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.
Highlights
In the last two decades contact effective field theory (EFT) has been successfully applied for studying low energy systems where the characteristic particle wave length is much larger than the interaction range
First we show explicitly using partial renormalization that up to order N9LO, given a scattering length, the Wigner bound loosens as more EFT orders are taken into account
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 LO
Summary
In the last two decades contact effective field theory (EFT) has been successfully applied for studying low energy systems where the characteristic particle wave length is much larger than the interaction range Such systems can be found, for example, in ultra cold atomic gases, clusters of He atoms, and atomic nuclei, see e.g. We demonstrate, for a concrete example at N2LO, that our finding holds when the LECs are renormalized to reproduce the effective range expansion to order p4 From this analysis we conjecture that for an arbitrary value of Λ, any finite effective range reff can be described by the theory if the EFT order is large enough. A method to pick the physical one is suggested
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
