Next-to-soft-virtual resummed rapidity distribution for the Drell-Yan process to NNLO + (NNLL)over-bar

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 (NNLO + (NNLL) over bar) accuracy. We perform the resummation in two-dimensional Mellin space using our recent formalism [A. H. Ajjath et al., Phys. Rev. D 103, L111502 (2021)] by limiting ourselves to contributions only from quark-antiquark (q (q) over bar) initiated channels. The resummed corrections to the fixed-order results arc 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. We also observe that the sensitivity to the renormalization scale gets improved substantially by the inclusion of NSV resummed predictions at (NNLL) over bar accuracy. Further, the lack of quark gluon (qg) initiated contributions to the NSV part in the (NNLL ) over bar resummed predictions leaves large factorization scale dependence, indicating their importance at NSV level as we go to higher orders in perturbation theory.