Going beyond Soft plus Virtual

TL;DR

This paper develops a formalism to sum soft-virtual and next-to-soft virtual contributions in QCD for hadron collider processes, enabling all-order predictions and improved resummation techniques.

Contribution

It introduces a novel all-order summation formalism for SV and NSV contributions using factorisation and transcendental structures, advancing precision in QCD calculations.

Findings

Exponential behavior of soft-collinear functions established.

All-order predictions for SV and NSV terms derived.

Integral representation suitable for Mellin space resummation provided.

Abstract

We present a formalism that sums up the soft-virtual (SV) and next-to-SV (NSV) diagonal contributions to inclusive colorless productions in hadron colliders to all orders in perturbative QCD. Using factorisation theorem, renormalisation group invariance and employing the transcendental structure of perturbative results, we show the exponential behavior of soft-collinear function. This allows us to predict certain SV and NSV terms to all orders from lower order information. We also present an integral representation for the coefficient functions which is suitable for Mellin $N$-space resummation.