Finite-volume spectrum of $\pi^+\pi^+$ and $\pi^+\pi^+\pi^+$ systems

TL;DR

This paper applies a formalism to analyze the finite-volume spectrum of three positively charged pions in lattice QCD, enabling the extraction of three-body amplitudes and resonance properties relevant for understanding complex hadronic systems.

Contribution

First application of a formalism to relate finite-volume spectra to three-body amplitudes for a physical system of three interacting pions in lattice QCD.

Findings

Ground state energies match existing lattice QCD results at unphysical pion masses.

Extrapolated results to physical pion masses using effective field theory.

Predicted excited energy spectrum for the three-pion system.

Abstract

The ab-initio understanding of hadronic three-body systems above threshold, such as exotic resonances or the baryon spectrum, requires the mapping of the finite-volume eigenvalue spectrum, produced in lattice QCD calculations, to the infinite volume. We present the first application of such a formalism to a physical system in form of three interacting positively charged pions. The results for the ground state energies agree with the available lattice QCD results by the NPLQCD collaboration at unphysical pion masses. Extrapolations to physical pion masses are performed using input from effective field theory. The excited energy spectrum is predicted. This demonstrates the feasibility to determine three-body amplitudes above threshold from lattice QCD, including resonance properties of axial mesons, exotics, and excited baryons.