Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order

Abstract

The transverse momentum dependent parton distribution/fragmentation functions (TMDs) are essential in the factorization of a number of processes like Drell-Yan scattering, vector boson production, semi-inclusive deep inelastic scattering, etc. We provide a comprehensive study of unpolarized TMDs at next-to-next-to-leading order, which includes an explicit calculation of these TMDs and an extraction of their matching coefficients onto their integrated analogues, for all flavor combinations. The obtained matching coefficients are important for any kind of phenomenology involving TMDs. In the present study each individual TMD is calculated without any reference to a specific process. We recover the known results for parton distribution functions and provide new results for the fragmentation functions. The results for the gluon transverse momentum dependent fragmentation functions are presented for the first time at one and two loops. We also discuss the structure of singularities of TMD operators and TMD matrix elements, crossing relations between TMD parton distribution functions and TMD fragmentation functions, and renormalization group equations. In addition, we consider the behavior of the matching coefficients at threshold and make a conjecture on their structure to all orders in perturbation theory.

40 pages, 2 figures. v2: minor changes, accepted for publication in JHEP. v3: typo corrected in eq.(2.21), results unchanged

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Cited by in corpus (132)

• Large-Momentum Effective Theory
• Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production
• Parton Fragmentation Functions
• Analysis of vector boson production within TMD factorization
• Transverse-momentum-dependent parton distributions up to N${}^3$LL from Drell-Yan data
• Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum
• Soft-/rapidity- anomalous dimensions correspondence
• Fiducial distributions in Higgs and Drell-Yan production at N${}^3$LL+NNLO
• Higgs boson production at the LHC using the $q_T$ subtraction formalism at N${}^3$LO QCD
• Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
• Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order
• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• Power corrections and renormalons in parton quasi-distributions
• Resummation of Transverse Momentum Distributions in Distribution Space
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
• Transverse momentum dependent PDFs at N${}^3$LO
• MiNNLO${}_{\text{PS}}$: A new method to match NNLO QCD to parton showers
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• Transverse-momentum-dependent gluon distribution functions in a spectator model
• Precise QCD Description of the Higgs Boson Transverse Momentum Spectrum
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case
• The transverse momentum spectrum of weak gauge bosons at N${}^3$LL+NNLO
• Transverse momentum dependent distributions with jets
• Di-lepton Rapidity Distribution in Drell-Yan Production to Third Order in QCD
• Transverse momentum dependent distributions in $e^{+}{e}^{-}$ and semi-inclusive deep-inelastic scattering using jets
• The Transverse Energy-Energy Correlator in the Back-to-Back Limit
• Third order fiducial predictions for Drell-Yan at the LHC
• Next-to-next-to-leading order event generation for top-quark pair production
• Self-contained definition of the Collins-Soper kernel
• The gluon-fusion production of Higgs boson pair: N${}^3$LO QCD corrections and top-quark mass effects
• Systematic analysis of double-scale evolution
• Transverse momentum dependent factorization for lattice observables
• Linearly polarized gluons at next-to-next-to leading order and the Higgs transverse momentum distribution
• Connecting Different TMD Factorization Formalisms in QCD
• Extraction of the Sivers function from SIDIS, Drell-Yan, and $W^{\pm }/Z$ boson production data with TMD evolution
• Proper TMD factorization for quarkonia production: $pp\to {\eta }_{c,b}$ as a study case
• Jet axes and universal transverse-momentum-dependent fragmentation
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Gluon Case
• Global analysis of the Sivers functions at NLO+NNLL in QCD
• Probing Transverse-Momentum Distributions With Groomed Jets
• PDF bias and flavor dependence in TMD distributions
• Twist-2 matching of transverse momentum dependent distributions
• Analytic Continuation and Reciprocity Relation for Collinear Splitting in QCD
• A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO
• Top-pair production at the LHC with MiNNLO${}_{\mathrm{PS}}$
• Fiducial Higgs and Drell-Yan distributions at N${}^3$LL${}^{\prime }$+NNLO with RadISH
• Towards a Global QCD Analysis of Fragmentation Functions at Next-To-Next-To-Leading Order Accuracy
• Collinear matching for Sivers function at next-to-leading order
• Transverse momentum dependent operator expansion at next-to-leading power
• N${}^3$LO extraction of the Sivers function from SIDIS, Drell-Yan, and $W^{\pm }/Z$ data
• Factorization connecting continuum and lattice TMDs
• Energy-energy correlators in Deep Inelastic Scattering
• Transverse momentum in double parton scattering: factorisation, evolution and matching
• Factorization and Resummation for Massive Quark Effects in Exclusive Drell-Yan
• Associated production of a $W$ boson and massive bottom quarks at next-to-next-to-leading order in QCD
• Pion-induced Drell-Yan processes within TMD factorization
• TMD Fragmentation Functions at N${}^3$LO
• Power corrections and renormalons in Transverse Momentum Distributions
• Mapping the Kinematical Regimes of Semi-Inclusive Deep Inelastic Scattering
• Updated QCD global analysis of single transverse-spin asymmetries I: Extracting $\tilde{H}$, and the role of the Soffer bound and lattice QCD
• Renormalization and Matching for the Collins-Soper Kernel from Lattice QCD
• Transverse-Energy-Energy Correlations in Deep Inelastic Scattering
• Challenges with Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering
• Matching NNLO to parton shower using N${}^3$LL colour-singlet transverse momentum resummation in GENEVA
• N${}^3$LO+N${}^3$LL QCD improved Higgs pair cross sections
• TMD factorization for dijet and heavy-meson pair in DIS
• Spin asymmetries in electron-jet production at the future electron ion collider
• Matching of transverse momentum dependent distributions at twist-3
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering Beyond Lowest Order
• Transverse momentum dependent transversely polarized distributions at next-to-next-to-leading-order
• Structure of the nucleon at leading and subleading twist in the covariant parton model
• Sivers Asymmetry in Photoproduction of $J/\psi$ and Jet at the EIC
• Predictive power of transverse-momentum-dependent distributions
• Precision boson-jet azimuthal decorrelation at hadron colliders
• Probing Transverse Momentum Dependent Structures with Azimuthal Dependence of Energy Correlators
• Soft factors for double parton scattering at NNLO
• Transverse momentum dependent distributions in dijet and heavy hadron pair production at EIC
• Collinear expansion for color singlet cross sections
• Gauge-invariant TMD factorization for Drell-Yan hadronic tensor at small x
• QCD resummation on single hadron transverse momentum distribution with the thrust axis
• One-loop matching for gluon lattice TMDs
• Two-loop splitting in double parton distributions
• Transverse Momentum Dependent Fragmentation Functions from recent BELLE data
• Definition and evolution of transverse momentum dependent distribution of twist-three
• Factorization of $e^{+}{e}^{-}\to HX$ cross section, differential in $z_h$, $P_T$ and thrust, in the $2$-jet limit
• Prospects for quarkonium studies at the high-luminosity LHC
• Universality-breaking effects in $e^{+}{e}^{-}$ hadronic production processes
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• Factorisation of soft gluons in multiparton scattering
• Quarkonium TMD fragmentation functions in NRQCD
• Quasi Transverse Momentum Dependent Distributions at Next-to-Next-to-Leading order
• A fast and accurate method for perturbative resummation of transverse momentum-dependent observables
• Structure of rapidity divergences in soft factors
• Conformal invariance of TMD rapidity evolution
• Twist-4 T-even proton TMDs in the light-front quark-diquark model
• Combining nonperturbative transverse momentum dependence with TMD evolution
• Transverse momentum moments
• Collinear functions for QCD resummations
• Sivers, Boer-Mulders and worm-gear distributions at next-to-leading order
• GTMDs and the factorization of exclusive double Drell-Yan
• QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider
• Quark and gluon two-loop beam functions for leading-jet $p_T$ and slicing at NNLO
• The Drell-Yan process with pions and polarized nucleons
• The NNLO quark beam function for jet-veto resummation
• Two-loop splitting in double parton distributions: the colour non-singlet case
• Transverse momentum dependent of charged pion, kaon and proton/antiproton fragmentation functions from $e^{+}{e}^{-}$ annihilation process
• QCD$\times$QED evolution of TMDs
• Gluon TMD fragmentation function into quarkonium
• Matching generalised transverse-momentum-dependent distributions onto generalised parton distributions at one loop
• Fracture Functions in Different Kinematic Regions and Their Factorizations
• 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
• Light-Cone Singularities and Transverse-Momentum-Dependent Factorization at Twist-3
• Analytic NNLO transverse-momentum-dependent soft function for heavy quark pair hadroproduction at threshold
• N${}^3$LL + $\mathcal{O}({\alpha }_s^2)$ predictions of lepton-jet azimuthal angular distribution in deep-inelastic scattering
• NNLO electron structure functions (PDFs) from SCET
• Two-loop evolution kernels for colour dependent double parton distributions
• $q_T$-slicing with multiple jets
• One-loop transverse-momentum-dependent soft function at higher orders in the dimensional regulator
• W-boson production in TMD factorization
• Non-perturbative uncertainties on the transverse momentum distribution of electroweak bosons and on the determination of the $W$ boson mass at the LHC
• Transverse momentum dependent distribution functions in the threshold limit
• Transverse Energy-Energy Correlator for Vector Boson-Tagged Hadron Production in $pp$ and $pA$ collisions
• Gauge invariant spectral analysis of quark hadronization dynamics
• QCD Beyond Leading Power
• Evolution of unpolarized transverse momentum dependent parton distributions of twist-3
• Soft background fields at next-to-leading power in transverse momentum dependent SIDIS with jets
• Fully differential Higgs boson pair production at N${}^3$LO with top quark mass effects
• Linearly polarised Transverse Momentum Dependent Parton Distribution Function at NNLO in QCD
• Transverse momentum dependence in double parton scattering