## 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 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.

Original language | American English |
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Article number | 135485 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 806 |

DOIs | |

State | Published - 10 Jul 2020 |

### Bibliographical note

Funding Information:We would like to thank Bira van Kolck, Chen Ji, Sebastian König, and Ronen Weiss for useful discussions and communications during the preparation of this manuscript. This work was supported by the Israel Science Foundation (grant number 1308/16 ). SB was also supported by Israel Ministry of Science and Technology (MOST).

Publisher Copyright:

© 2020 The Authors