Precise numerical results for limit cycles in the quantum three-body problem

Abstract

The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930's. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems ({\it e.g.}, few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed.

37 pages, 8 figures, LaTeX, uses graphicx

References in corpus (2)

• The Four-Boson System with Short-Range Interactions
• Effective theories of scattering with an attractive inverse-square potential and the three-body problem

Cited by in corpus (32)

• Modern Theory of Nuclear Forces
• Universality in Few-body Systems with Large Scattering Length
• Three-body forces: From cold atoms to nuclei
• Universal Properties of the Four-Body System with Large Scattering Length
• Effective field theory description of halo nuclei
• Efimov States in Nuclear and Particle Physics
• Universality and scaling limit of weakly-bound tetramers
• Four-boson scale near a Feshbach resonance
• Constraints on two-neutron separation energy in the Borromean ${}^{22}$C nucleus
• Efimov effect from functional renormalization
• Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework
• Effective Field Theory for Few-Boson Systems
• Two and Three Nucleons in a Trap and the Continuum Limit
• The role of nucleon recoil in low-energy antikaon-deuteron scattering
• Binding and structure of tetramers in the scaling limit
• Trajectory of neutron$-$neutron${-}^{18}C$ excited three-body state
• Neutron${-}^{19}$C scattering near an Efimov state
• Efimov physics from a renormalization group perspective
• The impact of bound states on similarity renormalization group transformations
• More on the infrared renormalization group limit cycle in QCD
• Three-boson recombination at ultralow temperatures
• The renormalisation group and nuclear forces
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Recoil corrections in antikaon-deuteron scattering
• An alternative scheme for effective range corrections in pionless EFT
• Limit cycles of effective theories
• Core momentum distribution in two-neutron halo nuclei
• Renormalization group procedure for potential $-g/r^2$
• Quantum Monte Carlo studies of a trimer scaling function with microscopic two- and three-body interactions
• Quantum N-Boson States and Quantized Motion of Solitonic Droplets: Universal Scaling Properties in Low Dimensions
• The role of the effective range in strongly-interacting few-body systems
• Limit Cycles from the Similarity Renormalization Group