Next-to-soft corrections for Drell-Yan and Higgs boson rapidity distributions beyond N$^3$LO

TL;DR

This paper develops a formalism to sum soft-virtual and next-to-soft corrections to all orders in perturbative QCD for rapidity distributions of colorless particles at hadron colliders, improving theoretical precision.

Contribution

It introduces a novel all-order resummation method for NSV contributions in rapidity distributions, extending beyond previous fixed-order calculations.

Findings

Complete NSV contributions at third order for Drell-Yan and Higgs production.

Resummation of NSV contributions in two-dimensional Mellin space.

Enhanced theoretical accuracy for rapidity distribution predictions.

Abstract

We present a formalism that sums up both soft-virtual (SV) and next to SV (NSV) contributions to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We have exploited the factorization properties and the renormalisation group (RG) invariance of the differential cross-section to achieve this. Using the state-of-the-art multiloop and multileg results, we determine the complete NSV contributions to third order in strong coupling constant for the rapidity distributions for a pair of leptons in Drell-Yan and also for Higgs boson in gluon fusion as well as bottom quark annihilation. Using the integral representation of our all order $z$ space result, we show how the NSV contributions can be resummed in two-dimensional Mellin space.