Electroweak corrections to hadronic photon production at large transverse momenta

TL;DR

This work evaluates electroweak corrections to direct high-pT photon production at hadron colliders, deriving the complete one-loop weak corrections for bar q q -> gamma g and presenting compact high-energy NNLL asymptotics for large s_hat relative to MW^2. It also computes the dominant two-loop electroweak contributions and validates the high-energy approximations against full results. Numerically, the one-loop corrections can reach about -17% at the LHC (with pT around 2 TeV), while two-loop terms can add roughly +3%, underscoring the need to include these effects for precision predictions; at the Tevatron they are smaller (around -4% and negligible two-loop). The electroweak corrections notably affect the gamma/Z production ratio, highlighting their significance for phenomenology at current and future hadron colliders.

Abstract

We study the impact of electroweak radiative corrections on direct production of photons with high transverse momenta at hadron colliders. Analytic results for the weak one-loop corrections to the parton scattering reaction $\bar q q \to γg$ and its crossed variants are presented. For the high-energy region, where the corrections are strongly enhanced by logarithms of $\hat s/M_W^2$, we derive simple asymptotic expressions which approximate the exact one-loop results with high precision. The dominant two-loop electroweak contributions are also calculated. Numerical results are presented for the LHC and the Tevatron. The corrections are negative and their size increases with transverse momentum. For the LHC, where transverse momenta of 2 TeV or more can be reached, the size of the one- and two-loop effects amounts up to -17% and +3%, respectively. At the Tevatron, with transverse momenta up to 400 GeV, the one-loop corrections do not exceed -4% and the two-loop effects are negligible. Finally we compare the cross sections for hadronic production of photons and Z bosons and find that the electroweak corrections have an important impact on their ratio.

Figures (10)

• Figure 1: Tree-level Feynman diagrams for the process $\bar{q} q \to \gamma g$.
• Figure 2: One-loop Feynman diagrams for the process $\bar{q} q \to \gamma g$. The diagrams v5, v6 and b3 involve only charged weak bosons, $W^\pm$, whereas the other diagrams receive contributions from neutral and charged weak bosons, $V=Z,W^\pm$.
• Figure 3: Relative one-loop corrections to the partonic differential cross sections ${\mathrm{d}} \hat{\sigma}^{ij} / {\mathrm{d}} \cos \theta$ at $\cos \theta =0$ for (a) $\bar{u} u$ channel, (b) $\bar{d} d$ channel, (c) $g u$ channel, (d) $g d$ channel. The solid, dashed and dot-dashed lines denote the modulus of the $\hat{\cal R}$ ratios, as defined in the text, for the full NLO cross section, the NLL approximation and the NNLL approximation of the one-loop cross section, respectively.
• Figure 4: Transverse momentum distribution for $pp{\rightarrow} \gamma j$ at $\sqrt{s}=14 \,\mathrm{TeV}$. (a) LO (solid), NLO (dashed), NLL (dotted) and NNLL (dot-dashed) predictions. (b) Relative NLO (solid), NLL (dotted) and NNLL (dot-dashed) weak correction wrt. the LO distribution. (c) NLL (dotted) and NNLL (dot-dashed) approximations compared to the full NLO result.
• Figure 5: Relative NLO (solid) and NNLO (dotted) corrections to the $p_{\mathrm{T}}$ distribution for $pp{\rightarrow} \gamma j$ at $\sqrt{s}=14 \,\mathrm{TeV}$.