Excited-state contribution to the axial-vector and pseudo-scalar correlators with two extra pions

TL;DR

This paper investigates the impact of multi-particle states, specifically three-meson states with two extra pions, on QCD correlators and finds their contribution to be negligible in current lattice simulations.

Contribution

It provides a chiral perturbation theory calculation showing the suppressed contribution of three-meson states to axial-vector and pseudo-scalar correlators.

Findings

Three-meson state contributions are strongly suppressed.

The contribution is too small to be observed in current lattice simulations.

The study clarifies the role of multi-particle states in QCD correlators.

Abstract

We study multi-particle state contributions to the QCD two-point functions of the axial-vector and pseudo-scalar quark bilinears in a finite spatial volume. For sufficiently small quark masses one expects three-meson states with two additional pions at rest to have the lowest total energy after the ground state. We calculate this three-meson state contribution using chiral perturbation theory. We find it to be strongly suppressed and too small to be seen in present-day lattice simulations.