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 $\mathcal{O}({\epsilon }^2)$ 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 $\mathcal{N}=1$ 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.

32 pages

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Cited by in corpus (39)

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• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
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• The $q_T$ and $\Delta \varphi$ spectra in W and Z production at the LHC at N${}^3$LL'+N${}^2$LO
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• Projected transverse momentum resummation in top-antitop pair production at LHC
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• Collinear functions for QCD resummations
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• QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider
• Jet-veto resummation at N${}^3$LL${}_{\text{p}}$+NNLO in boson production processes
• The NNLO quark beam function for jet-veto resummation
• Single-inclusive hadron production in electron-positron annihilation at next-to-next-to-next-to-leading order in QCD
• Two-loop bottom mass effects on the Higgs transverse momentum spectrum in top-induced gluon fusion
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• N${}^3$LL + $\mathcal{O}({\alpha }_s^2)$ predictions of lepton-jet azimuthal angular distribution in deep-inelastic scattering
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• Energy Correlators Beyond Angles
• Region analysis of $H\to \gamma \gamma$ via a bottom quark loop
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• $q_T$-slicing with multiple jets
• One-loop transverse-momentum-dependent soft function at higher orders in the dimensional regulator
• Transverse momentum dependent distribution functions in the threshold limit
• Fully differential Higgs boson pair production at N${}^3$LO with top quark mass effects
• Evolution of unpolarized transverse momentum dependent parton distributions of twist-3