Boosted top production: factorization and resummation for single-particle inclusive distributions
Andrea Ferroglia, Simone Marzani, Ben D. Pecjak, Li Lin Yang
TL;DR
The authors establish a factorization framework for boosted top production that separates hard virtual corrections from three distinct soft-radiation components in the small-mass, double-soft limit, enabling simultaneous resummation of soft and small-mass logarithms for single-particle inclusive observables. They identify five one-scale functions—three from soft real radiation (massless soft S, soft-collinear to the top S_D, soft-collinear to the anti-top S_B) plus two from hard physics (H and C_D)—and provide NNLO results for all but the heavy-quark loop virtual piece. The work connects the soft-soft-collinear structure to known objects like the heavy-quark fragmentation function and heavy-quark jet function, and computes a new NNLO massless soft function to complete the soft+virtual description near threshold. They also outline RG equations and the path to NNLL resummation in the small-mass regime, establishing a robust framework for precision predictions of boosted top-quark differential distributions. This offers a near-complete, high-precision tool for phenomenology of boosted tops and potential sensitivity to new physics in the high-p_T tail.
Abstract
We study single-particle inclusive (1PI) distributions in top-quark pair production at hadron colliders, working in the highly boosted regime where the top-quark p_T is much larger than its mass. In particular, we derive a novel factorization formula valid in the small-mass and soft limits of the differential partonic cross section. This provides a framework for the simultaneous resummation of soft gluon corrections and small-mass logarithms, and also an efficient means of obtaining higher-order corrections to the differential cross section in this limit. The result involves five distinct one-scale functions, three of which arise through the subfactorization of soft real radiation in the small-mass limit. We list the NNLO corrections to each of these functions, building on results in the literature by performing a new calculation of a soft function involving four light-like Wilson lines to this order. We thus obtain a nearly complete description of the small-mass limit of the differential partonic cross section at NNLO near threshold, missing only terms involving closed top-quark loops in the virtual corrections.