Renormalization of transverse-momentum-dependent parton distribution on the lattice

Abstract

To calculate the transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice QCD, an important goal yet to be realized, it is crucial to establish a viable non-perturbative renormalization approach for linear divergences in the corresponding Euclidean quasi-TMDPDF correlators in large-momentum effective theory. We perform a first systematic study of the renormalization property of the quasi-TMDPDFs by calculating the relevant matrix elements in a pion state at 5 lattice spacings ranging from 0.03 fm to 0.12 fm. We demonstrate that the square root of the Wilson loop combined with the short distance hadron matrix element provides a successful method to remove all ultraviolet divergences of the quasi-TMD operator, and thus provide the necessary justification to perform a continuum limit calculation of TMDPDFs. In contrast, the popular RI/MOM renormalization scheme fails to eliminate all linear divergences.

arXiv comment17 pages, 17 figures. accepted version with the TMD wave function case in the supplemental materials

References in corpus (32)

• The Chroma Software System for Lattice QCD
• Parton Physics on Euclidean Lattice
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Large-Momentum Effective Theory
• Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production
• Scaling studies of QCD with the dynamical HISQ action
• Parton distributions and lattice QCD calculations: toward 3D structure
• 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
• Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
• Collins-Soper Kernel for TMD Evolution from Lattice QCD
• Lattice-QCD Calculations of TMD Soft Function Through Large-Momentum Effective Theory
• A Hybrid Renormalization Scheme for Quasi Light-Front Correlations in Large-Momentum Effective Theory
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• TMD Soft Function from Large-Momentum Effective Theory
• Lattice QCD calculation of the Collins-Soper kernel from quasi TMDPDFs
• Determination of the Collins-Soper Kernel from Lattice QCD
• Lattice QCD Study of Transverse-Momentum Dependent Soft Function
• Self-Renormalization of Quasi-Light-Front Correlators on the Lattice
• Nonperturbative renormalization of staple-shaped Wilson line operators in lattice QCD
• Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
• Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach
• The three-dimensional distribution of quarks in momentum space
• One-loop renormalization of staple-shaped operators in continuum and lattice regularizations
• Renormalization and Matching for the Collins-Soper Kernel from Lattice QCD
• RI/MOM renormalization of the quasi-PDF in lattice regularization
• Renormalization and Mixing of Staple-Shaped Wilson Line Operators on the Lattice Revisited

Cited by in corpus (15)

• The Present and Future of QCD
• Flavor dependence of unpolarized quark Transverse Momentum Distributions from a global fit
• Lattice Calculation of the Intrinsic Soft Function and the Collins-Soper Kernel
• Light-cone distribution amplitudes of a light baryon in large-momentum effective theory
• Nonperturbative Collins-Soper Kernel from Chiral Quarks with Physical Masses
• Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
• Gluon Transverse-Momentum-Dependent Distributions from Large-Momentum Effective Theory
• Nonperturbative renormalization of asymmetric staple-shaped operators in twisted mass lattice QCD
• Light Cone Distribution Amplitude for the $\Lambda$ Baryon from Lattice QCD
• Improved renormalization scheme for nonlocal operators
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness
• Counting linearly polarized gluons with lattice QCD
• Collins-Soper kernel from lattice QCD at the physical pion mass
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• A Unified Neural-Network Framework for Nucleon Imaging from Numerical Simulations of QCD