NNLO soft function for top quark pair production at small transverse momentum

Abstract

The cross section for top quark pair production factorizes at small transverse momentum of the heavy quark pair, q T . One of the key ingredients that appears in the factorization formula is the soft function, which mediates soft gluon exchanges between particles and gives rise to colour correlations. We present the complete result for the small-q T soft function at the next-to-next-to-leading order. This is the last missing element needed to calculate the NNLO cross section for top quark pair production by means of the q T slicing method. In order to evaluate divergent integrals appearing in the calculation, we develop methods based on sector decomposition and differential equations. We present an extensive validation of our framework. In particular, we recover results predicted by the renormalization group, which constitutes a direct demonstration of validity of the small-q T factorization at NNLO. We provide complete results for the real and imaginary part of the soft function, which are ready for application in the calculation of the tt cross section at NNLO.

Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order

“…Once fully differential N 3 LO prediction with q T subtraction becomes available, it would also be important to consider the perturbative power corrections, where rapidity logarithms beyond leading power need to be understood better [28,91], see also [92,93]. It would also be interesting to study if the idea of generalized IBPs introduced in this Letter, perhaps with some modification, is helpful in problems where non-standard Feynman propagator are encountered, such as two-loop q T soft function for topquark pair production [94,95], or thrust and hemisphere soft function [89,90,96] with a step function in the integrand. Integrals with the latter form is particularly interesting since they appear frequently in precision jet substructure [97].…”

Bottom-quark production at hadron colliders: fully differential predictions in NNLO QCD

“…An independent computation of these contributions is presented in ref. [63] for the case of top-quark pair production. With the results of ref.…”

Top-quark hadroproduction in NNLO QCD

“…The integration of the missing soft contributions allowed us to implement top pair production 2 It is worth observing that, while we were progressing with our analytic computations, a fully numerical calculation has been carried out in the SCET formalism [38].…”