# Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD

## TL;DR

This paper computes the three-pion spectrum with maximal isospin in finite volume using lattice QCD, introducing a faster algorithm and extracting scattering amplitudes, thus advancing understanding of three-particle interactions.

## Contribution

The study presents a novel, efficient algorithm for calculating three-pion spectra in lattice QCD and provides the first extraction of the three-pion threshold scattering amplitude.

## Key findings

- Successfully computed three-pion spectra including excited states.
- Extracted nonzero three-pion threshold scattering amplitude.
- Made finite-volume spectrum publicly available.

## 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.