Next to soft corrections to Drell-Yan and Higgs boson productions

We present a framework that resums threshold enhanced large logarithms to all orders in perturbation theory for the production of pair leptons Drell-Yan process and Higgs boson gluon fusion as well bottom quark annihilation. restrict ourselves contributions from diagonal partonic channels. These include distributions $((1\ensuremath{-}z{)}^{\ensuremath{-}1}{\mathrm{ln}}^{i}(1\ensuremath{-}z){)}_{+}$ resulting soft plus virtual (SV) ${\mathrm{ln}}^{i}(1\ensuremath{-}z)$ next-to-SV contributions. use collinear factorization renormalization group invariance achieve this. The former allows one define soft-collinear (SC) function encapsulates dynamics perturbative results strong coupling constant. logarithmic structure these is governed by universal infrared anomalous dimensions process-dependent functions Sudakov differential equation SC satisfies. solution obtained proposing an all-order ansatz dimensional regularization, owing several state-of-the-art available third order. $z$ space solutions thus provide integral representation sum up originating both configurations, conveniently Mellin $N$ space. show space, tower ${a}_{s}^{n}/{N}^{\ensuremath{\alpha}}{\mathrm{ln}}^{2n\ensuremath{-}\ensuremath{\alpha}}(N),{a}_{s}^{n}/{N}^{\ensuremath{\alpha}}{\mathrm{ln}}^{2n\ensuremath{-}1\ensuremath{-}\ensuremath{\alpha}}(N)\ensuremath{\cdots}$ $\ensuremath{\alpha}=0$, 1 summed ${a}_{s}$.