2023/08/02 by Harald W. Grießhammer, U. van Kolck, Griesshammer, Harald W. +1 · 2 citations
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #Atomic and Molecular Clusters (physics.atm-clus) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Nuclear Theory (nucl-th) #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2308.01394
openalex publication_date 2023/08/02 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/28
"Resummed-Range Effective Field Theory'' is a consistent nonrelativistic effective field theory of contact interactions with large scattering length a and an effective range r0 large in magnitude but negative. Its leading order is non-perturbative. Its observables are universal, i.e.~they depend only on the dimensionless ratio ξ:=2r0/a, with the overall distance scale set by |r0|. In the two-body sector, the 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) Resummed-Range EFT at LO. 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 (|r0|≪|a|→∞) and obey discrete scaling relations. We explore in detail the ground state and the lowest three excitations and parametrise their trajectories as function of ξ and of the binding momentum κ2- of the shallowest \twoB state from where three-body and two-body binding energies are identical to zero three-body binding. As |r0|≪|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.