Universality for Three Bosons with Large, Negative Effective Range: Aspects and Addenda

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 \(r_0\) $r_0$ large in magnitude but negative. Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio \(\xi :=2r_0/a\) $\xi :=2r_0/a$ once \(|r_0|\) $|r_0|$ 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 \(0.366\ldots \ge \xi \ge -8.72\ldots \) $0.366\dots \ge \xi \ge -8.72\dots$ , and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero \(r_0\) $r_0$ .