Low-energy couplings of QCD from topological zero-mode wave functions

TL;DR

This paper derives a relation connecting topological zero-mode wave functions of the Dirac operator to QCD low-energy constants, and explores extracting the pion decay constant via lattice computations in quenched approximation.

Contribution

It introduces a novel method linking zero-mode wave functions to low-energy constants and demonstrates its potential for determining the pion decay constant from lattice data.

Findings

Derived a relation between zero-mode wave functions and QCD constants.

Showed feasibility of extracting pion decay constant from lattice zero-mode correlators.

Compared lattice results with quenched chiral perturbation theory expressions.

Abstract

By matching 1/m^2 divergences in finite-volume two-point correlation functions of the scalar or pseudoscalar densities with those obtained in chiral perturbation theory, we derive a relation between the Dirac operator zero-mode eigenfunctions at fixed non-trivial topology and the low-energy constants of QCD. We investigate the feasibility of using this relation to extract the pion decay constant, by computing the zero-mode correlation functions on the lattice in the quenched approximation and comparing them with the corresponding expressions in quenched chiral perturbation theory.