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We present the differential predictions for the rapidity distribution of apair of leptons through the Drell-Yan (DY) process at the LHC taking intoaccount the soft-virtual (SV) as well as next-to-soft virtual (NSV) resummationeffects in QCD perturbation theory to next-to-next-to-leading-order plusnext-to-next-to-leading-logarithmic ($\rm{{NNLO+\overline{NNLL}}}$) accuracy.We perform the resummation in two dimensional Mellin space using our recentformalism \cite{Ajjath:2020lwb} by limiting ourselves to contributions onlyfrom quark anti-quark ($q \bar q$) initiated channels. The resummed correctionsto the fixed order results are computed through a matched formula using theminimal prescription procedure. We find that the resummation atnext-to-leading-logarithmic (next-to-next-to-leading-logarithmic) level bringsabout 3.98\% (1.24\%) corrections respectively to the NLO (NNLO) results at thecentral scale value of $q=M_Z$ for 13 TeV LHC. We also observe that thesensitivity to the renormalisation scale gets improved substantially by theinclusion of NSV resummed predictions at $\rm \overline{NNLL}$ accuracy.Further, the lack of quark gluon ($qg$) initiated contributions to NSV part inthe $\rm \overline{NNLL}$ resummed predictions leaves large factorisation scaledependence indicating their importance at NSV level as we go to higher ordersin perturbation theory.

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