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

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.