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We present a systematic framework to study the threshold contributions of thedifferential rapidity distribution for the production of any number ofcolorless particles in the hadronic colliders. This has been achieved based onthe universality structure of the soft enhancements associated with the realemissions, along with the factorization property of the differential crosssection and the renormalization group invariance. In this formalism, we presenta universal soft-collinear operator to compute the soft virtual differentialcross section for a generic $2\rightarrow n$ scattering process up tonext-to-next-to-next-to-next-to-leading order (N$^4$LO) in perturbative QCD. Wealso provide a universal operator to perform the threshold resummation tonext-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. We explicitlypresent the approximate analytical results of the rapidity distributions atN$^4$LO and N$^3$LL for the Higgs boson production through gluon fusion andbottom quark annihilation, and also for the Drell-Yan production at thehadronic collider. \textcolor{black}{We extend our framework to include thenext to threshold contributions for the diagonal partonic channels.

Rapidity distribution at soft-virtual and beyond for n-colorless particles to N$^4$LO in QCD