TY - JOUR

T1 - Removing the Wigner bound in non-perturbative effective field theory

AU - Beck, Saar

AU - Bazak, Betzalel

AU - Barnea, Nir

N1 - Publisher Copyright:
© 2020 The Authors

PY - 2020/7/10

Y1 - 2020/7/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85084859843&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2020.135485

DO - 10.1016/j.physletb.2020.135485

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AN - SCOPUS:85084859843

SN - 0370-2693

VL - 806

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

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

M1 - 135485

ER -