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

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 ($\mathrm{NNLO}+\overline{\mathrm{NNLL}}$) 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 $\overline{\mathrm{NNLL}}$ accuracy. Further, the lack of quark gluon ($qg$) initiated contributions to NSV part in the $\overline{\mathrm{NNLL}}$ resummed predictions leaves large factorisation scale dependence indicating their importance at NSV level as we go to higher orders in perturbation theory.

Comments: 21 pages, 9 figures, 7 tables. We have corrected some typos in equations 10,11, B3 and B6 and also added Eq 12 in this version