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 -