Renormalization-group improved predictions for top-quark pair production at hadron colliders

Abstract

Precision predictions for phenomenologically interesting observables such as the $t\bar{t}$ invariant mass distribution and forward-backward asymmetry in top-quark pair production at hadron colliders require control over the differential cross section in perturbative QCD. In this paper we improve existing calculations of the doubly differential cross section in the invariant mass and scattering angle by using techniques from soft-collinear effective theory to perform an NNLL resummation of threshold logarithms, which become large when the invariant mass M of the top-quark pair approaches the partonic center-of-mass energy $\sqrt {{\hat{s}}}$. We also derive an approximate formula for the differential cross section at NNLO in fixed-order perturbation theory, which completely determines the coefficients multiplying the singular plus distributions in the variable $\left( {1 - {{{{M^2}}} \left/ {{\hat{s}}} \right.}} \right)$. We then match our results in the threshold region with the exact results at NLO in fixed-order perturbation theory, and perform a numerical analysis of the invariant mass distribution, the total cross section, and the forward-backward asymmetry. We argue that these are the most accurate predictions available for these observables at present. Using MSTW2008NNLO parton distribution functions (PDFs) along with α _s (M _Z ) = 0.117 and m _t = 173.1 GeV, we obtain for the inclusive production cross sections at the Tevatron and LHC the values ${{{\sigma }}_{\text{Tevatron}}} = \left( {6.30\pm 0.19_{ - 0.23}^{ + 0.31}} \right){\text{pb}}$ and σ _LHC = (149 ± 7 ± 8) pb, where the first error results from scale variations while the second reflects PDF uncertainties.