Model Independent Evolution of Transverse Momentum Dependent Distribution Functions (TMDs) at NNLL

Abstract

We discuss the evolution of the eight leading twist transverse momentum dependent parton distribution functions, which turns out to be universal and spin independent. By using the highest order perturbatively calculable ingredients at our disposal, we perform the resummation of the large logarithms that appear in the evolution kernel of transverse momentum distributions up to next-to-next-to-leading logarithms (NNLL), thus obtaining an expression for the kernel with highly reduced model dependence. Our results can also be obtained using the standard CSS approach when a particular choice of the $b^{\ast }$ prescription is used. In this sense, and while restricted to the perturbative domain of applicability, we consider our results as a "prediction" of the correct value of $b_{\max }$ which is very close to $1.5{\mathrm{GeV}}^{-1}$. We explore under which kinematical conditions the effects of the non-perturbative region are negligible, and hence the evolution of transverse momentum distributions can be applied in a model independent way. The application of the kernel is illustrated by considering the unpolarized transverse momentum dependent parton distribution function and the Sivers function.

To appear in EPJC. 17 pages, 7 figures

References in corpus (11)

• Parton distributions for the LHC
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Sivers Effect for Pion and Kaon Production in Semi-Inclusive Deep Inelastic Scattering
• Transverse-Spin and Transverse-Momentum Effects in High-Energy Processes
• Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production
• Equality of Two Definitions for Transverse Momentum Dependent Parton Distribution Functions
• Singular and Regular Gauges in Soft Collinear Effective Theory: The Introduction of the New Wilson Line T
• SCET, Light-Cone Gauge and the T-Wilson Lines
• Decoupling in QED and QCD
• Definition and Evolution of Transverse Momentum Distributions

Cited by in corpus (103)

• QCD and strongly coupled gauge theories: challenges and perspectives
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production
• Extraction of Quark Transversity Distribution and Collins Fragmentation Functions with QCD Evolution
• Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order
• Parton Fragmentation Functions
• QCD Evolution of the Sivers Asymmetry
• Universality of transverse-momentum resummation and hard factors at the NNLO
• Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum
• Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• Unpolarised Transverse Momentum Dependent Distribution and Fragmentation Functions from SIDIS Multiplicities
• 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
• A Unified Treatment of the QCD Evolution of All (Un-)Polarized TMD Functions: Collins Function as a Study Case
• 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
• Resummation of Transverse Momentum Distributions in Distribution Space
• QCD evolution of (un)polarized gluon TMDPDFs and the Higgs $q_T$-distribution
• Collins functions for pions from SIDIS and new e+e- data: a first glance at their transverse momentum dependence
• Non-perturbative QCD effects in $q_T$ spectra of Drell-Yan and $Z$-boson production
• Transverse momentum dependent distributions with jets
• Transverse momentum dependent distributions in $e^{+}{e}^{-}$ and semi-inclusive deep-inelastic scattering using jets
• Pion TMDs in light-front constituent approach, and Boer-Mulders effect in the pion-induced Drell-Yan process
• Determination of the Collins-Soper Kernel from Lattice QCD
• Collins azimuthal asymmetries of hadron production inside jets
• The transverse momentum distribution of hadrons within jets
• Systematic analysis of double-scale evolution
• Limits on TMD Evolution From Semi-Inclusive Deep Inelastic Scattering at Moderate $Q$
• 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
• Nonperturbative contributions to a resummed leptonic angular distribution in inclusive neutral vector boson production
• Probing Transverse-Momentum Distributions With Groomed Jets
• PDF bias and flavor dependence in TMD distributions
• Jet-based measurements of Sivers and Collins asymmetries at the future Electron-Ion Collider
• Polarized hadron pair production from electron-positron annihilation
• Associated production of a dilepton and a ${\rm Y}(J/\psi )$ at the LHC as a probe of gluon transverse momentum dependent distributions
• Analytic Continuation and Reciprocity Relation for Collinear Splitting in QCD
• Extracting the Transverse Momentum Dependent Polarizing Fragmentation Functions
• Proper definition and evolution of generalized transverse momentum distributions
• A Fixed-Target Programme at the LHC: Physics Case and Projected Performances for Heavy-Ion, Hadron, Spin and Astroparticle Studies
• Non-perturbative contributions to vector-boson transverse momentum spectra in hadronic collisions
• N${}^3$LO extraction of the Sivers function from SIDIS, Drell-Yan, and $W^{\pm }/Z$ data
• Transverse Momentum Dependent Fragmenting Jet Functions with Applications to Quarkonium Production
• Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC
• Pion-induced Drell-Yan processes within TMD factorization
• Jet fragmentation functions in proton-proton collisions using soft-collinear effective theory
• Matching factorization theorems with an inverse-error weighting
• 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
• Power corrections and renormalons in Transverse Momentum Distributions
• Next-to-leading order transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering: the role of the three-gluon correlator
• Where do we stand with a 3-D picture of the proton?
• TMD factorization for dijet and heavy-meson pair in DIS
• Feasibility Studies for Single Transverse-Spin Asymmetry Measurements at a Fixed-Target Experiment Using the LHC Proton and Lead Beams (AFTER@LHC)
• Production of two hadrons in semi-inclusive Deep Inelatic Scattering
• Phenomenology of transverse spin: past, present and future
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Jet fragmentation functions for $Z$-tagged jets
• Transverse-momentum-dependent quark splitting functions in $k_T$-factorization: real contributions
• Predictive power of transverse-momentum-dependent distributions
• Transverse momentum spectrum of dilepton pair in the unpolarized ${\pi }^{-}N$ Drell-Yan process within TMD factorization
• Sea quark Sivers distribution
• The Higgs Transverse Momentum Distribution at NNLL and its Theoretical Errors
• Improvement for Color Glass Condensate factorization: single hadron production in pA collisions at next-to-leading order
• The electron in three-dimensional momentum space
• Transverse Momentum Dependent Fragmentation Functions from recent BELLE data
• Di-hadron fragmentation and mapping of the nucleon structure
• Boer-Mulders effect in the unpolarized pion induced Drell-Yan process at COMPASS within TMD factorization
• Quarkonium TMD fragmentation functions in NRQCD
• Sivers and $\cos 2\varphi$ Asymmetries in Semi-inclusive Deep Inelastic Scattering in Light-front Holographic Model
• Transverse Single Spin Asymmetry in $p+p^{\uparrow }\to D+X$
• Quark Wigner Distributions and GTMDs of Pion in the Light-Front Holographic Model
• The transverse polarization of $\Lambda$ hyperons in $e^{+}{e}^{-}\to {\Lambda }^{\uparrow }hX$ processes within TMD factorization
• Study of worm-gear-T function $g_{1T}$ with semi-inclusive DIS data
• Collins and Sivers effects in p(transv. polarized) p --> jet pion X: Universality and process dependence
• Towards three-dimensional nucleon structures at the Electron-Ion Collider in China: A study of the Sivers function
• Efficient Fourier Transforms for Transverse Momentum Dependent Distributions
• Different approaches to TMD Evolution with scale
• QCD$\times$QED evolution of TMDs
• Sivers Asymmetry in the pion induced Drell-Yan process at COMPASS within TMD factorization
• Gluon TMD fragmentation function into quarkonium
• Does nuclear medium affect the transverse momentum-dependent parton distributions of valence quark of pions?
• Sivers and Boer-Mulders TMDs of proton in a light-front quark-diquark model
• Transverse single spin asymmetry $A_{UT}^{\sin ({\varphi }_h-{\varphi }_S)}$ for single hadron production in SIDIS
• The $\sin (2\varphi -{\varphi }_S)$ azimuthal asymmetry in the pion induced Drell-Yan process within TMD factorization
• Model predictions for azimuthal spin asymmetries for HERMES and COMPASS kinematics
• Unraveling sub-leading twist GTMDs of proton using LFQDM
• $\sin ({\varphi }_{\Lambda }-{\varphi }_S)$ azimuthal asymmetry in transversely polarized $\Lambda$ production in SIDIS within TMD factorization at EIC
• Polarized fragmenting jet functions in Inclusive and Exclusive Jet Production
• The Collins asymmetry in electroproduction of Kaon at the electron ion colliders within TMD factorization
• The $\sin 2{\varphi }_h$ azimuthal asymmetry of pion production in SIDIS within TMD factorization
• Overview of TMD evolution
• Extracting the QCD ${\Lambda }_{\overline{MS}}$ parameter in Drell-Yan Process using Collins-Sopper-Sterman approach
• Probing the Sivers asymmetries through $J/\psi$ photoproduction in ${\mathrm{p}}^{\uparrow }\mathrm{p}$ collision with forward proton tagging
• On the QCD Evolution of Transverse Momentum Dependent Distributions
• Sivers Asymmetry with QCD Evolution
• Investigating the transverse momentum dependent gluon Sivers function in quarkonium production at $pp$ colliders
• Universality of the Collins-Soper kernel in lattice calculations
• TMDs: Evolution, modeling, precision
• $\pi -N$ Drell-Yan process in TMD factorization
• Kotzinian-Mulders effect in semi-inclusive DIS within TMD factorization