Asymptotic Long-Distance Expansion of Euclidean Correlators in Lattice Parton Applications

TL;DR

This paper analyzes the large-distance decay of Euclidean correlators in lattice QCD, deriving asymptotic behaviors and demonstrating their impact on non-perturbative parton physics calculations.

Contribution

It introduces a detailed asymptotic expansion for Euclidean correlators using effective theory and dispersive analysis, connecting parameters to heavy-flavor hadron properties.

Findings

Correlators decay exponentially at large distances due to confinement.

Asymptotic behaviors are derived up to next-to-leading order.

Results improve error estimates in lattice QCD computations.

Abstract

Bilinear Euclidean quark and gluon correlators with Wilson links have been used widely for applications of large-momentum effective field theories to computing non-perturbative collinear and soft parton physics. Due to color confinement, these correlators decay exponentially at large spatial distances, a behavior crucial for computing momentum-space Fourier transformations with controlled errors from lattice QCD data. Using heavy-quark effective theory reduction, dispersive analysis, Lorentz symmetry, and heavy-flavor spectra, we determine the leading and next-to-leading asymptotic behaviors and relate the expansion parameters to binding energies of heavy-flavor hadrons. We demonstrate the results through two-loop calculations in $\phi^3$ theory and from the perspective of locality and analyticity. We also study the impact of the asymptotic analysis on realistic lattice QCD data and demonstrate reliable error estimates.