Impossibility of the Efimov effect for p-wave interactions

TL;DR

This paper demonstrates that the Efimov effect cannot occur for p-wave interactions because the assumed scattering amplitude leads to negative probabilities, making such states physically unrealizable.

Contribution

It clarifies that the Efimov effect is impossible for p-wave and higher partial-wave interactions, correcting recent claims and reinforcing previous theoretical arguments.

Findings

P-wave scattering amplitude causes negative probability.

Efimov states cannot be realized in physical systems.

The Efimov effect is impossible for higher partial waves.

Abstract

Whether the Efimov effect is possible, in principle, for p-wave or higher partial-wave interactions is a fundamental question. Recently, there has been a claim that three nonrelativistic particles with resonant p-wave interactions exhibit the Efimov effect. We point out that the assumed p-wave scattering amplitude inevitably causes a negative probability. This indicates that the Efimov states found there cannot be realized in physical situations. We also restate our previous argument that the Efimov effect, defined as an infinite tower of universal bound states characterized by discrete scale invariance, is impossible for p-wave or higher partial-wave interactions.