Abstract
We present a systematic framework to study the threshold contributions of the differential rapidity distribution for the production of any number of colorless particles in the hadronic colliders. This has been achieved based on the universality structure of the soft enhancements associated with the real emissions, along with the factorization property of the differential cross section and the renormalization group invariance. In this formalism, we present a universal soft-collinear operator to compute the soft virtual differential cross section for a generic 2rightarrow n scattering process up to next-to-next-to-next-to-next-to-leading order (hbox {N}^4LO) in perturbative QCD. We also provide a universal operator to perform the threshold resummation to next-to-next-to-next-to-leading logarithmic (hbox {N}^3LL) accuracy. We explicitly present the approximate analytical results of the rapidity distributions at hbox {N}^4LO and hbox {N}^3LL for the Higgs boson production through gluon fusion and bottom quark annihilation, and also for the Drell-Yan production at the hadronic collider. We extend our framework to include the next to threshold contributions for the diagonal partonic channels.
Highlights
IntroductionUnlike the inclusive crosssection, the differential rapidity distribution and its radiative corrections are computed only for a limited number of scattering processes
Sion, an enhanced amount of effort by the theoretical physicists will be called for
We restrict ourselves to the discussion of differential rapidity distribution for the production of n-number of colorless particles in the hadronic collision within the realm of perturbative quantum chromodynamics (QCD)
Summary
Unlike the inclusive crosssection, the differential rapidity distribution and its radiative corrections are computed only for a limited number of scattering processes. [7,8], a formalism to incorporate the soft-gluon contribution to the rapidity distribution for the production of a colorless final state in hadron collider is presented which, in this article, is extended to the case of any number of final state colorless particles. We extend the formalism for computing the SV differential rapidity distribution and its resummation to any 2 → n scattering process at the hadron collider and we provide the results to next-to-N3LO (N4LO) and next-to-NNLL (N3LL) in terms of generic quantities in Online Resource. We provide the approximate results of the rapidity distributions at N4LO and N3LL explicitly for the Higgs boson production through gluon fusion and bottom quark annihilation, and for the Drell-Yan production. All the results to N4LO and N3LL in terms of generic quantities are presented in Online Resource in Mathematica format which can be used for any generic 2 → n process once the corresponding virtual matrix element becomes available provided the soft distribution function for Sudakov type process is known
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