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We present a formalism that sums up both soft-virtual (SV) and next to SV(NSV) contributions to all orders in perturbative QCD for the rapiditydistribution of any colorless particle produced in hadron colliders. We haveexploited the factorization properties and the renormalisation group (RG)invariance of the differential cross-section to achieve this. Using thestate-of-the-art multiloop and multileg results, we determine the complete NSVcontributions to third order in strong coupling constant for the rapiditydistributions for a pair of leptons in Drell-Yan and also for Higgs boson ingluon fusion as well as bottom quark annihilation. Using the integralrepresentation of our all order $z$ space result, we show how the NSVcontributions can be resummed in two-dimensional Mellin space.

Next-to-soft corrections for Drell-Yan and Higgs boson rapidity distributions beyond N$^3$LO