Finite-volume energy shift of the three-pion ground state

TL;DR

This paper derives an explicit formula for the finite-volume energy shift of three pions in the I=1 channel, including relativistic corrections, aiding the extraction of three-body couplings from lattice data.

Contribution

It provides the first calculation of the three-pion ground-state energy shift up to order L^{-6} with relativistic effects included perturbatively.

Findings

Explicit expression for energy shift up to O(L^{-6})

Includes relativistic corrections perturbatively

Enables extraction of three-body couplings from lattice spectra

Abstract

Using the framework of non-relativistic effective field theory, the finite-volume ground-state energy shift is calculated up-to-and-including $O(L^{-6})$ for the system of three pions in the channel with the total isospin $I=1$. The relativistic corrections are included perturbatively, up to the same order in the inverse of the box size $L$. The obtained explicit expression, together with the known result for the system with maximal isospin $I=3$, can be used for the extraction of two independent effective three-body couplings from the measured ground-state spectrum of three pions.