# Removing the Wigner bound in non-perturbative effective field theory

## TL;DR

This paper investigates how the Wigner bound, which limits the effective range in scattering, can be relaxed or removed in non-perturbative effective field theories by considering higher orders and renormalization effects.

## Contribution

It demonstrates that the Wigner bound loosens with higher-order contact EFTs and vanishes at infinite order, allowing for better control of three-body systems without collapse.

## Key findings

- Wigner bound weakens with higher EFT orders
- Bound vanishes at infinite order
- Avoids Thomas collapse in three-body systems

## Abstract

The Wigner bound, setting an upper limit on the scattering effective range, is examined at different orders of contact effective field theory. Using cutoff regulator we show that the bound loosens when higher orders of the theory are considered. For a sharp and a Gaussian regulators, we conjecture an analytic formula for the dependence of the Wigner bound on the theory's order. It follows that the bound vanishes in the limit of infinite order. Using a concrete numerical example we demonstrate that the above surmise still holds after renormalization at finite cutoff. Studying the 3-body system with this example, we have found that limiting the permissible range of cutoffs by the Wigner bound, we avoid the Thomas collapse, and don't need to promote the 3-body force to leading order.