Combining nonperturbative transverse momentum dependence with TMD evolution

Abstract

Central to understanding the nonpertubative, intrinsic partonic nature of hadron structure are the concepts of transverse momentum dependent (TMD) parton distribution and fragmentation functions. A TMD factorization approach to the phenomenology of semi-inclusive processes that includes evolution, higher orders, and matching to larger transverse momentum, is ultimately necessary for reliably connecting with phenomenologically extracted nonperturbative structures, especially when widely different scales are involved. In this paper, we will address some of the difficulties that arise when phenomenological techniques that were originally designed for very high energy applications are extended to studies of hadron structures, and we will solidify the connection between standard high energy TMD implementations and the more intuitive, parton model based approaches to phenomenology that emphasize nonperturbative hadron structure. In the process, we will elaborate on differences between forward and backward TMD evolution, which in the context of this paper we call "bottom-up" and "top-down" approaches, and we will explain the advantages of a bottom-up strategy. We will also emphasize and clarify the role of the integral relations that connect TMD and collinear correlation functions. We will show explicitly how they constrain the nonperturbative "$g$-functions" of standard Collins-Soper-Sterman (CSS) implementations of TMD factorization. This paper is especially targeted toward phenomenologists and model builders who are interested in merging specific nonperturbative models and calculations (including lattice QCD) with TMD factorization at large $Q$. Our main result is a recipe for incorporating nonperturbative models into TMD factorization, and for constraining their parameters in a way that matches to perturbative QCD and evolution.

41 pages, 12 figures

References in corpus (104)

• LHAPDF6: parton density access in the LHC precision era
• The complete tree-level result up to order $1/Q$ for polarized deep-inelastic leptoproduction
• Semi-inclusive deep inelastic scattering at small transverse momentum
• QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum
• Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Unintegrated parton distributions
• TMD Parton Distribution and Fragmentation Functions with QCD Evolution
• QCD Factorization for Spin-Dependent Cross Sections in DIS and Drell-Yan Processes at Low Transverse Momentum
• Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering
• Light-Cone Representation of the Spin and Orbital Angular Momentum of Relativistic Composite Systems
• Transversity and Collins functions from SIDIS and e+e- data
• Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone
• Transverse-momentum distributions in a diquark spectator model
• The Nonperturbative Regime in QCD Resummation for Gauge Boson Production at Hadron Colliders
• Large-Momentum Effective Theory
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Single spin asymmetry for $p^{\uparrow }p\to \pi X$ in perturbative QCD
• Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production
• Unintegrated parton distributions and inclusive jet production at HERA
• Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order
• A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
• QCD Evolution of the Sivers Asymmetry
• Vector boson production at hadron colliders: hard-collinear coefficients at the NNLO
• Intrinsic transverse momentum and the polarized Drell-Yan process
• The QCD Evolution of the Sivers Function
• Parton distributions and lattice QCD calculations: toward 3D structure
• Universality of transverse-momentum resummation and hard factors at the NNLO
• Asymmetries in polarized hadron production in e^+e^- annihilation up to order 1/Q
• Transverse momentum dependent parton distributions in a light-cone quark model
• Next-to-next-to-leading logarithmic corrections at small transverse momentum in hadronic collisions
• 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
• W and Z transverse momentum distributions: resummation in qT-space
• Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
• Investigations into the flavor dependence of partonic transverse momentum
• The transverse momentum dependent distribution functions in the bag model
• Sivers effect in semi-inclusive deeply inelastic scattering
• TMD Evolution: Matching SIDIS to Drell-Yan and W/Z Boson Production
• Role of the nonperturbative input in QCD resummed Drell-Yan $Q_T$-distributions
• Simultaneous Monte Carlo analysis of parton densities and fragmentation functions
• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• Collins-Soper Kernel for TMD Evolution from Lattice QCD
• Intrinsic transverse parton momenta in deeply inelastic reactions
• A strategy towards the extraction of the Sivers function with TMD evolution
• Introduction to GPDs and TMDs
• Relating Transverse Momentum Dependent and Collinear Factorization Theorems in a Generalized Formalism
• TMDlib and TMDplotter: library and plotting tools for transverse-momentum-dependent parton distributions
• Sivers Function in the MIT Bag Model
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• Novel Transversity Properties in Semi-Inclusive Deep Inelastic Scattering
• QCD prediction for heavy boson transverse momentum distributions
• Rapidity renormalized TMD soft and beam functions at two loops
• Angular dependences in inclusive two-hadron production at BELLE
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case
• Vector boson production in hadronic collisions
• Phenomenology of single spin asymmetries in p(transv. polarized)-p -> pion + X
• Semi-Inclusive Deep Inelastic Scattering processes from small to large P_T
• Pion TMDs in light-front constituent approach, and Boer-Mulders effect in the pion-induced Drell-Yan process
• Energy Evolution for the Sivers Asymmetries in Hard Processes
• Transverse Momentum Dependent Fragmentation and Quark Distribution Functions from the NJL-jet Model
• Self-contained definition of the Collins-Soper kernel
• An Overview of Transverse Momentum Dependent Factorization and Evolution
• Limits on TMD Evolution From Semi-Inclusive Deep Inelastic Scattering at Moderate $Q$
• Transverse single spin asymmetries in Drell-Yan processes
• Connecting Different TMD Factorization Formalisms in QCD
• Transverse-momentum-dependent Multiplicities of Charged Hadrons in Muon-Deuteron Deep Inelastic Scattering
• Nonperturbative contributions to a resummed leptonic angular distribution in inclusive neutral vector boson production
• QCD predictions for new variables to study dilepton transverse momenta at hadron colliders
• Naive time-reversal odd phenomena in semi-inclusive deep-inelastic scattering from light-cone constituent quark models
• Pion transverse momentum dependent parton distributions in the Nambu and Jona-Lasinio model
• Nonperturbative partonic quasidistributions of the pion from chiral quark models
• Factorization connecting continuum and lattice TMDs
• Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC
• Transverse Single Spin Asymmetry in $e+p^{\uparrow }\to e+J/\psi +X$ and Transverse Momentum Dependent Evolution of the Sivers Function
• Transverse momentum in double parton scattering: factorisation, evolution and matching
• Sudakov Logarithm Resummation in Transverse Momentum Space for Electroweak Boson Production at Hadron Colliders
• O(alpha_s^2) QCD corrections to the electroproduction of hadrons with high transverse momentum
• Difficulties in the description of Drell-Yan processes at moderate invariant mass and high transverse momentum
• The transverse structure of the pion in momentum space inspired by the AdS/QCD correspondence
• Effects of TMD evolution and partonic flavor on $e^{+}{e}^{-}$ annihilation into hadrons
• Effect of flavor-dependent partonic transverse momentum on the determination of the $W$ boson mass in hadronic collisions
• Renormalization and Matching for the Collins-Soper Kernel from Lattice QCD
• Challenges with Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering
• On the use of the KMR unintegrated parton distribution functions
• Intrinsic Transverse Motion of the Pion's Valence Quarks
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering Beyond Lowest Order
• Structure of the nucleon at leading and subleading twist in the covariant parton model
• Transverse parton momenta in single inclusive hadron production in $e^{+}{e}^{-}$ annihilation processes
• A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes
• Predictive power of transverse-momentum-dependent distributions
• Pathologies of the KMR prescriptions for unintegrated PDFs: Which prescription should be preferred?
• Theory of W and Z boson production
• Collins Fragmentation Function within NJL-jet Model
• Quark-gluon correlation functions relevant to single transverse spin asymmetries
• Universality-breaking effects in $e^{+}{e}^{-}$ hadronic production processes
• Factorization of $e^{+}{e}^{-}\to HX$ cross section, differential in $z_h$, $P_T$ and thrust, in the $2$-jet limit
• The Drell-Yan process with pions and polarized nucleons
• Intrinsic Transverse Momentum and Evolution in Weighted Spin Asymmetries
• Role of transverse momentum dependence of unpolarised parton distribution and fragmentation functions in the analysis of azimuthal spin asymmetries
• Transverse Momentum and Transverse Momentum Distributions in the MIT Bag Model
• Collinear Factorization in Wide-Angle Hadron Pair Production in $e^{+}{e}^{-}$ Annihilation
• Transverse moments of TMD parton densities and ultraviolet divergences

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