Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO

Abstract

In this paper we calculate analytically the perturbative matching coefficients for unpolarized quark and gluon Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) through Next-to-Next-to-Next-to-Leading Order (N${}^3$LO) in QCD. The N${}^3$LO TMD PDFs are calculated by solving a system of differential equation of Feynman and phase space integrals. The TMD FFs are obtained by analytic continuation from space-like quantities to time-like quantities, taking into account the probability interpretation of TMD PDFs and FFs properly. The coefficient functions for TMD FFs exhibit double logarithmic enhancement at small momentum fraction $z$. We resum such logarithmic terms to the third order in the expansion of ${\alpha }_s$. Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments.

references added

References in corpus (15)

• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Soft-/rapidity- anomalous dimensions correspondence
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• 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
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• Renormalization, Wilson lines, and transverse-momentum dependent parton distribution functions
• Fiducial $q_T$ resummation of color-singlet processes at N${}^3$LL+NNLO
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Gluon Case
• Fully double-logarithm-resummed cross sections
• Collinear expansion for color singlet cross sections

Cited by in corpus (22)

• Higgs $p_T$ Spectrum and Total Cross Section with Fiducial Cuts at Third Resummed and Fixed Order in QCD
• Di-lepton Rapidity Distribution in Drell-Yan Production to Third Order in QCD
• Fiducial Drell-Yan production at the LHC improved by transverse-momentum resummation at N${}^4$LL+N${}^3$LO
• Third order fiducial predictions for Drell-Yan at the LHC
• The Four Loop QCD Rapidity Anomalous Dimension
• Factorization connecting continuum and lattice TMDs
• Factorization for Azimuthal Asymmetries in SIDIS at Next-to-Leading Power
• Global analysis of fragmentation functions to charged hadrons with high-precision data from the LHC
• Transverse momentum dependent distributions in dijet and heavy hadron pair production at EIC
• Projected transverse momentum resummation in top-antitop pair production at LHC
• Transverse momentum moments
• Combining nonperturbative transverse momentum dependence with TMD evolution
• Neutrino-tagged jets at the Electron-Ion Collider
• The NNLO quark beam function for jet-veto resummation
• Transverse Energy-Energy Correlators in the Color-Glass Condensate at the Electron-Ion Collider
• Global analysis of fragmentation functions to light neutral hadrons
• Transverse Momentum Dependent Gluon Distribution within High Energy Factorization at Next-to-Leading Order
• Region analysis of $H\to \gamma \gamma$ via a bottom quark loop
• Transverse Energy-Energy Correlator for Vector Boson-Tagged Hadron Production in $pp$ and $pA$ collisions
• Applying different angular ordering constraints and $k_t$-factorization approaches to the single inclusive hadron production in the $e^{+}{e}^{-}$ annihilation processes
• The Diphoton $q_T$ spectrum at N${}^3$LL${}^{\prime }$+NNLO
• Evolution of unpolarized transverse momentum dependent parton distributions of twist-3