Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD.

Ben Hörz,Andrew Hanlon

doi:10.1103/physrevlett.123.142002

Abstract

We present the three-pion spectrum with maximal isospin in a finite volume determined from lattice QCD, including excited states in addition to the ground states across various irreducible representations at zero and nonzero total momentum. The required correlation functions, from which the spectrum is extracted, are computed using a newly implemented algorithm which speeds up the computation by more than an order of magnitude. On a subset of the data we extract a nonzero value of the three-pion threshold scattering amplitude using the 1/L expansion of the three-particle quantization condition, which consistently describes all states at zero total momentum. The finite-volume spectrum is publicly available to facilitate further explorations within the available three-particle finite-volume approaches.

Highlights

We present the three-pion spectrum with maximal isospin in a finite volume determined from lattice QCD, including excited states in addition to the ground states across various irreducible representations at zero and nonzero total momentum
On a subset of the data we extract a nonzero value of the three-pion threshold scattering amplitude using the 1=L expansion of the three-particle quantization condition, which consistently describes all states at zero total momentum
This limitation has precluded a proper lattice QCD study of systems involving three or more stable hadrons at light pion masses, e.g., the Roper resonance which decays to both two- and threeparticle channels, the ωð782Þ decaying to three pions, many of the X, Y, and Z resonances, and three-nucleon interactions relevant for nuclear physics

Summary

Introduction

We present the three-pion spectrum with maximal isospin in a finite volume determined from lattice QCD, including excited states in addition to the ground states across various irreducible representations at zero and nonzero total momentum. On a subset of the data we extract a nonzero value of the three-pion threshold scattering amplitude using the 1=L expansion of the three-particle quantization condition, which consistently describes all states at zero total momentum.

Results

Conclusion