Mass-ratio condition for non-binding of three two-component particles with contact interactions

Abstract

The binding of two heavy fermions interacting with a light particle via a contact interaction is possible only for a sufficiently large heavy-light mass ratio. The two-variable inequality is derived to determine the specific mass-ratio bound providing the absence of three-body bound states for lower values of the mass ratio. By means of this inequality, the mass-ratio bound is found to be 5.26 for the total angular momentum and parity \(L^P = 1^-\). For other \(L^P\) sectors, the mass-ratio bounds providing the absence of three-body bound states is found in a similar way. For generality, the method is extended to determine also the mass-ratio bounds for a system consisting of two identical bosons and a distinct particle for different \(L^P\) (\(L > 0\)) sectors.