Multi-Pion States in Lattice QCD and the Charged-Pion Condensate

TL;DR

This study uses lattice QCD to analyze multi-pion systems, extracting scattering parameters and demonstrating a three-pion interaction, with results aligning with chiral perturbation theory and emphasizing high-precision computations.

Contribution

First lattice QCD calculation of up to twelve charged pions, providing detailed insights into multi-pion interactions and the equation of state of a pion gas.

Findings

Consistent pion-pion scattering length with previous results.

Evidence for a significant three-pion interaction.

Agreement with leading order chiral perturbation theory.

Abstract

The ground-state energies of systems containing up to twelve $\pi^+$'s in a spatial volume V ~ (2.5 fm)^3 are computed in dynamical, mixed-action lattice QCD at a lattice spacing of ~ 0.125 fm for four different values of the light quark masses. Clean signals are seen for each ground state, allowing for a precise extraction of both the $\pi^+\pi^+$ scattering length and $\pi^+\pi^+\pi^+$-interaction from a correlated analysis of systems containing different numbers of $\pi^+$'s. This extraction of the $\pi^+\pi^+$ scattering length is consistent with than that from the $\pi^+\pi^+$-system alone. The large number of systems studied here significantly strengthens the arguments presented in our earlier work and unambiguously demonstrates the presence of a low energy $\pi^+\pi^+\pi^+$-interaction. The equation of state of a $\pi^+$ gas is investigated using our numerical results and the density dependence of the isospin chemical potential for these systems agrees well with the theoretical expectations of leading order chiral perturbation theory. The chemical potential is found to receive a substantial contribution from the $\pi^+\pi^+\pi^+$-interaction at the lighter pion masses. An important technical aspect of this work is the demonstration of the necessity of performing propagator contractions in greater than double precision to extract the correct results.