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We present the resummed predictions for inclusive cross section for Drell-Yan(DY) production up to next-to-next-to leading logarithmic ($\rm \overline{NNLL}$) accuracy taking into account both soft virtual (SV) and next-to SV(NSV) threshold logarithms. We restrict ourselves to resummed contributionsonly from quark anti-quark ($q \bar q$) initiated channels. The resummation isperformed in Mellin-$N$ space. We derive the $N$-dependent coefficients and the$N$-independent constants to desired accuracy for our study. The resummedresults are matched through the minimal prescription procedure with the fixedorder results. We find that the resummation, taking into account the NSV terms,appreciably increases the cross section while decreasing the sensitivity torenormalisation scale. \textcolor{black}{We observe that, at 13 TeV LHCenergies, the SV+NSV resummation at $\rm \overline{ NLL} (\rm \overline{NNLL})$gives about 8\% (2\%) corrections respectively to the NLO (NNLO) results forthe considered $Q$ range: 150-3500 GeV}. In addition, the absence of quarkgluon initiated contributions to NSV part in the resummed terms leaves largefactorisation scale dependence indicating their importance at NSV level. Wealso study the numerical impact of $N$-independent constants and explore theambiguity involved in exponetiating them. Finally we present our predictionsfor the neutral Drell-Yan process at various center of mass of energies.

Next-to SV resummed Drell-Yan cross section beyond leading-logarithm