Three-particle bound states in a finite volume: unequal masses and higher partial waves

TL;DR

This paper derives an explicit formula for the finite-volume energy shifts of shallow three-body bound states with unequal masses, incorporating higher partial waves, and generalizes previous methods to broader conditions.

Contribution

It extends the existing finite-volume energy shift calculations to include unequal masses and higher angular momenta for three-body bound states.

Findings

Explicit expression for energy shifts in non-identical particle systems

Method generalized to arbitrary angular momenta and unequal masses

Reproduces known results in the equal mass S-wave case

Abstract

An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of arXiv:1412.4969 (Mei{\ss}ner et al.) is generalized for the case of unequal masses and arbitrary angular momenta. It is shown that in the S-wave and in the equal mass limit, the result from arXiv:1412.4969 is reproduced.