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 mathcal{O} (ϵ2) in dimensional regulator. We find a nontrivial momentum conservation sum rule for the linearly polarized component for both TMDPDFs and TMDFFs in the mathcal{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.
Highlights
In this paper, we present the results for the perturbative matching coefficients at Next-to-Next-to Leading Orders (NNLO) for gluon transverse momentum dependent parton distribution functions (TMDPDFs) and TMDFFs
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 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
Summary
The bare gluon TMDPDF can be defined in terms of SCET [65,66,67,68,69] collinear gauge fields. Where Aan,⊥μ is the gauge invariant collinear gluon field with color index a and Lorentz index μ. For sufficiently small b⊥, the gluon TMDPDFs admit operator production expansion onto the usual collinear PDFs, Bgb/aNre,μν (x, b⊥) =. The coefficient functions can be decomposed into two independent Lorentz structures, Igbiare,μν (ξ, b⊥). The matching coefficients Igbiare,μν(ξ, b⊥) in eq (2.2) do not depend on the actual hadron. The usual bare partonic collinear PDFs are just φbi/ajre(x) = δijδ(1 − x), so one has Igbiare,μν (x, b⊥) = Bgbiare,μν (x, b⊥). The TMDPDFs, as well as their matching coefficients, contain both UV and rapidity divergences. We present the bare results for the coefficient functions through two loops in QCD
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