Three particles in a finite volume

Abstract

The volume-dependence of a shallow three-particle bound state in the cubic box with a size $L$ is studied. It is shown that, in the unitary limit, the energy-level shift from the infinite-volume position is given by $\Delta E=c({\kappa }^2/m)(\kappa L{)}^{-3/2}|A{|}^2\exp (-2\kappa L/\sqrt{3})$, where $\kappa$ is the bound-state momentum and $|A{|}^2$ denotes the three-body analog of the asymptotic normalization constant, which encodes the information about the short-range interactions in the three-body system.

Comments: Talk presented at the 33rd International Symposium on Lattice Field Theory, 14 -18 July 2015, Kobe, Japan. In version 2, a mistake is corrected in the calculation of the overlap integral, which affects only the numerical value of the coefficient c in Eq. (3.11). The algebraic expression for the energy shift remains the same