Finite-Volume Spectrum of π^{+}π^{+} and π^{+}π^{+}π^{+} Systems.

M Mai,M Döring

doi:10.1103/physrevlett.122.062503

Abstract

The abinitio 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.

Highlights

Introduction.—Many pressing questions in hadronic physics require the understanding of three-body systems above threshold
Almost all excited baryons have sizable couplings to ππN states, making the understanding of the three-body problem mandatory for the entire sector. Due to their key role in understanding confinement and other properties of quantum chromodynamics (QCD), and due to the missing resonance problem, excited baryons are subject of large experimental campaigns at Jefferson Lab, ELSA, MAMI, and other facilities [3,4,5]
Three-body effects play a crucial role in the understanding of axial mesons like the a1ð1260Þ → πρ → 3π and exotics whose existence would be a direct signal of gluon dynamics at low energies

Summary

Introduction

Introduction.—Many pressing questions in hadronic physics require the understanding of three-body systems above threshold. We will fix the remaining parameter (genuine three-body coupling) to the ground-state energy level of the πþπþπþ system [33,34], predicting higher levels up to the 5π threshold.

Results

Conclusion