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

Abstract

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 rapidity distribution of any colorless particle produced in hadron colliders. We have exploited the factorization properties and the renormalisation group (RG) invariance of the differential cross-section to achieve this. Using the state-of-the-art multiloop and multileg results, we determine the complete NSV contributions to third order in strong coupling constant for the rapidity distributions for a pair of leptons in Drell-Yan and also for Higgs boson in gluon fusion as well as bottom quark annihilation. Using the integral representation of our all order $z$ space result, we show how the NSV contributions can be resummed in two-dimensional Mellin space.

6 Pages and 1 Table

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• Next-to-Next-to-Leading Order QCD Corrections to Polarized Semi-Inclusive Deep-Inelastic Scattering
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• Higgs boson rapidity distribution in bottom annihilation at NNLL and beyond
• Next to Soft Threshold Resummation for $VH$ Production
• Threshold resummation for $Z$-boson pair production at NNLO+NNLL