Weak corrections to four-parton processes

TL;DR

This work evaluates the purely weak one-loop corrections of order $O(\alpha_S^2 \alpha_W)$ to all relevant four-parton (two-to-two) subprocesses contributing to single-jet production at hadron colliders. Using infrared dipole subtraction and ${\overline{\mathrm{DR}}}$ renormalization with $\mu = M_Z$, the authors compute virtual weak corrections across 19 partonic channels, employing helicity-amplitude techniques and cross-checks to ensure reliability. They find negligible impact on the total cross section at the Tevatron, but substantial, energy-dependent effects at the LHC, with differential corrections reaching up to ~ $-40\%$ at high $E_T$ due to Sudakov logarithms, especially in quark-quark initiated channels. The study highlights the importance of including these EW effects in high-$E_T$ jet analyses, the potential influence of real $W/Z$ emission and NNLO EW terms, and provides a detailed appendix on the helicity formalism and topologies used for the calculation.

Abstract

We report on a calculation of the `mixed' strong and (purely) weak corrections through the order $α_{\mathrm{S}}^2α_{\mathrm{W}}$ to parton-parton processes in all possible channels at hadron colliders entering the single jet inclusive cross section. At both Tevatron and LHC, such effects are always negligible (below permille level) in the total integrated cross section whilst they become sizable in differential rates. Specifically, if such corrections are defined with respect to the full leading-order result of ${\cal O}(α_{\mathrm{S}}^2 +α_{\mathrm{S}}α_{\mathrm{EW}}+α_{\mathrm{EW}}^2)$, we find that, at the FNAL accelerator, they can reach the -5% benchmark in the jet transverse energy (at the kinematical limit of the machine, rendering their detection quite difficult). At the CERN collider, in the same observable, they exceed the -10% level already at 1 TeV and can reach -40% at 4 TeV, kinematic regions where such corrections will be comfortably observable for standard luminosity. In addition, such corrections are somewhat sensitive to the factorisation/renormalisation scale choice.

Figures (24)

• Figure 1: The set of interferences that contributes to process 1 ($gg\rightarrow q\bar{q}$) and, if we reverse the direction of time, 2 ($q\bar{q}\rightarrow gg$).
• Figure 2: Continuing the set of interferences that contribute to process 1 ($gg\rightarrow q\bar{q}$) and, if we reverse the direction of time, 2 ($q\bar{q}\rightarrow gg$).
• Figure 3: The set of interferences that contribute to process 3 ($qg\rightarrow qg$) and, if we reverse the direction of the fermion arrow, 4 ($\bar{q}g\rightarrow \bar{q}g$).
• Figure 4: Continuing the set of interferences that contribute to process 3 ($qg\rightarrow qg$) and, if we reverse the direction of the fermion arrow, 4 ($\bar{q}g\rightarrow \bar{q}g$).
• Figure 5: The set of interferences that contributes to process 5 ($qq\rightarrow qq$) and 6 ($\bar{q}\bar{q}\rightarrow \bar{q}\bar{q}$), the latter obtained by reversing the arrows on all fermion lines of the former.