Weak corrections to gluon-induced top-antitop hadro-production

TL;DR

This paper computes purely weak virtual one-loop corrections to gluon-induced top-antitop production at the LHC, focusing on the gg→tt̄ subprocess at order α_s^2 α_W and excluding real Z bremsstrahlung. The authors implement a thorough one-loop calculation in the DRbar scheme, verify results with independent tools, and analyze both inclusive and differential observables, including spin asymmetries. They find a small overall cross-section correction (~-0.6%) but sizeable differential effects (up to -10% in high-p_T regions) and notable corrections to parity-conserving spin asymmetries (up to ±12% near LO-zero points), with parity-violating asymmetries at permille levels. The findings underscore the necessity of incorporating weak corrections into comprehensive LHC predictions and indicate directions for combining with related QCD/EW studies and exploring real Z contributions and NNLO effects.

Abstract

We calculate purely weak virtual one-loop corrections to the production cross section of top-antitop pairs at the Large Hadron Collider via the gluon-gluon fusion subprocess. We find very small negative corrections to the total cross section, of order -0.6%, but significantly larger effects to the differential one, particularly in the transverse momentum distribution, of order -5% to -10% (in observable regions). In case of parity-conserving spin-asymmetries of the final state, $α_{\mathrm{S}}^2α_{\mathrm{W}}$ corrections are typically of a few negative percent, with the exception of positive and negative peaks at $+12%$ and -5%, respectively (near where the tree-level predictions change sign), while those arising in parity-violating asymmetries (which are identically zero in QCD) are typically at a level of a few permille.

Figures (4)

• Figure 1: Differential distributions of the subprocess $gg\to t\bar{t}$ through the ${\cal O}(\alpha_{\mathrm{S}}^2)$ (top frames, dotted) and the ${\cal O}(\alpha_{\mathrm{S}}^2\alpha_{\mathrm{W}})$ (top frames, solid) as well as the percentage of the latter with respect to the former (bottom frames, solid) for the (anti)top transverse momentum $p_T$, the top-antitop invariant mass $M_{t\bar{t}}$ and the (anti)top pseudorapidity $\eta_t$. (Lightly/Red coloured solid tracts in logarithmic scale are intended to be negative.)
• Figure 2: The differential spin asymmetry $A_{LL}$ (as defined in the text) of the subprocess $gg\to t\bar{t}$ through the ${\cal O}(\alpha_{\mathrm{S}}^2)$ (top frame, dotted) and the ${\cal O}(\alpha_{\mathrm{S}}^2\alpha_{\mathrm{W}})$ (top frame, solid). (Note that the LO QCD contribution changes sign at $\approx900$ GeV and is heavily dependent on $M_{t\bar{t}}$ whereas the ${\cal O}(\alpha_{\mathrm{S}}^2\alpha_{\mathrm{W}})$ correction is not.) Just below the top frame we show the percentage correction to the (non-zero) LO QCD asymmetry for $A_{LL}$ due to ${\cal O}(\alpha_{\mathrm{S}}^2\alpha_{\mathrm{W}})$ effects. The lower two frames display the asymmetries $A_L$ and $A_{PV}$ (as defined in the text), which vanish exactly in LO QCD, through the same order. The asymmetries are calculated along the helicity axis as a function of the top-antitop invariant mass $M_{t\bar{t}}$.
• Figure 3: The absolute size of the ${\cal O}(\alpha_{\mathrm{S}}^2\alpha_{\mathrm{W}})$ corrections to the subprocess $gg\to t\bar{t}$ for the distribution in (anti)top pseudorapidity $\eta_t$ (top-left frame) and the differential spin asymmetries (as defined in the text), for $M_H=150$ GeV (solid) and $M_H=200$ GeV (dotted). The asymmetries are calculated along the helicity axis as a function of the top-antitop invariant mass $M_{t\bar{t}}$.
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