Cross-section measurements of final states with photons and jets with the ATLAS experiment

The ATLAS Collaboration has performed precise measurements of the cross-section of final states with photons and/or jets at centre-of-mass energies of 8 and 13 TeV. The results are compared with state-of-the-art theory predictions and with predictions of several Monte Carlo generators. We also present new measurements of transverse energy-energy correlations and their associated asymmetries in multi-jet events at 8 TeV. Both measurements are used to extract the strong coupling constant and test the renormalization group equations.


Introduction
The modeling of a proton-proton collision at the Large Hadron Collider (LHC) can be divided in four main steps. The hard-scatter process is described by perturbative quantum chromodynamics (pQCD) and it depends on the parton distribution function (PDF) of the protons. The partons resulting from the hard-scatter process are taken to the non-perturvatibe regime through parton emission and splitting in the fragmentation process. Hadronisation evolves the confined quarks to the state we observe in the ATLAS detector [1]. Color-connected beam-beam remnants and multiple-parton interactions within the colliding protons, the "underlying event", are also described by non-perturbative models. Photons are a hard colourless probe of the hard-scatter process, which provides a good test of pQCD calculations and helps constrain the proton PDF. The analyses described in this paper include both photons coming from the matrix element (direct production) and from the fragmentation process. An isolation requirement is applied in order to reduce the background resulting from photons produced during hadronisation.
In the ATLAS experiment, detector-level jets are formed by clustering topological energy clusters from both the hadronic and electromagnetic calorimeters. On the simulations side, the particles resulting from the fragmentation and the hadronisation are clustered into particle-level jets. When only parton-level predictions are available, these are first clustered into jets, which are then corrected to account for the effect of fragmentation and hadronisation. Monte Carlo (MC) simulations are used to correct the effects of detector efficiency and resolution in both photon and jet measurements in order to compare them to theory predictions at particle level. This allows ATLAS data not only to be confronted to PDF models and perturbative calculations but also to test the modeling of factorisation and hadronisation. e-mail: Miguel.Villaplana.Perez@cern.ch The production of jets and prompt isolated photons at hadron colliders provides a stringent test of pQCD and can be used to probe the proton structure. The production of prompt photons in association with jets provides an additional testing ground for pQCD with a hard colourless probe less affected by hadronisation effects than jet production. Jet production can also be used to probe the gluon density function of the proton. Specific topologies can be used to extract the strong coupling constant.
This paper presents recent measurements of the cross-section of final states involving photons or jets at center-of-mass energies of 8 and 13 TeV performed by the ATLAS Collaboration. We also present new measurements of transverse energy-energy correlations (TEEC) and their associated asymmetries (ATEEC) in multi-jet events at 8 TeV and the extraction of the strong coupling constant from them.

Inclusive isolated photon production
Inclusive isolated photon production at 13 TeV has been studied using a data set with an integrated luminosity of 3.2 fb −1 [2]. Cross-sections as a function of E γ T are measured in four different regions of η γ for photons with E γ T > 125 GeV and |η γ | < 2.37. Values of E γ T up to 1.5 TeV are measured. The predictions of the Pythia [3] and Sherpa [4] Monte Carlo models give a good description of the shape of the measured cross-section distributions except for E γ T 500 GeV in the regions |η γ | < 0.6 and 0.6 < |η γ | < 1.37. Figure 1 shows the individual components of the systematic uncertainties added in quadrature in representative phase-space regions. Photon energy scale is the dominant uncertainty at high E γ T , while at low E γ T it is the uncertainty related to the background subtraction method that dominates. Uncertainties are larger in the forward regions. The NLO pQCD predictions, using Jetphox [5] and based on different sets of proton PDFs, provide an adequate description of the data within the experimental and theoretical uncertainties. For most of the phase space the theoretical uncertainties are larger than those of experimental nature and dominated by the terms beyond NLO, from which it is concluded that NNLO pQCD corrections are needed to make an even more stringent test of the theory. The ratios of the theoretical predictions based on different PDF sets to the measured cross-sections are found to be very similar, the differences being much smaller than the theoretical scale uncertainties.
NNLO predictions have been also compared to ATLAS inclusive photon measurements at 8 TeV [7]. These new calculations, displayed in figure 2, show a trend to be above the data at high E T . Accounting for both NNLO QCD and electroweak effects provides an improved prediction. The theoretical uncertainty is reduced by a factor close to 3 with respect to NLO predictions.

Photon pair production
Measurements of the production cross-section of two isolated photons at a center-of-mass energy of 8 TeV have been published [9]. The uncertainties are dominated by systematic effects that have been reduced, compared to the previous ATLAS measurement at 7 TeV, due to an improved method to estimate the background and improved corrections to the modeling of the calorimeter isolation variable in simulated samples.
Predicted cross-sections from fixed-order QCD calculations implemented in DIPHOX [10] and RESBOS [11] at NLO, and in 2γNNLO [12] at NNLO, shown in figure 3, are lower than the data. The relative errors associated to the predictions from DIPHOX (2γNNLO) are 10%-15% (5%-10%). Differential cross-sections are measured as functions of six observables: the diphoton invariant mass, the absolute value of the cosine of the scattering angle with respect to the direction of the proton beams, the opening angle between the photons in the azimuthal plane, the diphoton transverse momentum and two related variables (a T and φ η ), with uncertainties typically below 5% per bin, reaching as high as 25% in a few bins with low numbers of data events.
The effects of infrared emissions, probed precisely by measuring the cross-section as functions of a T (see figure 4) and φ η , are well reproduced by the inclusion of soft-gluon resummation at the NNLL accuracy. However, in most parts of the phase space, the predictions above are unable to reproduce the data. The discrepancies can reach a factor of 2 in many regions, beyond the theoretical uncertainties, which are typically below 20%.
The predictions of a parton-level calculation of varying jet multiplicity up to NLO matched to a parton-shower algorithm in SHERPA 2.2.1 provide an improved description of the data compared to all the other computations considered in the study and are in good agreement with the measurements, for both the integrated and differential cross-sections.

Photon plus jet production
Measurements of the cross-sections for the production of an isolated photon in association with one, two or three jets have been studied with the ATLAS detector at 8 TeV [16]. The photon is required to have E γ T > 130 GeV and |η γ | < 2.37. The jets are reconstructed using the anti-kt algorithm with radius parameter R = 0.6.  dependence on m γ− jet1 and |cos θ * | is also measured for m γ− jet1 > 467 GeV and extends up to m γ− jet1 of 2.45 TeV. The NLO QCD predictions from Jetphox, corrected for hadronisation and underlying-event effects, give a good description of the measured cross-section distributions in both shape and normalisation. In particular, the measured dependence on |cos θ * | and its scale dependence is consistent with the dominance of processes in which a quark is being exchanged; the experimental (theoretical) uncertainty in dσ/d|cosθ * | amounts to ≈ 3% (10%). Photon plus two-jet production is investigated by measuring cross-sections as functions of E γ T , p jet2 T and angular correlations between the final-state objects for p jet1 T > 100 GeV and p jet2 T > 65 GeV. The NLO QCD predictions from Blackhat [17] provide a good description of the measurements except for E γ T > 750 GeV, as shown on the left panel of figure 5. The predictions from Sherpa, which include higher-order tree-level matrix elements, are found to be superior to those from Pythia, based on 2 → 2 processes, in describing the distributions in p jet2 T and the angular correlations. The patterns of QCD radiation around the photon and the leading jet are compared by measuring the production of the subleading jet in an annular region centred on the given final-state object, β ob ject . The cross-sections as functions of β γ and β jet1 are observed to be different. The ratio of the cross-sections (see figure 5) shows enhancements in the directions towards the beams (β = 0 and π).
Photon plus three-jet production is characterised by measurements of cross-sections as functions of p jet3 T and angular correlations for p jet1 T > 100 GeV, p jet2 T > 65 GeV and p jet3 T > 50 GeV. The NLO QCD predictions from Blackhat provide an adequate description of the measurements. Whereas the prediction from Sherpa for p jet3 T is superior to that from Pythia, both give adequate descriptions of the angular correlations.
The dynamics of isolated-photon production in association with a jet have also been studied using 3.2 fb −1 of ATLAS data at 13 TeV [18]. Photons are required to have transverse energies above 125 GeV. Jets are identified using the anti-kt algorithm with radius parameter R=0.4 and required to have transverse momenta above 100 GeV. Measurements of isolated-photon plus jet cross-sections are presented as functions of the leading photon transverse energy, the leading jet transverse momentum, the angular separation in azimuth between the photon and the jet, the photon-jet invariant mass and the scattering angle in the photon-jet centre-of-mass system. The measurements extend up to values of 1.5 TeV in E γ T and p jet T , and the dependence on m γ− jet and |cos θ * | is measured for m γ− jet > 450 GeV.
The predictions of the tree-level plus parton-shower Monte Carlo models Pythia and LO Sherpa give a reasonable description of the shape of the data, except for p jet T in the case of Pythia. The fixedorder NLO QCD calculations of Jetphox, corrected for hadronisation and underlying-event effects, and the multi-leg NLO QCD plus parton-shower calculations of Sherpa describe the measured crosssections within the experimental and theoretical uncertainties. The comparison of predictions based on different parameterisations of the proton PDFs shows that the description of the data achieved does not depend significantly on the specific PDF set used. The only meaningful prediction for dσ/d∆φ γ− jet is that of NLO Sherpa, which is able to reproduce the data down to ∆φ γ− jet = π/2 due to the inclusion of the matrix elements for 2 → n processes with n = 4 and 5. The measured dependence on |cos θ * |, shown in figure 6, is consistent with the dominance of processes in which a quark is being exchanged; the experimental (theoretical) uncertainty on dσ/d|cos θ * | amounts to 3-4% (10% for Jetphox and 15-25% for NLO Sherpa).
All these studies provide stringent tests of pQCD and validate the description of the dynamics of isolated photon in association with jets production in pp collisions at 8 and 13 TeV.

Jet production
The double-differential inclusive jet cross-sections have been measured using the ATLAS 8 TeV data set. Jets are reconstructed with the anti-kt algorithm with jet radius parameter values of R = 0.4 and R = 0.6, in the kinematic region of the jet transverse momentum from p T = 70 GeV to about 2.5 TeV and jet rapidities |y| < 3 [13]. The cross-sections are measured double-differentially in the jet transverse momentum and rapidity. The dominant systematic uncertainty arises from the jet energy calibration. Compared to previous jet cross-section measurements a significant reduction of the uncertainties is achieved.
A quantitative comparison of the measurements to fixed-order NLO QCD calculations, corrected for non-perturbative and electroweak effects, shows overall fair agreement (with p-values in the percent range) when considering jet cross-sections in individual jet rapidity bins treated independently. Some tension between data and theory is observed in the central rapidity region for anti-kt jets with R = 0.6. Strong tension between data and theory is observed when considering data points from all jet transverse momentum and rapidity regions, with a full treatment of the correlations. This tension can be reduced, but not completely resolved, using alternative correlation scenarios for the experimental and theoretical two-point systematic uncertainties. The remaining tension could be due either to the breakdown of the assumptions that need to be made in the treatment of two-point systematic uncertainty components, or to an incomplete theoretical description, such as missing higher-order corrections.
The inclusive jet and dijet cross-sections have also been measured using 3.2 fb −1 of ATLAS data at 13 TeV [14]. Jets are identified with the anti-kt algorithm with a jet radius parameter value of R = 0.4. The inclusive jet cross-sections are measured double-differentially as a function of the jet transverse momentum, covering the range from 100 GeV to 3.5 TeV, and the absolute jet rapidity up to |y|<3. In addition, the double-differential dijet production cross-sections are presented as a function of the dijet mass, covering the dijet mass from 300 GeV to 9 TeV and the half absolute rapidity separation between the two leading jets, y * , up to y * < 3. Figure 7 shows the individual components of the systematic uncertainties added in quadrature for the inclusive jet cross-section measurements in representative phase-space regions. The dominant systematic uncertainty arises from the jet energy scale. NLO and NNLO pQCD calculations for the inclusive jet measurement, corrected for nonperturbative and electroweak effects, are compared to the measured cross-sections in figure 8. Similarly to the study at 8 TeV, a quantitative comparison of the measurements to fixed-order NLO QCD calculations shows overall fair agreement when considering jet cross-sections in individual jet rapidity bins independently. In the inclusive jet measurement, a strong tension (with p-values 10 −3 ) between data and theory is observed when considering data points from all jet transverse momentum and rapidity regions. No significant deviations between the inclusive jet cross-sections and the fixedorder NNLO QCD calculations corrected for non-perturbative and electroweak effects are observed when using p jet T as QCD scale.

Transverse energy-energy correlations and the extraction of α s
TEEC and ATEEC in multi-jet events have been measured using the ATLAS 8 TeV data set [15]. The data, binned in six intervals of the sum of transverse momenta of the two leading jets, H T 2 = p T 1 + p T 2 , are corrected for detector effects and compared to the predictions of pQCD, corrected for hadronisation and multi-parton interaction effects. The results show that the data are compatible with the theoretical predictions, within the uncertainties. The data are used to determine the strong coupling constant α s and its evolution with the interaction scale Q = (p T 1 + p T 2 )/2 by means of a χ 2 fit to the theoretical predictions for both TEEC and ATEEC in each energy bin. Additionally, global fits to the TEEC and ATEEC data are performed, as it is shown in figure 9, leading to  −0.0013 (scale) ± 0.0017(PDF) ± 0.0004(NP), respectively. Conservatively, the values obtained using the NNPDF 3.0 PDF set are chosen, as they provide the largest PDF uncertainty among the different PDF sets investigated. These two values are in good agreement with the determinations in previous experiments and with the current world average s(m Z ) = 0.1181 ± 0.0011. The correlation coefficient between the two determinations is equal to 0.60. The present results are limited by the theoretical scale uncertainties, which amount to 6% of the value of s(m Z ) in the case of the TEEC determination and to 4% in the case of the ATEEC. This uncertainty is expected to decrease as higher orders are calculated for the perturbative expansion.

Summary
High-precision measurements involving photons and jets on 8 TeV data are being complemented by the first results at 13 TeV. The ATLAS Collaboration has achieved a strong performance in jet and photon reconstruction and many of the results are now dominated by the uncertainties on the predictions and the PDFs. This highlights the importance of the NNLO predictions, which will reduce the renormalisation and factorisation scale uncertainty. Complex measurements of final states involving photons and jets explore regions of phase-space where the current theory struggles to match the data, providing valuable physics input to PDF and α s fits, and to the description of various aspects of QCD radiation. Diphoton production processes are particularly sensitive to higher-order QCD phenomenology. For the future, the systematic exploration of more complex variables and final states, Figure 9. Comparison of the values of α s (Q) obtained from fits to the TEEC (left) and the ATEEC (right) functions at the energy scales given by < H T 2 > /2 (red star points) with the uncertainty band from the global fit (orange full band) and the 2016 world average (green hatched band) [15]. Determinations from other experiments are also shown as data points. The error bars, as well as the orange full band, include all experimental and theoretical sources of uncertainty. The strong coupling constant is assumed to run according to the two-loop solution of the RGE.
combining several beam energies, will be crucial for fine-tuning descriptions of the Standard Model, and providing precise background estimates for new physics searches.