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.

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

References in corpus (4)

• Scaling studies of QCD with the dynamical HISQ action
• Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
• Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
• One-loop renormalization of staple-shaped operators in continuum and lattice regularizations

Cited by in corpus (15)

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• 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