Abstract
Resummed-range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length a and an effective range \(r_0\) large in magnitude but negative. Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio \(\xi :=2r_0/a\) once \(|r_0|\) is chosen as base unit. This presentation highlights aspects for three identical spinless bosons and adds details to a previous discussion (Griesshammer and van Kolck in Eur Phys J A 59:289, 2023). At leading order, no three-body interaction is needed. A ground state exists only in the range \(0.366\ldots \ge \xi \ge -8.72\ldots \), and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero \(r_0\).
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H.W. Grießhammer and U. van Kolck, in preparation
Acknowledgements
It continues to be a pleasure to collaborate with Ubirajara van Kolck. I am grateful to the organisers and participants of EuroFewB 2023 in Mainz for spirited, stimulating and profound discussions, a delightful atmosphere, and for indulging such a topic as the last plenary presentation. Instrumental for this research were the warm hospitality and financial support for stays at IJCLab Orsay and at the Kavli Institute for Theoretical Physics which is supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. This material is based upon work supported in part by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under award DE-SC0015393.
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Grießhammer, H.W. Universality for Three Bosons with Large, Negative Effective Range: Aspects and Addenda. Few-Body Syst 65, 53 (2024). https://doi.org/10.1007/s00601-024-01923-3
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DOI: https://doi.org/10.1007/s00601-024-01923-3