Factorization connecting continuum and lattice TMDs

Abstract

Transverse-momentum-dependent parton distribution functions (TMDs) can be studied from first principles by a perturbative matching onto lattice-calculable quantities: so-called lattice TMDs, which are a class of equal-time correlators that includes quasi-TMDs and TMDs in the Lorentz-invariant approach. We introduce a general correlator that includes as special cases these two Lattice TMDs and continuum TMDs, like the Collins scheme. Then, to facilitate the derivation of a factorization relation between lattice and continuum TMDs, we construct a new scheme, the Large Rapidity (LR) scheme, intermediate between the Collins and quasi-TMDs. The LR and Collins schemes differ only by an order of limits, and can be matched onto one another by a multiplicative kernel. We show that this same matching also holds between quasi and Collins TMDs, which enables us to prove a factorization relation between these quantities to all orders in ${\alpha }_s$. Our results imply that there is no mixing between various quark flavors or gluons when matching Collins and quasi TMDs, making the lattice calculation of individual flavors and gluon TMDs easier than anticipated. We cross-check these results explicitly at one loop and discuss implications for other physical-to-lattice scheme factorizations.

arXiv comment33 pages + appendices, 6 figures

References in corpus (79)

• LHAPDF6: parton density access in the LHC precision era
• An effective field theory for collinear and soft gluons: heavy to light decays
• Parton distributions from high-precision collider data
• New parton distribution functions from a global analysis of quantum chromodynamics
• Soft-Collinear Factorization in Effective Field Theory
• Parton distributions in the LHC era: MMHT 2014 PDFs
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Invariant Operators in Collinear Effective Theory
• Parton Physics on Euclidean Lattice
• QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum
• Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• Parton Distribution Functions, ${\alpha }_s$ and Heavy-Quark Masses for LHC Run II
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Transverse momentum dependence in gluon distribution and fragmentation functions
• Parton Distributions in Light-Cone Gauge: Where Are the Final-State Interactions?
• Calculation of the quark and gluon form factors to three loops in QCD
• The Rapidity Renormalization Group
• Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone
• Quark and gluon form factors to three loops
• Large-Momentum Effective Theory
• Three-Loop Results for Quark and Gluon Form Factors
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Factorization of heavy-to-light form factors in soft-collinear effective theory
• Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order
• Nucleon structure functions from lattice operator product expansion
• Exclusive processes in position space and the pion distribution amplitude
• The Quark Form Factor at Higher Orders
• Two-Loop Quark and Gluon Form Factors in Dimensional Regularisation
• Vector boson production at hadron colliders: hard-collinear coefficients at the NNLO
• Calculation of the transverse parton distribution functions at next-to-next-to-leading order
• Origin of Difference between $\overline{d}$ and $\overline{u}$ Partons in the Nucleon
• Deep-inelastic scattering and the operator product expansion in lattice QCD
• Renormalization in Large Momentum Effective Theory of Parton Physics
• Transverse-momentum-dependent parton distributions up to N${}^3$LL from Drell-Yan data
• The Quark Beam Function at NNLL
• Exploring quark transverse momentum distributions with lattice QCD
• Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum
• Analytic Regularization in Soft-Collinear Effective Theory
• Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field
• Sivers and Boer-Mulders observables from lattice QCD
• Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case
• Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order
• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• Collins-Soper Kernel for TMD Evolution from Lattice QCD
• Subleading Power Rapidity Divergences and Power Corrections for $q_T$
• Soft Factor Subtraction and Transverse Momentum Dependent Parton Distributions on Lattice
• Analytic Results for Massless Three-Loop Form Factors
• Lattice-QCD Calculations of TMD Soft Function Through Large-Momentum Effective Theory
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• Electroweak Sudakov Corrections using Effective Field Theory
• Soft-Collinear Factorization and Zero-Bin Subtractions
• Transverse momentum dependent PDFs at N${}^3$LO
• Rapidity renormalized TMD soft and beam functions at two loops
• Intrinsic quark transverse momentum in the nucleon from lattice QCD
• Accessing gluon parton distributions in large momentum effective theory
• QCD evolution of (un)polarized gluon TMDPDFs and the Higgs $q_T$-distribution
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case
• TMD Soft Function from Large-Momentum Effective Theory
• Lattice QCD calculation of the Collins-Soper kernel from quasi TMDPDFs
• Transverse-Momentum-Dependent Parton Distribution Functions from Large-Momentum Effective Theory
• Nucleon Transverse Momentum-dependent Parton Distributions in Lattice QCD: Renormalization Patterns and Discretization Effects
• Transverse Momentum Dependent Quasi-Parton-Distributions
• Determination of the Collins-Soper Kernel from Lattice QCD
• Lattice QCD Study of Transverse-Momentum Dependent Soft Function
• Restoration of Rotational Symmetry in the Continuum Limit of Lattice Field Theories
• Lattice QCD study of the Boer-Mulders effect in a pion
• Transverse momentum dependent factorization for lattice observables
• Connecting Different TMD Factorization Formalisms in QCD
• Nonperturbative renormalization of staple-shaped Wilson line operators in lattice QCD
• Twist-2 matching of transverse momentum dependent distributions
• Computing Light-Front Wave Functions Without Light-Front Quantization: A Large-Momentum Effective Theory Approach
• Transverse momentum dependent operator expansion at next-to-leading power
• Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach
• One-loop renormalization of staple-shaped operators in continuum and lattice regularizations
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Single Transverse-Spin Asymmetry and Sivers Function in Large Momentum Effective Theory

Cited by in corpus (19)

• 50 Years of Quantum Chromodynamics
• Nonperturbative Determination of Collins-Soper Kernel from Quasi Transverse-Momentum Dependent Wave Functions
• Lattice Calculation of the Intrinsic Soft Function and the Collins-Soper Kernel
• Threshold resummation for computing large-$x$ parton distribution through large-momentum effective theory
• Gauge Invariance of Non-Abelian Field Strength Correlators: the Axial Gauge Puzzle
• One-loop matching for gluon lattice TMDs
• Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators
• One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions
• Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
• Quasi Transverse Momentum Dependent Distributions at Next-to-Next-to-Leading order
• Combining nonperturbative transverse momentum dependence with TMD evolution
• Gluon Transverse-Momentum-Dependent Distributions from Large-Momentum Effective Theory
• Nonperturbative renormalization of asymmetric staple-shaped operators in twisted mass lattice QCD
• Collins-Soper Kernel in the QCD Instanton Vacuum
• Universality of the Collins-Soper kernel in lattice calculations
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Collins-Soper kernel from lattice QCD at the physical pion mass
• One-loop Matching Factors for Singlet Quasi-Parton Distribution Functions in the Hybrid-Ratio Scheme
• Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses