Transverse parton distribution and fragmentation functions at NNLO: the gluon case

Abstract

We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through O( 2 ) in dimensional regulator (finding discrepancy for the linearly polarized gluon TMDPDFs with a previous result in the literature). We find a nontrivial momentum conservation sum rule for the linearly polarized component for both TMDPDFs and TMDFFs in the N = 1 super-Yang-Mills theory. The TMDFFs are used to calculate the two-loop gluon jet function for the energy-energy correlator in Higgs gluonic decay in the back-to-back limit.

Transverse momentum dependent PDFs at N3LO

“…A natural future direction of this research is the calculation of the closely related TMD fragmentation functions at N 3 LO, which are required to describe the small-q T limit semi-inclusive deep inelastic scattering and are currently only known at NNLO [49,50,53].…”

“…TMDPDFs are composed of the TMD beam function B i (z, q T ) and the TMD soft function S( q T ). The soft function has been known at three loops since quite some time [43][44][45], and the quark beam function has been calculated at this accuracy recently [46][47][48][49][50][51], while the gluon beam function so far is only known at two loops [48,49,52,53]. In this paper, we fill this gap by calculating the full matching coefficient for the gluon beam function at N 3 LO.…”

“…[45], and the bare results through O( 4 ) at NLO and through O( 2 ) are verified against refs. [50,53]. Given that the logarithmic terms in eq.…”

Linearly polarized gluons at next-to-next-to leading order and the Higgs transverse momentum distribution

“…These results have been recently obtained in ref. [55] with an independent calculation using the exponential regulator of ref. [56] to regularize rapidity divergences.…”

Renormalization and matching for the Collins-Soper kernel from lattice QCD

“…TMDPDFs measure the transverse momentum q T carried by the struck parton. For perturbative q T Λ QCD , they can be calculated in terms of collinear parton distribution functions, and the resulting matching formula is known to next-to-next-to-leading order (NNLO) [20][21][22][23][24][25][26][27]. In contrast, for nonperturbative q T Λ QCD , TMDPDFs become genuinely nonperturbative objects which so far have only been extracted from measurements by performing global fits to a variety of experimental data sets, see e.g.…”