The Three-Boson System with Short-Range Interactions

Abstract

We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be summed, which leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in one local three-body force counterterm and compute the running of the three-body force with the cutoff. This allows a calculation of the scattering of a particle and the two-particle bound state if the corresponding scattering length is used as input. We also obtain a model-independent relation between binding energy of a shallow three-body bound state and this scattering length. We comment on the power counting that organizes higher-order corrections and on relevance of this result for the effective field theory program in nuclear and molecular physics.

24 pages, RevTex, 15 PS figures included with epsf.sty

References in corpus (4)

• Renormalization of the Three-Body System with Short-Range Interactions
• Chiral Symmetry and Three-Nucleon Forces
• Gamma-Deuteron Compton Scattering in Effective Field Theory
• Systematic Power Counting in Cutoff Effective Field Theories for Nucleon-Nucleon Interactions and the Equivalence With PDS

Cited by in corpus (277)

• Modern Theory of Nuclear Forces
• Universality in Few-body Systems with Large Scattering Length
• Three-Nucleon Forces from Chiral Effective Field Theory
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Nuclear effective field theory: status and perspectives
• Efimov Physics: a review
• Renormalization of One-Pion Exchange and Power Counting
• Three-body forces: From cold atoms to nuclei
• Towards a Perturbative Theory of Nuclear Forces
• Effective Field Theory for Halo Nuclei: Shallow p-Wave States
• Three-boson problem near a narrow Feshbach resonance
• Three-body recombination in Bose gases with large scattering length
• NNLO Corrections to Nucleon-Nucleon Scattering and Perturbative Pions
• Universal Properties of the Four-Body System with Large Scattering Length
• The Four-Boson System with Short-Range Interactions
• Three-particle scattering amplitudes from a finite volume formalism
• The nucleon-nucleon interaction
• Power counting with one-pion exchange
• Low Energy Expansion in the Three Body System to All Orders and the Triton Channel
• Effective field theory description of halo nuclei
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Singular Potentials and Limit Cycles
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• Efimov Physics in Cold Atoms
• Three-body recombination into deep bound states in a Bose gas with large scattering length
• Rearranging Pionless Effective Field Theory
• Heavy-quark spin and flavour symmetry partners of the X(3872) revisited: what can we learn from the one boson exchange model?
• Three-body spectrum in a finite volume: the role of cubic symmetry
• On the correlation between the binding energies of the triton and the alpha-particle
• Coulomb Effects in Low Energy Proton-Proton Scattering
• Conformal Invariance for Non-Relativistic Field Theory
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Anomalies in Quantum Mechanics: the 1/r^2 Potential
• Subleading contributions to the three-nucleon contact interaction
• Effective Field Theory for Dilute Fermi Systems
• Efimov States in Nuclear and Particle Physics
• A renormalized approach to neutrinoless double-beta decay
• alpha-alpha Scattering in Halo Effective Field Theory
• Anomaly in conformal quantum mechanics: From molecular physics to black holes
• Improved Convergence in the Three-Nucleon System at Very Low Energies
• An Infrared Renormalization Group Limit Cycle in QCD
• A renormalisation group approach to two-body scattering in the presence of long-range forces
• Nuclear Physics Around the Unitarity Limit
• Efimov physics beyond universality
• Quantum Computing for Neutrino-nucleus Scattering
• Wigner symmetry in the limit of large scattering lengths
• Three-body problem in heteronuclear mixtures with resonant interspecies interaction
• Range Corrections to Doublet S-Wave Neutron-Deuteron Scattering
• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• Two-Nucleon Systems in a Finite Volume: (I) Quantization Conditions
• Naive Dimensional Analysis for Three-Body Forces Without Pions
• Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass
• Renormalization of Singular Potentials and Power Counting
• Stability of the fermionic gases close to a p-wave Feshbach resonance
• Precision neutron interferometric measurements and updated evaluations of the n-p and n-d coherent neutron scattering lengths
• Effective Theory for Trapped Few-Fermion Systems
• Adiabatic hyperspherical study of triatomic helium systems
• Quartet S Wave Neutron Deuteron Scattering in Effective Field Theory
• Efimov physics in a finite volume
• The singular inverse square potential, limit cycles and self-adjoint extensions
• Universality of an impurity in a Bose-Einstein condensate
• Universal Properties of Two-Dimensional Boson Droplets
• Scattering Models for Ultracold Atoms
• Towards grounding nuclear physics in QCD
• Super Efimov effect of resonantly interacting fermions in two dimensions
• ${}^6$He nucleus in halo effective field theory
• Lattice chiral effective field theory with three-body interactions at next-to-next-to-leading order
• Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
• Universality in the Three-Body Problem for 4He Atoms
• Low-Energy Universality in Atomic and Nuclear Physics
• Three particles in a finite volume: The breakdown of spherical symmetry
• Pion-less effective field theory for atomic nuclei and lattice nuclei
• Enhanced Dimer Relaxation in an Atomic/Molecular BEC
• Range Corrections to Three-Body Observables near a Feshbach Resonance
• On the modification of the Efimov spectrum in a finite cubic box
• Fully Perturbative Calculation of $nd$ Scattering to Next-to-next-to-leading-order
• Properties of the strongly paired fermionic condensates
• Energetics and structural properties of three-dimensional bosonic clusters near threshold
• How (not) to renormalize integral equations with singular potentials in effective field theory
• Precise numerical results for limit cycles in the quantum three-body problem
• Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons
• $Nd\to {}^{3}H\gamma$ with Effective Field Theory
• Four-Body Scale in Universal Few-Boson Systems
• A renormalized equation for the three-body system with short-range interactions
• The three-body problem with short-range forces: renormalized equations and regulator-independent results
• Universal Equation for Efimov States
• Two- and three-body interactions in ${\phi }^4$ theory from lattice simulations
• Three-Body Recombination of Identical Bosons with a Large Positive Scattering Length at Nonzero Temperature
• The Hypertriton in Effective Field Theory
• Spectra and Scattering of Light Lattice Nuclei from Effective Field Theory
• Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory
• Efimov effect from functional renormalization
• Effective theories of scattering with an attractive inverse-square potential and the three-body problem
• Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework
• Effective field theory calculation of nd radiative capture at thermal energies
• The three-boson system at next-to-leading order in an effective field theory for systems with a large scattering length
• Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order
• An effective field theory for coupled-channel scattering
• Solving relativistic three-body integral equations in the presence of bound states
• On the limit cycle for the 1/r^2 potential in momentum space
• Effective Field Theory for Few-Boson Systems
• Functional renormalization for trion formation in ultracold fermion gases
• Comparative study of three-nucleon force models in $A=3,4$ systems
• Quartet S-wave p-d scattering in EFT
• Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs
• Efimov States in a Bose-Einstein Condensate near a Feshbach Resonance
• Liberating Efimov physics from three dimensions
• The ^4He trimer as an Efimov system
• Efimov Physics and Connections to Nuclear Physics
• The triton and three-nucleon force in nuclear lattice simulations
• Renormalization group study of the four-body problem
• Three-body scattering from nonperturbative flow equations
• Effective Field Theory and the Gamow Shell Model: The 6He Halo Nucleus
• Field Redefinitions at Finite Density
• ${}^3\mathrm{He}$ and $pd$ Scattering to Next-to-Leading Order in Pionless Effective Field Theory
• Effective density functionals beyond mean field
• Building light nuclei from neutrons, protons, and pions
• Confinement-induced Efimov resonances in Fermi-Fermi mixtures
• Spectral convexity for attractive SU(2N) fermions
• Two and Three Nucleons in a Trap and the Continuum Limit
• Scale Invariance in Heavy Hadron Molecules
• The Long and Short of Nuclear Effective Field Theory Expansions
• On the convergence of nuclear effective field theory with perturbative pions
• Embedding nuclear physics inside the unitary window
• Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei
• The Triton Charge Radius to Next-to-next-to-leading order in Pionless Effective Field Theory
• Universality in the triton charge form factor
• Naturalness in Nuclear Effective Field Theories
• Renormalization in conformal quantum mechanics
• Dissecting reaction calculations using Halo EFT and ab initio input
• How to renormalize integral equations with singular potentials in effective field theory
• Ground-state properties of unitary bosons: from clusters to matter
• Efimov correlations in strongly interacting Bose gases
• Dilute resonating gases and the third virial coefficient
• Probing strongly interacting atomic gases with energetic atoms
• Three-body loss in lithium from functional renormalization
• Few-nucleon matrix elements in pionless effective field theory in a finite volume
• Nature of 3D Bose Gases near Resonance
• Impurity-induced multi-body resonances in a Bose gas
• Beyond universality in three-body recombination: an Effective Field Theory treatment
• Investigation of the $nn\Lambda$ bound state in pionless effective theory
• Three-nucleon bound states and the Wigner-SU(4) limit
• Aspects of Non-Relativistic Quantum Field Theories
• On the three-particle analog of the Lellouch-Lüscher formula
• The Anapole Form Factor of the Deuteron
• Universal Relations for Range Corrections to Efimov Features
• Nuclear Reactions from Lattice QCD
• Effective Field Theory for Fermi Systems in a large N expansion
• Scattering length of the helium atom - helium dimer collision
• The impact of bound states on similarity renormalization group transformations
• More on the infrared renormalization group limit cycle in QCD
• Fate of the neutron-deuteron virtual state as an Efimov level
• N-body Efimov states from two-particle noise
• Renormalisation-group analysis of repulsive three-body systems
• Regularized zero-range model and an application to the triton and the hypertriton
• $\theta$-dependence of light nuclei and nucleosynthesis
• Three-body repulsive forces among identical bosons in one dimension
• Resonant Dimer Relaxation in Cold Atoms with a Large Scattering Length
• Energies and radii of light nuclei around unitarity
• Tritium $\beta$-decay in pionless effective field theory
• The renormalisation group and nuclear forces
• Parity Violation in nd Interactions
• New Calculations of Recombination Rates for Cold ${}^4$He Atoms and Determination of Universal Scaling Functions
• Effective Range Corrections to Three-Body Recombination for Atoms with Large Scattering Length
• Clustering of Four-Component Unitary Fermions
• Nuclear Effective Field Theories: Reverberations of the early days
• Conformality Lost in Efimov Physics
• Renormalization Group Limit Cycle for Three-Stranded DNA
• Triton Photodisintegration with Effective Field Theory
• Universal few-body physics in a harmonic trap
• Perturbative Effective Field Theory at Finite Density
• Numerical renormalization using dimensional regularization: a simple test case in the Lippmann-Schwinger equation
• Temperature-dependent errors in nuclear lattice simulations
• Resonant Atom-Dimer Relaxation in Ultracold Atoms
• Particle-dimer approach for the Roper resonance in a finite volume
• Three-body resonances in pionless effective field theory
• Renormalization of the three-boson system with short-range interactions revisited
• The $D^{\ast }{D}^{\ast }\bar{D}$ and $D^{\ast }{D}^{\ast }{\bar{D}}^{\ast }$ Three-Body Systems
• Bound states in the B-matrix formalism for the three-body scattering
• Five-body calculation of $s$-wave $n$-${}^4$He scattering at next-to-leading order pionless effective field theory
• Anomalous frequency shifts in a one-dimensional trapped Bose gas
• Universality Constraints on Three-Body Recombination for Cold Atoms: from 4He to 133Cs
• Three Bosons in One Dimension with Short Range Interactions I: Zero Range Potentials
• Recombination rates from potential models close to the unitary limit
• Effective field theory for dilute Fermi systems at fourth order
• An alternative scheme for effective range corrections in pionless EFT
• Heavy hadron molecules in effective field theory: the emergence of exotic nuclear landscapes
• Quantum Corrections to Dilute Bose Liquids
• Neutron interferometric measurement of the scattering length difference between the triplet and singlet states of n-${}^3$He
• Structure Factors of Neutron Matter at Finite Temperature
• Effective interactions and operators in no-core shell model
• Few-body states of bosons interacting with a heavy quantum impurity
• Few nucleons scattering in pionless effective field theory
• An effective-field-theory analysis of Efimov physics in heteronuclear mixtures of ultracold atomic gases
• Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances
• More on the universal equation for Efimov states
• Constraining the neutron-neutron scattering length with \eftnopi
• DVCS-Dissociation of the Deuteron and the EMC Effect
• Van der Waals universality in homonuclear atom-dimer elastic collisions
• Supersymmetric Galilean Electrodynamics
• Renormalization group analysis of resonantly interacting anyons
• Atom-dimer scattering in heteronuclear mixture with finite intra-species scattering length
• Time fractals and discrete scale invariance with trapped ions
• Renormalization Group Improved Gap Equation for Color Superconductors
• Three-body systems in pionless effective field theory
• Local realizations of contact interactions in two- and three-body problems
• Parity-Violating Three Nucleon Interactions at Low Energies and Large-$N_C$
• Efimov like phase of a three stranded DNA (Efimov-DNA) and the renormalization group limit cycle
• Convergence Properties of the Effective Theory for Trapped Bosons
• Weakly bound molecules trapped with discrete scaling symmetries
• The van der Waals interaction as the starting point for an effective field theory
• General aspects of effective field theories and few-body applications
• Application of EFT at Thermal Energies
• Charge and Matter Form Factors of Two-Neutron Halo Nuclei in Halo Effective Field Theory at Next-to-leading-order
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• Describing Nuclear Matter with Effective Field Theories
• Efimov effect at the Kardar-Parisi-Zhang roughening transition
• P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED
• Large-$N_c$ constraints for elastic dark matter-light nucleus scattering in pionless effective field theory
• How to renormalize coupled cluster theory
• Topological origin of universal few-body clusters in Efimov physics
• Hypernuclei in Halo/Cluster Effective Field Theory
• Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions
• Few-body universality in the deuteron-alpha system
• Galilean fermions: Classical and quantum aspects
• The Similarity Renormalization Group for Three-Body Interactions in One Dimension
• Universal physics of the few-body system of two neutrons and one flavored meson
• Spurious poles in a finite volume
• Few-body physics in effective field theory
• Universal Efimov Scaling in the Rabi-Coupled Few-Body Spectrum
• Lattice Improvement in Lattice Effective Field Theory
• Three-Boson Bound States in Two Dimensions
• Second root of dilute Bose-Fermi mixtures
• Causality bounds for neutron-proton scattering
• The ${\bar{D}}^{\ast }{\bar{D}}^{\ast }{\Sigma }_c$ Three-Body System
• Theoretical evaluation of solar proton-proton fusion reaction rate and its uncertainties
• Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons
• Flow equation of functional renormalization group for three-body scattering problems
• Cold Neutron-Deuteron Capture and Wigner-SU(4) Symmetry
• Investigations of the $D$-multi-$\rho$ interactions
• Effective field theory for one-dimensional nonrelativistic particles with contact interaction
• Selected Topics in Three- and Four-Nucleon Systems
• Lattice methods and effective field theory
• New near-threshold mesons
• Quantum Monte Carlo studies of a trimer scaling function with microscopic two- and three-body interactions
• Worldline Monte Carlo method for few body nuclear physics
• The Four-Boson First-Excited State Near Two-Body Unitarity
• Four-Body Systems at Large Cutoffs in Effective Field Theory
• Efimov-like physics in fraction-dimensional Bose systems with three-body interaction
• Electric dipole moments of three-nucleon systems in the pionless effective field theory
• On the Determination of Elastic and Inelastic Nuclear Observables from Lattice QCD
• Efimov Effect in Long-range Quantum Spin Chains
• The Efimov effect for heteronuclear three-body systems at positive scattering length and finite temperature
• Effective field theory analysis of boson-trimer bond lengths to next-to-leading order
• Corrections to reaction-diffusion dynamics above the upper critical dimension
• Universality in the physics of cold atoms with large scattering length
• Two-Body Triton Photodisintegration and Wigner-SU(4) Symmetry
• Weinberg and few-nucleon forces
• The role of the effective range in strongly-interacting few-body systems
• Universal Bound States in Long-range Spin Chains with an Impurity
• Condensates of Strongly-interacting Atoms and Dynamically Generated Dimers
• Coboson many-body formalism for atom-dimer scattering length
• Investigation of ${\Xi }^{-}nn$ ($S=-2$) Hypernucleus in Low-energy Pionless Halo Effective Theory
• ${}_{\Lambda \Lambda }^5$H and ${}_{\Lambda \Lambda }^5$He Hypernuclei reexamined in Halo/Cluster Effective Theory
• Three-body halo states in effective field theory
• Paired fermionic superfluids with s- and p-wave interactions
• A renormalization method for three-boson system with a triboson field
• Short-distance production of three particles with large scattering length
• Semisuper Efimov effect induced by resonant pair exchange in mixed dimensions
• Universal Relations in Long-range Quantum Spin Chains
• Low Energy Continuum and Lattice Effective Field Theories
• Limit Cycles from the Similarity Renormalization Group
• Developments in non-relativistic field theory and complexity
• Model-independent mass determination of near-threshold states from short-range production
• The fractal geometry and the mapping of Efimov states to Bloch states
• Transverse Asymmetry in Nucleon Deuteron Scattering in Pionless Effective Field Theory
• Analysis of three-nucleon forces effects in the $A=3$ system