Next-to-soft-virtual resummed rapidity distribution for Drell-Yan process to $\rm{\textbf{NNLO}+\overline{\textbf{NNLL}}}$

TL;DR

This paper provides advanced QCD predictions for the Drell-Yan rapidity distribution at the LHC, incorporating next-to-soft virtual resummation effects up to NNLO+NNLL accuracy, improving theoretical precision.

Contribution

It introduces a formalism for resumming next-to-soft virtual effects in the Drell-Yan process at NNLO+NNLL accuracy, focusing on quark-antiquark channels and demonstrating improved scale sensitivity.

Findings

Resummation adds approximately 4% correction at NLO and 1.2% at NNLO.

Inclusion of NSV resummation improves renormalization scale stability.

Absence of quark-gluon contributions indicates the need for higher-order NSV effects.

Abstract

We present the differential predictions for the rapidity distribution of a pair of leptons through the Drell-Yan (DY) process at the LHC taking into account the soft-virtual (SV) as well as next-to-soft virtual (NSV) resummation effects in QCD perturbation theory to next-to-next-to-leading-order plus next-to-next-to-leading-logarithmic ($\rm{{NNLO+\overline{NNLL}}}$) accuracy. We perform the resummation in two dimensional Mellin space using our recent formalism \cite{Ajjath:2020lwb} by limiting ourselves to contributions only from quark anti-quark ($q \bar q$) initiated channels. The resummed corrections to the fixed order results are computed through a matched formula using the minimal prescription procedure. We find that the resummation at next-to-leading-logarithmic (next-to-next-to-leading-logarithmic) level brings about 3.98\% (1.24\%) corrections respectively to the NLO (NNLO) results at the central scale value of $q=M_Z$ for 13 TeV LHC. We also observe that the sensitivity to the renormalisation scale gets improved substantially by the inclusion of NSV resummed predictions at $\rm \overline{NNLL}$ accuracy. Further, the lack of quark gluon ($qg$) initiated contributions to NSV part in the $\rm \overline{NNLL}$ resummed predictions leaves large factorisation scale dependence indicating their importance at NSV level as we go to higher orders in perturbation theory.