The NNLO soft function for the pair invariant mass distribution of boosted top quarks

TL;DR

This paper computes the NNLO corrections to the soft function in top-quark pair production at high invariant mass, completing the theoretical framework for precise differential cross section predictions.

Contribution

It provides the first calculation of the NNLO soft function for boosted top quark pair production, using Wilson loop techniques and non-abelian exponentiation.

Findings

The NNLO soft function is surprisingly simple in form.

The calculation completes the NNLO theoretical description for the soft radiation.

Results facilitate more accurate predictions of top-quark pair production at colliders.

Abstract

At high values of the pair invariant mass the differential cross section for top-quark pair production at hadron colliders factorizes into soft, hard, and fragmentation functions. In this paper we calculate the next-to-next-to-leading-order (NNLO) corrections to the soft function appearing in this factorization formula, thus providing the final piece needed to evaluate at NNLO the differential cross section in the virtual plus soft approximation in the large invariant-mass limit. Technically, this amounts to evaluating the vacuum expectation value of a soft Wilson loop operator built out of light-like Wilson lines for each of the four partons participating in the hard scattering process, with a certain constraint on the total energy of the soft radiation. Our result turns out to be surprisingly simple, because in the sum of all graphs the three and four parton contributions multiply color structures whose coefficients are governed by the non-abelian exponentiation theorem.