Off-lightcone Wilson-line operators in gradient flow

Abstract

Off-lightcone Wilson-line operators are constructed using local operators connected by time-like or space-like Wilson lines, which ensure gauge invariance. Off-lightcone Wilson-line operators have broad applications in various contexts. For instance, space-like Wilson-line operators play a crucial role in determining quasi-distribution functions (quasi-PDFs), while time-like Wilson-line operators are essential for understanding quarkonium decay and production within the potential non-relativistic QCD (pNRQCD) framework. In this work, we establish a systematic approach for calculating the matching from the gradient-flow scheme to the $\overline{\mathrm{MS}}$ scheme in the limit of small flow time for off-lightcone Wilson-line operators. By employing the one-dimensional auxiliary-field formalism, we simplify the matching procedure, reducing it to the matching of local current operators. We provide one-loop level matching coefficients for these local current operators. For the case of hadronic matrix element related to the quark quasi-PDFs, we show at one-loop level that the finite flow time effect is very small as long as the flow radius is smaller than the physical distance $z$, which is usually satisfied in lattice gradient flow computations. Applications include lattice gradient flow computations of quark/gluon quasi-PDFs, gluonic correlators related to quarkonium decay and production in pNRQCD, and spin-dependent potentials in terms of chromoelectric and chromomagnetic field insertions into a Wilson loop.

arXiv commentPublished version, including updating footnote 5 and Note Added for comparison with existing calculation, and correcting several text typos

References in corpus (48)

• Properties and uses of the Wilson flow in lattice QCD
• Parton Physics on Euclidean Lattice
• Potential NRQCD: an effective theory for heavy quarkonium
• Effective field theories for heavy quarkonium
• FLAG Review 2021
• Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• High-precision scale setting in lattice QCD
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• The Pole Mass of The Heavy Quark. Perturbation Theory and Beyond
• Trivializing maps, the Wilson flow and the HMC algorithm
• Infinite N phase transitions in continuum Wilson loop operators
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Field correlators in QCD. Theory and applications
• Large-Momentum Effective Theory
• Exclusive processes in position space and the pion distribution amplitude
• Chiral symmetry and the Yang--Mills gradient flow
• Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions
• Perturbative Renormalization of quasi-PDFs
• On the Renormalizability of Quasi Parton Distribution Functions
• Renormalization in Large Momentum Effective Theory of Parton Physics
• The QCD Potential at $O(1/m)$
• Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field
• Two-loop renormalization of the effective field theory of a static quark
• Lattice energy-momentum tensor from the Yang-Mills gradient flow -- inclusion of fermion fields
• Accessing gluon parton distributions in large momentum effective theory
• Inclusive Decays of Heavy Quarkonium to Light Particles
• Three-loop anomalous dimension of the heavy-light quark current in HQET
• Quasi parton distributions and the gradient flow
• Complete Matching for Quasi-distribution Functions in Large Momentum Effective Theory
• The two-loop energy-momentum tensor within the gradient-flow formalism
• Multiplicative renormalizability of quasi-parton operators
• New predictions for inclusive heavy-quarkonium P-wave decays
• Two-Loop Anomalous Dimension of the Chromo-Magnetic Moment of a Heavy Quark
• Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD
• Renormalization of parton quasi-distributions beyond the leading order: spacelike vs. timelike
• HQET chromomagnetic interaction at two loops
• Inclusive production of $J/\psi$, $\psi (2S)$, and ${\rm Y}$ states in pNRQCD
• Inclusive Hadroproduction of $P$-Wave Heavy Quarkonia in Potential Nonrelativistic QCD
• Inclusive Production of Heavy Quarkonia in pNRQCD
• Four quark operators for kaon bag parameter with gradient flow
• Production and polarization of $S$-wave quarkonia in potential nonrelativistic QCD
• Effective electroweak Hamiltonian in the gradient-flow formalism
• The static force from generalized Wilson loops using gradient flow
• QCD Static Force in Gradient Flow
• Hadronic vacuum polarization using gradient flow
• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow
• Conserved vector current in QCD-like theories and the gradient flow

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