Universality of Three Identical Bosons with Large, Negative Effective Range
Harald W. Griesshammer (George Washington U.)🇺🇸 · Ubirajara van Kolck (CNRS/IN2P3 and U. of Arizona)🇫🇷
"Resummed-Range Effective Field Theory'' is a consistent nonrelativistic effective field theory of contact interactions with large scattering length and an effective range large in magnitude but negative. Its leading order is non-perturbative. Its observables are universal, i.e.~they depend only on the dimensionless ratio , with the overall distance scale set by . In the two-body sector, the position of the two shallow -wave poles in the complex plane is determined by . We investigate three identical bosons at leading order for a two-body system with one bound and one virtual state (), or with two virtual states (). 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 . Three-body excitations appear for even smaller ranges of around the ``quasi-unitarity point'' () and obey discrete scaling relations. We explore in detail the ground state and the lowest three excitations and parametrise their trajectories as function of and of the binding momentum of the shallowest \twoB state from where three-body and two-body binding energies are identical to zero three-body binding. As 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 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.