The three-boson system at next-to-leading order in an effective field theory for systems with a large scattering length

Abstract

We analyze how corrections linear in the effective range, r_0, affect quantities in the three-body sector within an effective field theory for short-range interactions. We demonstrate that observables can be obtained straightforwardly using a perturbative expansion in powers of r_0. In particular, we show that two linear-in-r_0 counterterms are needed for renormalization at this order if scattering-length-dependent observables are considered. We exemplify the implications of this result using various three-body observables. Analytic results for the running of the next-to-leading-order portion of the three-body force in this effective field theory are provided. Expressions which incorporate O(r_0) corrections and relate the positions of features observed in three-atom recombination near a Feshbach resonance are presented.

revtex4, 30 pages, 6figures, version2 accepted for publication in Annals of Physics, section on universal relations at NLO rewritten

References in corpus (8)

• Universality in Three- and Four-Body Bound States of Ultracold Atoms
• Observation of universality in ultracold 7Li three-body recombination
• Universal Relations for Identical Bosons from 3-Body Physics
• Efimov States in Nuclear and Particle Physics
• Scattering Models for Ultracold Atoms
• Range Corrections to Three-Body Observables near a Feshbach Resonance
• The Three-Boson System at Next-To-Next-To-Leading Order
• Beyond universality in three-body recombination: an Effective Field Theory treatment

Cited by in corpus (37)

• Nuclear effective field theory: status and perspectives
• Efimov Physics: a review
• Three-body forces: From cold atoms to nuclei
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Finite range corrections near a Feshbach resonance and their role in the Efimov effect
• Few-body physics in resonantly interacting ultracold quantum gases
• Implications of a matter-radius measurement for the structure of Carbon-22
• Energy shift of the three-particle system in a finite volume
• ${}^6$He nucleus in halo effective field theory
• Pion-less effective field theory for atomic nuclei and lattice nuclei
• Four-Body Scale in Universal Few-Boson Systems
• Effective Field Theory for Few-Boson Systems
• ${}^3\mathrm{He}$ and $pd$ Scattering to Next-to-Leading Order in Pionless Effective Field Theory
• Charge form factors of two-neutron halo nuclei in halo EFT
• The Triton Charge Radius to Next-to-next-to-leading order in Pionless Effective Field Theory
• Efimov-van-der-Waals universality for ultracold atoms with positive scattering lengths
• Efimov states near a Feshbach resonance and the limits of van der Waals universality at finite background scattering length
• Three-nucleon bound states and the Wigner-SU(4) limit
• Universal Relations for Range Corrections to Efimov Features
• Finite-range effects in Efimov physics beyond the separable approximation
• An alternative scheme for effective range corrections in pionless EFT
• Few nucleons scattering in pionless effective field theory
• An effective-field-theory analysis of Efimov physics in heteronuclear mixtures of ultracold atomic gases
• Universal and non-universal effective $N$-body interactions for ultracold harmonically-trapped few-atom systems
• Three-body systems in physics of cold atoms and halo nuclei
• The Avalanche Mechanism for Atom Loss near an Atom-Dimer Efimov Resonance
• Parity-Violating Three Nucleon Interactions at Low Energies and Large-$N_C$
• Avalanche Mechanism for the Enhanced Loss of Ultracold Atoms
• Spurious poles in a finite volume
• Neutron transfer reactions in halo effective field theory
• Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons
• Four-Body Systems at Large Cutoffs in Effective Field Theory
• Modeling atom-atom interactions at low energy by Jost-Kohn potentials
• The Efimov effect for heteronuclear three-body systems at positive scattering length and finite temperature
• Neutron-neutron distribution of the triton from pionless EFT
• Model-independent mass determination of near-threshold states from short-range production
• Finite-range bias in fitting three-body loss to the zero-range model