Rapidity distribution at soft-virtual and beyond for n-colorless particles to N$^4$LO in QCD

TL;DR

This paper develops a universal framework for calculating rapidity distributions of colorless particles in hadron colliders at very high perturbative orders, improving precision for processes like Higgs and Drell-Yan production.

Contribution

It introduces a universal soft-collinear operator for N$^4$LO calculations and extends threshold resummation to N$^3$LL accuracy in QCD.

Findings

Explicit N$^4$LO rapidity distribution results for Higgs and Drell-Yan production.

Universal operators enable systematic high-order calculations.

Enhanced theoretical precision for collider predictions.

Abstract

We present a systematic framework to study the threshold contributions of the differential rapidity distribution for the production of any number of colorless particles in the hadronic colliders. This has been achieved based on the universality structure of the soft enhancements associated with the real emissions, along with the factorization property of the differential cross section and the renormalization group invariance. In this formalism, we present a universal soft-collinear operator to compute the soft virtual differential cross section for a generic $2\rightarrow n$ scattering process up to next-to-next-to-next-to-next-to-leading order (N$^4$LO) in perturbative QCD. We also provide a universal operator to perform the threshold resummation to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. We explicitly present the approximate analytical results of the rapidity distributions at N$^4$LO and N$^3$LL for the Higgs boson production through gluon fusion and bottom quark annihilation, and also for the Drell-Yan production at the hadronic collider. \textcolor{black}{We extend our framework to include the next to threshold contributions for the diagonal partonic channels.