Three-boson stability for boosted interactions towards the zero-range limit

TL;DR

This paper investigates the stability and properties of three-boson systems with zero-range interactions in a relativistic framework, showing model independence and avoiding Thomas collapse, with comparisons to other approaches.

Contribution

It demonstrates that three-boson relativistic masses and wave functions are model-independent in the zero-range limit and explains the stability mechanism involving boosted potentials.

Findings

Relativistic three-boson masses are model-independent in the zero-range limit.

Thomas collapse is avoided in the relativistic framework.

The stability arises from the reduction of boosted potential with increasing virtual pair momentum.

Abstract

We study the three-boson bound-state mass and wave functions for ground and excited states within the three-body relativistic framework with Kamada and Gl\"ocke boosted potentials in the limit of a zero-range interaction. We adopt a nonrelativistic short-range separable potential, with Yamaguchi and Gaussian form factors, and drive them towards the zero-range limit by letting the form factors' momentum scales go to large values while keeping the two-body binding fixed. We show that the three-boson relativistic masses and wave functions are model-independent towards the zero-range limit, and the Thomas collapse is avoided, while the nonrelativistic limit kept the Efimov effect. Furthermore, the stability in the zero-range limit is a result of the reduction of boosted potential with the increase of the virtual pair center of mass momentum within the three-boson system. Finally, we compare the present results with Light-Front and Euclidean calculations.