Energy shift of the three-particle system in a finite volume

Abstract

Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order $L^{-6}$. Furthermore, assuming that a stable dimer exists in the infinite volume, the shift for the lowest particle-dimer scattering state is obtained up to and including order $L^{-3}$. The result for the lowest three-particle state agrees with the results from the literature, and the result for the lowest particle-dimer state reproduces the one obtained by using the Luescher equation.

Comments: Final version published in Phys. Rev. D. Corrected typos: factor of 2 in Eq. (115) [previously Eq. (114)] and factor 6 in Eq. (120) [previously Eq. (119)]