Next-to-next-to-leading order soft-gluon corrections in top quark hadroproduction

TL;DR

The paper advances precise predictions for top-quark hadroproduction by extending NNLO soft-gluon corrections to include subleading NNLO terms (NNNLL) and selected virtual contributions in both $q\overline{q}$ and $gg$ initial states, across 1PI and PIM kinematics. By providing full soft-plus-virtual structures for the partonic cross sections and scaling functions, it demonstrates that near threshold the 1PI and PIM results converge when these subleading terms are included, while away from threshold kinematic differences are diminished. Hadronic predictions for Tevatron and LHC show reduced scale dependence and improved convergence, with NNLO corrections enhancing the cross sections and preserving the differential distribution shapes. These results offer improved theoretical control over top-quark production, informing experimental analyses and PDF/scale choices at current and future colliders.

Abstract

We calculate next-to-next-to-leading order soft-gluon corrections to top quark total and differential cross sections in hadron colliders. We increase the accuracy of our previous estimates by including additional subleading terms, including next-to-next-to-next-to-leading-logarithmic and some virtual terms. We show that the kinematics dependence of the cross section vanishes near threshold and is reduced away from it. The factorization and renormalization scale dependence of the cross section is also greatly reduced. We present results for the top quark total cross sections and transverse momentum distributions at the Tevatron and the LHC.

Figures (10)

• Figure 1: The $\overline{\rm MS}$ scheme scaling functions multiplying the scale-dependent logarithms, $f_{ij}^{(2,1)}$ (left-hand side) and $f_{ij}^{(2,2)}$ (right-hand side). The upper plots are for the $q \overline q$ channel while the lower plots are for the $gg$ channel. The solid curves are for 1PI kinematics, the dashed for PIM kinematics.
• Figure 2: The $f_{ij}^{(2,0)}$ scaling functions in the $\overline{\rm MS}$ scheme. The left-hand side shows the results for the $q \overline q$ channel while the right-hand side shows the results for the $gg$ channel. The top plots show the NNLL result from Ref. KLMV. The center plots give the results through NNNLL and the bottom plots give the results including the virtual $\zeta$ terms. The solid curves are for 1PI kinematics, the dashed for PIM kinematics.
• Figure 3: The $q \overline q$ (left-hand side) and $gg$ (right-hand side) parton luminosities in $p \overline p$ collisions at $\sqrt{S} = 1.96$ TeV. The solid curves are calculated with $\mu = m = 175$ GeV while the upper dashed curves are with $\mu = m/2$ and the lower dashed curves with $\mu = 2m$.
• Figure 4: The $t \overline t$ total cross sections in $p \overline p$ collisions at $\sqrt{S} = 1.8$ TeV (left-hand side) and 1.96 TeV (right-hand side) as functions of $m$ for $\mu = m$. The NLO (solid), and approximate NNLO 1PI (dashed), PIM (dot-dashed) and average (dotted) results are shown.
• Figure 5: The NNLO $K$ factors at $\sqrt{S} = 1.8$ TeV as functions of top quark mass in $p \overline p$ collisions with $\mu = m$ (upper), $\mu = 2m$ (middle) and $\mu = m/2$ (lower). The curves show the ratio of the approximate NNLO 1PI (dashed), PIM (dot-dashed) and average (solid) cross sections to the NLO cross section.