Effective Chiral Lagrangians and Lattice QCD

TL;DR

This paper introduces a method using lattice QCD simulations to accurately estimate low-energy constants in chiral Lagrangians, aiding tests of fundamental QCD hypotheses and discretization effects.

Contribution

The paper presents a novel approach to determine low-energy constants via lattice QCD, including initial quenched approximation results and applications to decay constant ratios and scaling tests.

Findings

Good statistical precision achieved in quenched approximation

Estimated F_K/F_pi ratio is 10% below experimental value

Method enables testing of discretization scaling and dynamical quark effects

Abstract

We propose a general method to obtain accurate estimates for some of the "low-energy constants" in the one-loop effective chiral Lagrangian by means of simulating lattice QCD. In particular, the method is sensitive to those constants whose values are required to test the hypothesis of a massless up-quark. Initial tests performed in the quenched approximation confirm that good statistical precision can be achieved. As a byproduct we obtain an accurate estimate for the ratio of pseudoscalar decay constants, F_K/F_pi, in the quenched approximation, which lies 10% below the experimental result. The quantities that serve to extract the low-energy constants also allow a test of the scaling behaviour of different discretizations of QCD and a search for the effects of dynamical quarks.