Two-pion excited state contribution to pseudo-scalar correlators

TL;DR

This paper investigates multi-particle contributions to pseudo-scalar correlators in QCD, finding that three-meson states are too weak to detect in current lattice simulations, and suggesting observed curvature may indicate a resonance, 300.

Contribution

It provides a chiral perturbation theory analysis of multi-particle states in pseudo-scalar correlators, clarifying their expected size and impact in lattice QCD.

Findings

Three-meson states have negligible amplitude in current simulations.

Curvature in effective mass plots likely indicates a resonance, 00.

Multi-particle contributions are smaller than previously anticipated.

Abstract

We study multi-particle state contributions to the QCD two-point functions of 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. Using chiral perturbation theory, we find the amplitude of this state to be too small to be seen in present-day lattice simulations. We speculate that curvature in the effective mass plot extracted from the pseudo-scalar density two-point function instead corresponds to a genuine resonance, the \pi(1300).