Prompt diphoton production compared to measurements at 13 TeV in $k_t$-factorization: A comparative analysis of unintegrated PDF models

TL;DR

This work addresses prompt diphoton production at the LHC in the k_t-factorization framework by comparing three UPDF models (PB, NLO-MRW, MKMRW) against ATLAS 13 TeV data across multiple observables. It computes tree-level off-shell partonic channels with KaTie and includes the loop-induced gg contribution separately, assessing how UPDF choices shape differential spectra. The PB UPDF consistently provides the best overall agreement with data, while NLO-MRW tends to overshoot at higher factorization scales and MKMRW shows suppression from an extended Sudakov integral. The findings demonstrate that k_t-factorization with carefully chosen UPDFs, particularly PB, offers a robust description of diphoton production and informs UPDF development for accurate QCD predictions at the LHC.

Abstract

We perform an in-depth comparative analysis of unintegrated parton distribution function (UPDF) models for isolated prompt diphoton production in proton-proton collisions at $\sqrt{s}=13$~TeV within the $k_t$-factorization framework. Predictions are obtained with three UPDF approaches: Parton Branching (PB), NLO-MRW, and Modified KMRW (MKMRW). Tree-level $q + \bar q\!\to\!γ+γ$, $q + \bar q\!\to\!γ+ γ+ g$, and $q + g\!\to\!γ+γ+ q$ subprocesses are generated with \textsc{KaTie} using off-shell initial states; the loop-induced $g + g\!\to\!γ+ γ$ channel is evaluated independently. We compare differential cross sections with ATLAS measurements across a broad set of observables, including the photon transverse momenta, diphoton invariant mass and transverse momentum, the Collins-Soper angle, acoplanarity, $φ^*_η$, and a transverse thrust-related variable. This comparative study quantifies the impact of the UPDF choice on the diphoton spectra. We find that the PB model provides the most consistent agreement over all distributions, whereas NLO-MRW tends to overshoot in regions correlated with larger factorization scales and MKMRW generally undershoots due to stronger Sudakov suppression. With standard scale variations, our results indicate that $k_t$-factorization with PB UPDFs can accurately describe diphoton production, while fixed-order collinear predictions typically require higher-order corrections together with parton-shower effects to achieve a comparable description.

Figures (5)

• Figure 1: Comparison of different gluon UPDF models at $\mu = 70~\mathrm{GeV}$ (top) and $\mu = 500~\mathrm{GeV}$ (bottom). The colour scale shows the ratio of UPDFs as a function of the longitudinal momentum fraction $x$ of the gluon (horizontal axis) and its transverse momentum $k_T$ in GeV (vertical axis), both on logarithmic scales. From left to right the panels display the ratios $PB/MKMRW$, $PB/NLO\text{-}MRW$, and $MKMRW/NLO\text{-}MRW$
• Figure 2: Comparison of different up-quark UPDF models at $\mu = 70~\mathrm{GeV}$ (top) and $\mu = 500~\mathrm{GeV}$ (bottom). The colour scale shows the ratio of UPDFs as a function of the longitudinal momentum fraction $x$ of the up quark (horizontal axis) and its transverse momentum $k_T$ in GeV (vertical axis), both on logarithmic scales. From left to right the panels display the ratios $PB/MKMRW$, $PB/NLO\text{-}MRW$, and $MKMRW/NLO\text{-}MRW$.
• Figure 3: Comparison of the theoretical predictions from the NLO-MRW, MKMRW, and PB UPDF models with the experimental data for the transverse momenta of the two final-state photons. The left panel shows the distribution for the leading photon, while the right panel corresponds to the subleading photon.
• Figure 4: Comparison of the theoretical predictions from the NLO-MRW, MKMRW, and PB UPDF models with experimental data for four observables: (top-left) $a_{T,\gamma\gamma}$, (top-right) $\phi^{*}_{\eta}$, (bottom-left) $\pi - \Delta\phi_{\gamma\gamma}$, and (bottom-right) $p_{T,\gamma\gamma}$. The PB model provides the best overall agreement with the experimental data across all observables, while the MKMRW and NLO-MRW models tend to underestimate the data in the intermediate regions but reproduce the measurements within uncertainties at low and high values.
• Figure 5: Comparison of the theoretical predictions from the NLO-MRW, MKMRW, and PB UPDF models with experimental data for (left) the diphoton invariant mass $m_{\gamma\gamma}$ and (right) the Collins–Soper angle $\left|\cos \theta^{*}_{\mathrm{(CS)}}\right|$. The PB model provides the best overall agreement with the data across both observables, whereas the NLO-MRW and MKMRW models tend to overestimate and underestimate the data, respectively, particularly in regions sensitive to higher factorization scales.