Finite-Size Scaling of Vector and Axial Current Correlators

TL;DR

This paper uses quenched chiral perturbation theory to analyze the finite-size scaling of vector and axial current correlators, providing predictions for lattice QCD simulations to extract low-energy constants.

Contribution

It offers new theoretical predictions for current correlators in finite volumes, including effects of quenching and fixed topology, aiding lattice QCD studies.

Findings

Vector correlator vanishes to all orders in quenched approximation.

Axial correlator remains robust and moderately sensitive to quenching.

Results enable extraction of chiral Lagrangian constants from small-volume lattice simulations.

Abstract

Using quenched chiral perturbation theory, we compute the long-distance behaviour of two-point functions of flavour non-singlet axial and vector currents in a finite volume, for small quark masses, and at a fixed gauge-field topology. We also present the corresponding predictions for the unquenched theory at fixed topology. These results can in principle be used to measure the low-energy constants of the chiral Lagrangian, from lattice simulations in volumes much smaller than one pion Compton wavelength. We show that quenching has a dramatic effect on the vector correlator, which is argued to vanish to all orders, while the axial correlator appears to be a robust observable only moderately sensitive to quenching.