Direct photon production and PDF fits reloaded

Abstract

Direct photon production in hadronic collisions provides a handle on the gluon PDF by means of the QCD Compton scattering process. In this work we revisit the impact of direct photon production on a global PDF analysis, motivated by the recent availability of the next-to-next-to-leading (NNLO) calculation for this process. We demonstrate that the inclusion of NNLO QCD and leading-logarithmic electroweak corrections leads to a good quantitative agreement with the ATLAS measurements at 8 and 13 TeV, except for the most forward rapidity region in the former case. By including the ATLAS 8 TeV direct photon production data in the NNPDF3.1 NNLO global analysis, we assess its impact on the medium-x gluon. We also study the constraining power of the direct photon production measurements on PDF fits based on different datasets, in particular on the NNPDF3.1 no-LHC and collider-only fits. We also present updated NNLO theoretical predictions for direct photon production at 13 TeV that include the constraints from the 8 TeV measurements.

Fig. 1

Feynman diagrams for direct photon production at leading order via the QCD Compton scattering process (left) and $q\overline{q}$ annihilation (right)

Fig. 2

The coverage in the $(x,Q^2)$ kinematic plane of the 8 TeV ATLAS photon measurements (using LO kinematics), compared to the dataset used in the global NNPDF3.1 fit

Fig. 3

The NNLO QCD K-factor, Eq. (3.5), and the LL electroweak correction $[1+{\mathrm{\Delta }}_V^{\mathrm{ew}}(E_T^{\gamma },s)]$, Eq. (3.4), in the four rapidity bins of the ATLAS 8 TeV measurement. We also show the results of its multiplicative combination, which indicates the overall correction applied to the NLO QCD cross-section

Fig. 4

The ratio of the APPLgrid computations of the NLO QCD cross-section to the corresponding MCFM v6.8 result for the kinematics of the first three rapidity bins of the ATLAS 8 TeV measurement, using in both cases the NNPDF3.1 set as input

Fig. 5

Comparison between the theoretical predictions for direct photon production data computed with different PDF sets and the ATLAS 8 TeV data, normalized to the central value of the former. The experimental statistical and systematic uncertainties have been added in quadrature. The error bands for the theory predictions include only the PDF uncertainties

Fig. 6

Left: comparison of the gluon PDF at $Q=100$ GeV between the NNPDF3.1 and NNPDF3.1 + ATLAS$\gamma$ fits, normalized to the central value of the former. Right: the corresponding relative one-sigma PDF uncertainties in each case

Fig. 7

Comparison of the quark PDFs at $Q=100$ GeV between the NNPDF3.1 and NNPDF3.1 + ATLAS$\gamma$ fits, normalized to the central value of the former

Fig. 8

Same as Fig. 5, now comparing the NNPDF3.1 and NNPDF3.1 + ATLAS$\gamma$ sets for the three rapidity bins of the ATLAS 8 TeV data included in the fit

Fig. 9

Same as Fig. 6 for the NNPDF3.1 no-LHC (upper) and collider-only (lower plots) fits

Fig. 10

Same as Fig. 8 for the ATLAS 13 TeV direct photon measurements. In addition to the PDF uncertainties shown in the previous cases (darker bands), here we also include the scale uncertainties associated to the NNLO QCD calculation (lighter bands)

Fig. 11

Comparison between the experimental measurements of the $R_{13/8}(E_T^{\gamma },{\eta }^{\gamma })$ ratio and the corresponding theoretical calculations using NNPDF3.1 and NNPDF3.1 + ATLAS$\gamma$, normalized to the central experimental value. The theory band includes only the contribution from the PDF uncertainties

Fig. 12

Same as in Fig. 11 without normalizing to the experimental data

Fig. 13

Same as Fig. 6, now adding to the comparison the results of the fit including the correlations between the experimental systematic uncertainties (labelled as “refit”)

Fig. 14

Same as Fig. 6 now adding to the comparison the results of the NNPDF3.1 + ATLAS$\gamma$(rw) set obtained by applying the Bayesian reweighting procedure