1. Universality of three identical bosons with large, negative effective range.
- Author
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Grießhammer, Harald W. and van Kolck, Ubirajara
- Subjects
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BOUND states , *SCATTERING (Physics) , *BINDING energy , *BOSONS , *SHEAR waves , *MESONS - Abstract
"Resummed-Range Effective Field Theory" is a consistent nonrelativistic Effective Field Theory of contact interactions with large scattering length a and an effective range r 0 large in magnitude but negative. Its leading order is non-perturbative, and its observables are universal in the sense that they depend only on the dimensionless ratio ξ : = 2 r 0 / a once the overall distance scale is set by | r 0 | . In the two-body sector, the relative position of the two shallow S-wave poles in the complex plane is determined by ξ . We investigate three identical bosons at leading order for a two-body system with one bound and one virtual state ( ξ ≤ 0 ), or with two virtual states ( 0 ≤ ξ < 1 ). Such conditions might, for example, be found in systems of heavy mesons. We find that no three-body interaction is needed to renormalise (and stabilise) the leading order. A well-defined ground state exists for 0.366 ... ≥ ξ ≥ - 8.72 ... . Three-body excitations appear for even smaller ranges of ξ around the "quasi-unitarity point" ξ = 0 ( | r 0 | ≪ | a | → ∞ ) and obey discrete scaling relations. We explore in detail the ground state and the lowest three excitations. We parametrise their trajectories as function of ξ and of the binding momentum κ 2 - of the shallowest 2 B state. These stretch from the point where three- and two-body binding energies are identical to the point of zero three-body binding. As | r 0 | ≪ | a | becomes perturbative, this version turns into the "Short-Range EFT" which needs a stabilising three-body interaction and exhibits Efimov's Discrete Scale Invariance. By interpreting that EFT as a low-energy version of Resummed-Range EFT, we match spectra to determine Efimov's scale-breaking parameter Λ ∗ in a renormalisation scheme with a "hard" cutoff. Finally, we compare phase shifts for scattering a boson on the two-boson bound state with that of the equivalent Efimov system. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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