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

References in corpus (17)

• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• FIRE5: a C++ implementation of Feynman Integral REduction
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Production of Drell--Yan lepton pairs in hadron collisions: transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy
• QCD transverse-momentum resummation in gluon fusion processes
• Soft-/rapidity- anomalous dimensions correspondence
• The Collinear Limit of the Energy-Energy Correlator
• Next-to-Next-to-Leading Order Evolution of Non-Singlet Fragmentation Functions
• Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
• On Third-Order Timelike Splitting Functions and Top-Mediated Higgs Decay into Hadrons
• Transverse-momentum resummation for top-quark pairs at hadron colliders
• Lepton-jet Correlations in Deep Inelastic Scattering at the Electron-Ion Collider
• Gluon-gluon contributions to the production of continuum diphoton pairs at hadron colliders
• Analytic Next-To-Leading Order Calculation of Energy-Energy Correlation in Gluon-Initiated Higgs Decays
• Linearly polarized gluons in charmonium and bottomonium production in color octet model
• Improvement for Color Glass Condensate factorization: single hadron production in pA collisions at next-to-leading order

Cited by in corpus (6)

• Top-pair production at the LHC with MiNNLO${}_{\mathrm{PS}}$
• The $q_T$ and $\Delta \varphi$ spectra in W and Z production at the LHC at N${}^3$LL'+N${}^2$LO
• Collinear expansion for color singlet cross sections
• Two-loop bottom mass effects on the Higgs transverse momentum spectrum in top-induced gluon fusion
• One-loop corrections to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD
• Fully differential Higgs boson pair production at N${}^3$LO with top quark mass effects