Collinear expansion for color singlet cross sections

Abstract

We demonstrate how to efficiently expand cross sections for color-singlet production at hadron colliders around the kinematic limit of all final state radiation being collinear to one of the incoming hadrons. This expansion is systematically improvable and applicable to a large class of physical observables. We demonstrate the viability of this technique by obtaining the first two terms in the collinear expansion of the rapidity distribution of the gluon fusion Higgs boson production cross section at next-to-next-to leading order (NNLO) in QCD perturbation theory. Furthermore, we illustrate how this technique is used to extract universal building blocks of scattering cross section like the N-jettiness and transverse momentum beam function at NNLO.

Unpolarized quark and gluon TMD PDFs and FFs at N3LO

“…Recently a first step towards N 3 LO TMD distributions have been achieved in [47] by calculating the unpolarized quark TMD PDFs, extending and significantly improving upon the methods in [26,27]. Subsequently, both unpolarized quark and gluon TMD PDFs are obtained in [48], based on an independent method from [49]. In this paper we continue our calculation in [47], and present the N 3 LO results for unpolarized quark TMD FFs, and unpolarized gluon TMD PDFs and FFs.…”

TMD fragmentation functions at N3LO

“…In particular, in ref. [62] we showed that the corresponding partonic coefficient function is given by…”

“…In this section we briefly review the method introduced in ref. [62] to expand cross sections in the kinematic limit where all final-state radiation becomes collinear to the parton with momentum p 1 or p 2 . In order to illustrate this, it is instructive to decompose the momentum k into its components along these directions,…”

“…More details on how such an expansion can be performed for multiloop partonic coefficient functions can be found in ref. [62].…”

“…TMD parton distribution functions (TMDPDFs), the initial-state counterparts of TMDFFs, are already known at this order [60,61]. Our calculation relies on a recently developed method to expand hadron collider cross sections around the limit where final state QCD radiation is collinear to an incoming parton [62]. We demonstrate explicitly how partonic cross sections for the production of electro-weak gauge bosons can be related to DIS cross sections via analytic continuation.…”