hadronic showers.Hence, H/E is required to be less than 0.08 (0.05) for photon candidates in the EB (EE), respectively.The sum of the E T of other photons in a cone of size ∆R < 0.3 (photon isolation) around the photon candidate is required to be less than 15 GeV, and the sum of p T of charged hadrons in the same cone (hadron isolation) is required to be less than 2.0 (1.5) GeV for photon candidates in the EB (EE).To further suppress photons from decays of neutral mesons (π 0 , η, etc.) that survive the isolation and HCAL energy leakage criteria, a selection on the EM shower shape is imposed by requiring that its second moment σ ηη [25], which is a measure of the lateral extension of the shower along the η direction, be <0.015(0.045) for photon candidates in the EB (EE).The photon candidate with the highest E T that satisfies the above selection criteria in each event is referred to as the leading photon.The data consist of 212 134 events after applying inclusive isolated-photon selections and 207 120 events after applying the photon+jets requirements.
The photon reconstruction and selection efficiencies are estimated using simulated events and imposing the experimental constraints on the isolated-photons present in the fiducial region in the generator events.The efficiency is about 90-92% (83-85%) for EB (EE) photons, depending on the E T of the photon candidate.Multiplicative scale factors (SF) are applied to correct potential differences in efficiencies between data and simulation.The SFs are obtained from the ratio of the efficiency in data to that in simulated control samples.The photon SF is derived from Drell-Yan Z → e + e − events, where one of the electrons is reconstructed as a photon.The events are selected by requiring the invariant mass of the electron pair to be between 60-120 GeV.The electron veto SF is determined using final-state radiation photons in Z → µ + µ − γ events.All SFs are within 1% of unity, and their uncertainties are included in the total systematic uncertainty.All efficiencies and SF are measured as functions of photon E T and rapidity y using the same binning as the cross section measurement.
The absolute photon trigger efficiency, as a function of photon E T , is measured using events collected with a jet trigger that contains a photon candidate, which satisfies the signal selection criteria and is spatially separated from the jet that triggered the event by ∆R(γ, jet) > 0.7.The trigger efficiency is above 99% for EB (EE) photons above 200 (220) GeV.The E T -dependent trigger efficiency is used to compute the cross section, and the associated uncertainties are incorporated into the uncertainty calculation for the cross section.
For the cross section measurement as a function of jet y, the jets are required to (1) satisfy a set of selection criteria that remove detector noise [38], (2) have a separation from the leading photon of ∆R > 0.4, and (3) have p T greater than 30 GeV.The jet candidate with the highest p T satisfying the above requirements is selected.

Cross section measurement
To further suppress remaining backgrounds originating from jets faking photons, a BDT is constructed utilizing the following discriminating variables: 1. Photon η, φ, and energy; 2. Several shower shape variables: (a) The energy sum of the 3 × 3 crystals centered on the most energetic crystal in the photon divided by the energy of the photon; (b) The ratio of E 2×2 , the maximum energy sum collected in a 2 × 2 crystal matrix that includes the largest energy crystal in the photon, and E 5×5 , the energy collected in a 5 × 5 crystal matrix centered around the same crystal (E 2×2 /E 5×5 ); (c) The second moment of the EM cluster shape along the η direction (σ ηη ); (d) The diagonal component of the covariance matrix that is constructed from the energyweighted crystal positions within the 5 × 5 crystal array (q ηφ ); (e) The energy-weighted spreads along η (σ η ) and φ (σ φ ), calculated using all crystals in the photon cluster, which provide further measures of the lateral spread of the shower.
3. For photon candidates in the EE, the preshower shower width, , where σ xx and σ yy measure the lateral spread in the two orthogonal sensor planes of the detector, and the fraction of energy deposits in the preshower.
4. The median energy density per unit area in the event ρ [27] to minimize the effect of pileup.
The distributions of the BDT values are used in a two-template binned likelihood fit to estimate the photon yield.A separate BDT is constructed for each bin of photon y and E T .The signal BDT template is obtained from the sample of simulated photon+jets events generated using PYTHIA 8.This template is validated using Z → µ + µ − γ data samples and also a data sample of Z → e + e − candidates where each candidate contains an electron reconstructed as a photon.
The signal templates have a systematic uncertainty due to differences in the distributions of the BDT input variables in data and simulation.To evaluate this uncertainty, the distribution of each variable obtained from a sample of simulated Z → e + e − events is modified until good agreement is obtained with the data.Signal templates are made using the same modification.The difference in the templates is treated as a nuisance parameter in the fit procedure.
The background BDT template is derived from the data, using a sideband region defined using the same signal selection, but relaxing the hadron isolation criterion.The energy in the isolation cone for the sideband region is required to be between 7 and 13 (6 and 12) GeV for EB (EE) photons, where the chosen ranges ensure negligible signal contamination.Possible biases in the photon yields due to differences between the background BDT templates in the control and signal regions are estimated using simulated events, and are found to be less than 5%.Photon yields extracted from the fits are corrected for these biases.The statistical uncertainties in each bin of the background template constructed from the data sideband events are also included as nuisance parameters in the fitting procedure.Figure 1 shows the BDT templates obtained for a particular photon E T and y bin for the data sideband and for the signal and sideband regions from simulated QCD multijet events.The distributions of BDT outputs for EB and EE photons in data are shown in Fig. 2 for photon E T between 200 and 220 GeV and jet |y| < 1.5.
The fit results with signal, background, and combined distributions and ratio of data over fit are shown.The fitted results match well with data distributions as shown in χ 2 over the degree of freedom, goodness-of-fit, in the residual ratio plot of data over fit results.
The corrected signal yield is unfolded using the iterative D'Agostini method [39], as implemented in the RooUnfold software package [40], to take into account migrations between different bins due to the photon energy scale and resolution.The unfolding response matrix is obtained from the PYTHIA 8 photon+jets sample.The unfolding corrections are small, of the order of 1%.The size of the corrections is also verified using an independent photon+jets sample generated with MADGRAPH.The inclusive isolated-photon differential production cross section is calculated as and the photon+jets as where U (N γ ) denotes the unfolded photon yields in bins of width ∆E γ T and ∆y, and y is the rapidity of either the photon or the jet.In these equations, denotes the product of trigger, reconstruction, and selection efficiencies; SF the product of the selection and electron veto scale factors; and L is the integrated luminosity.

Systematic uncertainties
The uncertainty in the efficiency of the event selection is typically small except in the high-E T region, where statistical uncertainties in both data and simulated events dominate.A summary of the systematic uncertainties is given in Table 1.
The systematic uncertainties in the signal and background templates are incorporated into the fit as nuisance parameters.For the signal template uncertainty, the nuisance parameter is assigned a Gaussian prior, while log-normal priors are assigned to the background template nuisances.A description of the general methodology can be found in Ref. [41].The bias correction, The points represent data, and the solid histograms, approaching the data points, represent the fit results with the signal (dashed) and background (dotted) components displayed.The bottom panels show the ratio of the difference between the data and the fit to the statistical uncertainty in the data, along with the resulting reduced χ 2 over degrees of freedom (dof).applied on the photon yields, due to the selection of the sideband range is also considered as a systematic uncertainty.
The impact on photon yields from the unfolding uncertainties, which include photon energy scale and resolution uncertainties, is roughly 5%.The uncertainties of the event selection efficiency due to the jet selection and jet rapidity migration are negligible.
The uncertainty in the measurement of the CMS integrated luminosity is 2.3% [19].
The total uncertainty in the yield per bin, excluding the highest photon E T bin in each y range, is about 5-8% for EB and 9-17% for EE photons.The highest photon E T bins in all y region have limited events in data and simulated samples for the evaluation of systematics.

Results and comparison with theory
The measured inclusive isolated-photon and photon+jets cross sections are shown in Figs. 3  and 5, respectively, and in Tables 2 and 3.
The measured cross sections are compared with NLO perturbative QCD calculations from the JETPHOX 1.3.1 generator [11,42,43], using the NNPDF3.0NLO [13] PDFs and the Bourhis-Fontannaz-Guillet (BFG) set II parton fragmentation functions [44].The renormalization, factorization, and fragmentation scales are all set to be equal to the photon E T .To estimate the effect of the choice of theoretical scales on the predictions, the three scales are varied indepen- dently from E T /2 to 2E T , while keeping their ratio between one-half and two.The impact of JETPHOX cross section predictions due to the uncertainties in the PDF and in the strong coupling α S = 0.118 at the mass of Z boson is calculated using the 68% confidence level NNPDF3.0NLO replica.The total theoretical uncertainties of the cross section predictions are evaluated as the quadratic sum of the scale, PDF, and α S uncertainties.
The ratio of the theoretical predictions to data, together with the experimental and theoretical uncertainties, are shown in Figs. 4 and 6 for the isolated-photon and photon+jets cross section measurements respectively.The uncertainties in the theoretical predictions and ratios to data are symmetrized in the tables; the largest value between the positive and negative uncertainties is listed.Measured cross sections are in agreement with theoretical expectations within statistical and systematic uncertainties.
The ratio of the theoretical predictions to data based on JETPHOX at NLO with different PDF sets, including MMHT14 [14], CT14 [15], and HERAPDF2.0[45] together with NNPDF3.0, are shown in Fig. 7.The differences between JETPHOX predictions using different PDF sets are small, within the theoretical uncertainties estimated with NNPDF3.0.

Summary
The differential cross sections for inclusive isolated-photon and photon+jets production in proton-proton collisions at a center-of-mass energy of 13 TeV are measured with a data sample collected by the CMS experiment corresponding to an integrated luminosity of 2.26 fb −1 .The measurements of inclusive isolated-photon production cross sections are presented as functions of photon transverse energy and rapidity.The photon+jets production cross sections are presented as functions of photon transverse energy, and photon and jet rapidities.

Figure 1 :
Figure 1: Distributions of the BDT for background photons in the 200-220 GeV bin for the EB region.The points show events from a sideband region of the photon isolation selection criteria, the solid histogram shows the events in the signal region in simulated QCD multijet events, and the dashed histogram shows the sideband region for simulated QCD multijet events.All three samples have their statistical uncertainties shown as error bars.

Figure 2 :
Figure2: Distributions of the BDT output for an EB (left) and an EE (right) bin with photon E T between 200-220 GeV and |y jet | < 1.5.The points represent data, and the solid histograms, approaching the data points, represent the fit results with the signal (dashed) and background (dotted) components displayed.The bottom panels show the ratio of the difference between the data and the fit to the statistical uncertainty in the data, along with the resulting reduced χ 2 over degrees of freedom (dof).

Figure 4 :
Figure 4: The ratios of theoretical NLO predictions to data for the differential cross sections for isolated-photon production in four photon rapidity bins, |y γ | < 0.8, 0.8 < |y γ | < 1.44, 1.57 < |y γ | < 2.1, and 2.1 < |y γ | < 2.5, are shown.The error bars on data points represent the statistical uncertainty, while the hatched area shows the total experimental uncertainty.The errors on the ratio represent scale uncertainties, and the shaded regions represent the total theoretical uncertainties.

Figure 6 :
Figure 6: The ratios of theoretical NLO prediction to data for the differential cross sections for photon+jets production in two photon rapidity (|y γ | < 1.44 and 1.57 < |y γ | < 2.5) and two jet rapidity (|y jet | < 1.5 and 1.5 < |y jet | < 2.4) bins , are shown.The error bars on the data points represent their statistical uncertainty, while the hatched area shows the total experimental uncertainty.The error bars on the ratios show the scale uncertainties, and the shaded area shows the total theoretical uncertainties.

Figure 7 :
Figure 7: Ratios of JETPHOX NLO predictions to data for various PDF sets as a function of photon E T for inclusive isolated-photons (top four panels) and photon+jets (four bottom panels).Data are shown as points, the error bars represent statistical uncertainties, while the hatched area represents the total experimental uncertainties.The theoretical uncertainty in the NNPDF3.0prediction is shown as a shaded area.

Table 2 :
Measured and predicted differential cross section for isolated-photon production, along with the statistical and systematical uncertainties in the various E T and y bins.Predictions use JETPHOX at NLO with the NNPDF3.0PDF set.The ratio of the JETPHOX predictions to data are listed in the last column, with the total uncertainty estimated assuming uncorrelated experimental and theoretical uncertainties.