Full order_alpha electroweak and order alpha_s corrections to e^+e^- --> t t H

TL;DR

This paper delivers a complete one-loop treatment of both electroweak and QCD radiative corrections to the process $e^+e^- \rightarrow t\bar t H$ in the Standard Model, computed with the GRACE-loop framework in an on-shell scheme. It shows that, depending on the Higgs mass and collider energy, QCD corrections can be dominant near threshold due to Coulomb enhancement, while electroweak corrections can dominate near the cross-section maximum, with genuine weak corrections remaining sizable after QED subtraction. The results, including both the $\alpha$-scheme and the $G_\mu$-scheme, demonstrate the necessity of including full EW and QCD effects for a precision extraction of the top-Higgs Yukawa coupling at future linear colliders. The study also emphasizes scheme choices and the non-negligible impact of beyond-leading-log corrections on the predicted cross sections across the energy range 0.5–1 TeV.

Abstract

We present the full ${\cal O}(α)$ electroweak radiative corrections to associated Higgs top pair production in $e^+e^-$ collisions. We combine these results with a new calculation of the full one-loop QCD corrections. The computation is performed with the help of {\tt GRACE-loop}. We find that the ${\cal O}(α)$ correction can be larger than the ${\cal O}(α_s)$ corrections around the peak of the cross section especially for a light Higgs mass. At threshold these corrections are swamped by the QCD corrections which are enhanced by the gluon Coulomb contribution. We have also subtracted the complete QED corrections and expressed the genuine weak correction both in the $α$-scheme and the $G_μ$-scheme. This reveals that the genuine weak corrections are not negligible and should be taken into account for a precision measurement of this cross section and the extraction of the Yukawa $t \bar t H$ coupling.

Figures (2)

• Figure 1: A small selection of different classes of loop diagrams contributing to $e^+ e^-\rightarrow t \bar{t} H$. We keep the same graph numbering as that produced by the system. The first class of diagrams (the first 5 diagrams) are QED corrections, with the first row consisting of final state corrections. The QCD corrections diagrams can be inferred from the latter. The pentagon is a QED initial-final state interference. The second class groups genuine electroweak corrections including self-energy, triangle, box and pentagon corrections. Note that for the self-energy diagrams we collect all contributions including the counterterms in the blob. Note that the top self-energy Graph 2260 also contains a photonic correction that should be included in the first class of diagrams.
• Figure 2: (a) Total cross section as a function of the centre of mass energy for $M_H=120$GeV. We show the total cross sections for the tree level, full ${\cal O}(\alpha)$ and ${\cal O}(\alpha_s)$ level in (a). The relative corrections are shown in (b). Solid lines are tree level, dashed lines are the full ${\cal O}(\alpha)$ and dotted lines are the ${\cal O}(\alpha_s)$ corrections. We take $\alpha_s(M_t)=0.10754$. In addition, the genuine weak correction $\delta_W$ and the relative correction $\delta_W^{G_\mu}$ in the $G_\mu$ scheme are presented.