Using the framework of nonrelativistic 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.

• Received 11 December 2020
• Accepted 25 February 2021

DOI:https://doi.org/10.1103/PhysRevD.103.054506

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Published by the American Physical Society