Soft-gluon resummation for boosted top-quark production at hadron colliders

TL;DR

The paper develops a unified factorization framework for boosted top-quark pair production, combining soft-gluon resummation with the double-soft and small-mass limits ($z\to1$, $m_t\ll M$). It constructs and evolves hard, soft, fragmentation, and heavy-flavor components to NNLL accuracy, and derives approximate NNLO corrections by exploiting known higher-order pieces. Through analytic resummation and limited numerical studies, the work demonstrates that including small-mass logarithms can refine predictions in the high invariant-mass region and provides a pathway to improved delta-function terms in NNLO. The framework offers a foundation for more precise predictions of the $M$-dependent top-pair cross section and can extend to other boosted, heavy-quark observables.

Abstract

We investigate the production of highly energetic top-quark pairs at hadron colliders, focusing on the case where the invariant mass of the pair is much larger than the mass of the top quark. In particular, we set up a factorization formalism appropriate for describing the differential partonic cross section in the double soft and small-mass limit, and explain how to resum simultaneously logarithmic corrections arising from soft gluon emission and from the ratio of the pair-invariant mass to that of the top quark to next-to-next-to-leading logarithmic accuracy. We explore the implications of our results on approximate next-to-next-to-leading order formulas for the differential cross section in the soft limit, pointing out that they offer a simplified calculational procedure for determining the currently unknown delta-function terms in the limit of high invariant mass.