Effective Field Theory for Short-Range Forces

Abstract

The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that the renormalized EFT is equivalent to the effective range expansion, to a Schroedinger equation with a pseudo-potential, and to an energy expansion of a generic boundary condition at the origin. The roles of regulators and potentials are also discussed. These ideas are exemplified in a toy model.

38 pages, 6 figures

References in corpus (6)

• A New Expansion for Nucleon-Nucleon Interactions
• Nucleon-Deuteron Scattering from an Effective Field Theory
• Non-perturbative regularization and renormalization: simple examples from non-relativistic quantum mechanics
• The potential of effective field theory in NN scattering
• Electromagnetic Corrections to the One-Pion-Exchange Potential
• Regularization Methods for Nucleon-Nucleon Effective Field Theory

Cited by in corpus (319)

• Modern Theory of Nuclear Forces
• Universality in Few-body Systems with Large Scattering Length
• Effective Field Theory for Few-Nucleon Systems
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Nuclear effective field theory: status and perspectives
• Three-body forces: From cold atoms to nuclei
• Quantum Simulation for High Energy Physics
• Towards a Perturbative Theory of Nuclear Forces
• Nucleon-Nucleon Effective Field Theory Without Pions
• Effective Field Theory of Nuclear Forces
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Effective Field Theory for Halo Nuclei: Shallow p-Wave States
• Two Nucleons on a Lattice
• Pion Interactions in the X(3872)
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• Universal Properties of the Four-Body System with Large Scattering Length
• The Four-Boson System with Short-Range Interactions
• A method to measure the antikaon-nucleon scattering length in lattice QCD
• Power counting with one-pion exchange
• A renormalisation-group treatment of two-body scattering
• Effective field theory description of halo nuclei
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Narrow Resonances in Effective Field Theory
• Light Flavour and Heavy Quark Spin Symmetry in Heavy Meson Molecules
• Nuclear Parity-Violation in Effective Field Theory
• Rearranging Pionless Effective Field Theory
• Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
• Entanglement Suppression and Emergent Symmetries of Strong Interactions
• Anatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Simulations of Subatomic Many-Body Physics on a Quantum Frequency Processor
• Neutrino-Deuteron Scattering in Effective Field Theory at Next-to-Next-to Leading Order
• Improving the Convergence of NN Effective Field Theory
• Heavy Quark Symmetry Predictions for Weakly Bound B-Meson Molecules
• A renormalized approach to neutrinoless double-beta decay
• alpha-alpha Scattering in Halo Effective Field Theory
• Power Counting and Perturbative One Pion Exchange in Heavy Meson Molecules
• Effective Field Theory for Lattice Nuclei
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• No-core shell model in an effective-field-theory framework
• Exploring Hyperons and Hypernuclei with Lattice QCD
• Hadronic Decays of the X(3872) to chi_{cJ} in Effective Field Theory
• Ground-State Properties of ${}^4$He and ${}^{16}$O Extrapolated from Lattice QCD with Pionless EFT
• A renormalisation group approach to two-body scattering in the presence of long-range forces
• Nuclear Physics Around the Unitarity Limit
• Exploring Bayesian parameter estimation for chiral effective field theory using nucleon-nucleon phase shifts
• Chiral Corrections to Matrix Elements of Twist-2 Operators
• Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves
• Wigner symmetry in the limit of large scattering lengths
• Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD
• Range Corrections to Doublet S-Wave Neutron-Deuteron Scattering
• Baryon-Baryon Interactions and Spin-Flavor Symmetry from Lattice Quantum Chromodynamics
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge
• Ab initio calculation of the $np\to d\gamma$ radiative capture process
• Short-range nuclear forces in singlet channels
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• 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
• Electric properties of the Beryllium-11 system in Halo EFT
• Quartet S Wave Neutron Deuteron Scattering in Effective Field Theory
• Scattering Models for Ultracold Atoms
• The $P_{cs}(4459)$ pentaquark from a combined effective field theory and phenomenological perspective
• Bayesian Methods for Parameter Estimation in Effective Field Theories
• Experiments in Fundamental Neutron Physics
• Higher Partial Waves in an Effective Field Theory Approach to nd Scattering
• Towards grounding nuclear physics in QCD
• An effective-field-theory analysis of low-energy parity-violation in nucleon-nucleon scattering
• Implications of a matter-radius measurement for the structure of Carbon-22
• From bound states to the continuum
• ${}^6$He nucleus in halo effective field theory
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• What is ab initio in nuclear theory?
• Low-Energy Universality in Atomic and Nuclear Physics
• Minimally-Entangled State Preparation of Localized Wavefunctions on Quantum Computers
• Pion-less effective field theory for atomic nuclei and lattice nuclei
• Elastic and Inelastic Neutrino-Deuteron Scattering in Effective Field Theory
• Proton-Proton Fusion in Effective Field Theory
• Electromagnetic Structure of the Z_c(3900)
• Double-$\beta$ Decay Matrix Elements from Lattice Quantum Chromodynamics
• Proton-Proton Fusion in Effective Field Theory to Fifth Order
• Deconstructing triplet nucleon-nucleon scattering
• Subleading contributions to the decay width of the $T_{cc}^{+}$ tetraquark
• Coupled-channel approach in hadron-hadron scattering
• The isotensor axial polarisability and lattice QCD input for nuclear double-$\beta$ decay phenomenology
• Effective field theory of the deuteron with dibaryon field
• Four-Body Scale in Universal Few-Boson Systems
• General considerations on the nature of $Z_b(10610)$ and $Z_b(10650)$ from their pole positions
• Isoscalar M1 and E2 Amplitudes in n+p -> d+gamma
• The Energy of n Identical Bosons in a Finite Volume at O(L^{-7})
• Nuclear Currents in Chiral Effective Field Theory
• Minimal Entanglement and Emergent Symmetries in Low-energy QCD
• The Time-Reversal- and Parity-Violating Nuclear Potential in Chiral Effective Theory
• An effective field theory approach to two trapped particles
• A renormalized equation for the three-body system with short-range interactions
• Halo effective field theory constrains the solar Beryllium-7 + proton -> Boron-8 + photon rate
• Renormalization of Singlet NN-Scattering with One Pion Exchange and Boundary Conditions
• Wilsonian renormalization group versus subtractive renormalization in effective field theories for nucleon--nucleon scattering
• The three-body problem with short-range forces: renormalized equations and regulator-independent results
• Renormalization of NN-Scattering with One Pion Exchange and Boundary Conditions
• The Hypertriton in Effective Field Theory
• New Ideas in Constraining Nuclear Forces
• Spectra and Scattering of Light Lattice Nuclei from Effective Field Theory
• Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory
• 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
• Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures
• Charged multi-hadron systems in lattice QCD+QED
• Effective field theory of 3He
• Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order
• An effective field theory for coupled-channel scattering
• The three-boson system at next-to-leading order in an effective field theory for systems with a large scattering length
• Three-Body Hypernuclei in Pionless Effective Field Theory
• Nucleon-Nucleon Interaction: A Typical/Concise Review
• Renormalization Group Analysis of Boundary Conditions in Potential Scattering
• Effective Field Theory for Few-Boson Systems
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Lattice Calculation of Thermal Properties of Low-Density Neutron Matter with Pionless NN Effective Field Theory
• Heavy Baryon-Antibaryon Molecules in Effective Field Theory
• Quartet S-wave p-d scattering in EFT
• Two parity violating asymmetries from $np\to d\gamma$ in pionless effective field theories
• New results from a number operator interpretation of the compositeness of bound and resonant states
• Efimov Physics and Connections to Nuclear Physics
• Marrying ab initio calculations and Halo EFT: the case of ${}^7\mathrm{Be}+p\to {}^8\mathrm{B}+\gamma$
• Constraining the Leading Weak Axial Two-body Current by SNO and Super-K
• Deuteron electromagnetic properties and the viability of effective field theory methods in the two-nucleon system
• About the Equivalence of Cut-off and Renormalised Effective Field Theories
• Effective Field Theory and the Gamow Shell Model: The 6He Halo Nucleus
• The Two-Nucleon 1S0 Amplitude Zero in Chiral Effective Field Theory
• Carbon-19 in Halo EFT: Effective-range parameters from Coulomb-dissociation experiments
• Low-energy Scattering and Effective Interactions of Two Baryons at $m_{\pi }\sim 450$ MeV from Lattice Quantum Chromodynamics
• Constraints on Two-Body Axial Currents from Reactor Antineutrino-Deuteron Breakup Reactions
• Power counting in chiral effective field theory and nuclear binding
• Effective Field Theory for Rydberg Polaritons
• Systematically Localizable Operators for Quantum Simulations of Quantum Field Theories
• Perturbative $NN$ scattering in chiral effective field theory
• ${}^3\mathrm{He}$ and $pd$ Scattering to Next-to-Leading Order in Pionless Effective Field Theory
• Two-Particle Elastic Scattering in a Finite Volume Including QED
• Low-energy p-d scattering and He-3 in pionless EFT
• Resolving the $\Lambda$ hypernuclear overbinding problem in pionless effective field theory
• The path from lattice QCD to the short-distance contribution to $0\nu \beta \beta$ decay with a light Majorana neutrino
• Building light nuclei from neutrons, protons, and pions
• Two and Three Nucleons in a Trap and the Continuum Limit
• From Low-Density Neutron Matter to the Unitary Limit
• Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime
• Marrying {\it ab initio} calculations and Halo-EFT: the case of ${}^7\mathrm{Li}+n\to {}^8\mathrm{Li}+\gamma$
• Compton Scattering on the Deuteron in Baryon Chiral Perturbation Theory
• Heavy-hadron molecules from light-meson-exchange saturation
• Resonance Contribution to Radiative Neutron Capture on Lithium-7
• The N N -> NN pi+ Reaction near Threshold in a Chiral Power Counting Approach
• Geometry and entanglement in the scattering matrix
• The Triton Charge Radius to Next-to-next-to-leading order in Pionless Effective Field Theory
• Embedding nuclear physics inside the unitary window
• $S$-factor and scattering-parameter extractions from ${}^3\mathrm{He}+{}^4\mathrm{He}\to {}^7\mathrm{Be}+\gamma$
• Naturalness in Nuclear Effective Field Theories
• Coupled-channel effective field theory and proton-${}^7$Li scattering
• Ab initio calculations of low-energy nuclear scattering using confining potential traps
• Deuteron form factors in chiral effective theory: regulator-independent results and the role of two-pion exchange
• Ground-state properties of unitary bosons: from clusters to matter
• Energy Spectrum of Neutron-Rich Helium Isotopes: Complex Made Simple
• Few-nucleon matrix elements in pionless effective field theory in a finite volume
• Interpretations of the new LHCb $P_c(4337{)}^{+}$ pentaquark state
• Effective Field Theory for Dilute Fermions with Pairing
• Efimov physics from a renormalization group perspective
• Three-nucleon bound states and the Wigner-SU(4) limit
• The onset of $\Lambda \Lambda$ hypernuclear binding
• Nuclear Reactions from Lattice QCD
• Effective Field Theory for Fermi Systems in a large N expansion
• Consistency of the effective-field-theory approach to the nucleon-nucleon interaction problem revisited
• The proton-deuteron system in pionless EFT revisited
• Ground state energy of the interacting Bose gas in two dimensions: an explicit construction
• Scheming in Dimensional Regularization
• Renormalisation-group analysis of repulsive three-body systems
• Fate of the neutron-deuteron virtual state as an Efimov level
• Regularized zero-range model and an application to the triton and the hypertriton
• Deconstructing 1S0 nucleon-nucleon scattering
• n + p -> d + gamma in Effective Field Theory
• Extracting free-space observables from trapped interacting clusters
• Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory
• Peaks within peaks and the possible two-peak structure of the Pc(4457): the effective field theory perspective
• Narrow resonances and short-range interactions
• Anomalous dimensions determine the power counting -- Wilsonian RG analysis of nuclear EFT --
• Effective Field Theory of Nucleon-Nucleon Scattering on Large Discrete Lattices
• The renormalisation group and nuclear forces
• Weinberg's Compositeness
• Electromagnetic characteristics of $A\le 3$ physical and lattice nuclei
• Quark mass dependence of H-dibaryon in $\Lambda \Lambda$ scattering
• Second-order perturbation theory for 3He and pd scattering in pionless EFT
• The Continuum Spectrum of Hypernuclear Trios
• Universal Two-Body Spectra of Ultracold Harmonically Trapped Atoms in Two and Three Dimensions
• Relativistic chiral description of the ${}^1{S}_0$ nucleon-nucleon scattering
• Pions in the Pionless Effective Field Theory
• Quantum Monte Carlo calculations of two neutrons in finite volume
• Do we know how to count powers in pionless and pionful effective field theory?
• Range corrections in Proton Halo Nuclei
• On the Extraction of Low-energy Constants of Single- and Double-$\beta$ Decays from Lattice QCD: A Sensitivity Analysis
• Pions are neither perturbative nor nonperturbative: Wilsonian renormalization group analysis of nuclear effective field theory including pions
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Two-neutrino double-beta decay in pionless effective field theory from a Euclidean finite-volume correlation function
• Nuclear Effective Field Theories: Reverberations of the early days
• Renormalization of chiral two-pion exchange NN interactions with Delta-excitations: Central Phases and the Deuteron
• NNLO Calculation of Two-Nucleon Scattering in EFT for a Two Yukawa Toy Model
• Perturbative Effective Field Theory at Finite Density
• Nuclear physics uncertainties in light hypernuclei
• Three-body resonances in pionless effective field theory
• Effective range corrections from effective field theory with di-baryon fields and perturbative pions
• Off-shell effects and consistency of many-body treatments of dense matter
• From few to many bosons inside the unitary window: a transition between universal to non-universal behavior
• Five-body calculation of $s$-wave $n$-${}^4$He scattering at next-to-leading order pionless effective field theory
• Models, measurements, and effective field theory: proton capture on Beryllium-7 at next-to-leading order
• Quasiparticle Properties in Effective Field Theory
• Effective field theory for dilute Fermi systems at fourth order
• Nonlocality of the NN interaction in an effective field theory
• Heavy hadron molecules in effective field theory: the emergence of exotic nuclear landscapes
• The interplay between compact and molecular structures in tetraquarks
• An alternative scheme for effective range corrections in pionless EFT
• Ground-state energy shift of n pions and m kaons in a finite volume
• Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system
• Tan's distributions and Fermi-Huang pseudopotential in momentum space
• ${}_{\Lambda \Lambda }^{6}He$ in cluster effective field theory
• Effective interactions and operators in no-core shell model
• Structure Factors of Neutron Matter at Finite Temperature
• More about the Wilsonian analysis on the pionless NEFT
• Nonrelativistic Effective Field Theory with a Resonance Field
• Large-$N_c$ Relationships Among Two-Derivative Pionless Effective Field Theory Couplings
• Effective Field Theory with Dibaryon Fields: Nucleon-Nucleon amplitudes at NNLO
• Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances
• The Coulomb interaction in Helium-3: Interplay of strong short-range and weak long-range potentials
• Wilsonian renormalization group and the Lippmann-Schwinger equation with a multitude of cutoff parameters
• Properties of infrared extrapolations in a harmonic oscillator basis
• Constraining the neutron-neutron scattering length with \eftnopi
• A Higher-Order Calculation of $np$ Scattering in Cut-Off Effective Field Theory
• Toward a systematic strategy for defining power counting in the construction of the energy density functional theory
• Three-body systems in physics of cold atoms and halo nuclei
• The Operator Product Expansion Beyond Leading Order for Two-Component Fermions
• Contact operators in renormalization of attractive singular potentials
• Precision calculation of the quartet-channel p-d scattering length
• From Short-Range to Contact Interactions in Two-dimensional Many-Body Quantum Systems
• Local realizations of contact interactions in two- and three-body problems
• On-shell approximation for the s-wave scattering theory
• Large-$N_c$ analysis of magnetic and axial two-nucleon currents in pionless effective field theory
• Deuteron Compton Scattering in Effective Field Theory: Spin-Dependent Cross Sections and Asymmetries
• Deuteron Compton Scattering in Effective Field Theory And Spin-Independent Nucleon Polarizabilities
• A Two Potential Formula and its Application to Proton-Proton Scattering
• Drell-Hearn-Gerasimov Sum-Rule for the Deuteron in Nuclear Effective Field Theory
• Towards a power counting in nuclear energy-density-functional theories through a perturbative analysis
• Cascades and Collapses, Great Walls and Forbidden Cities: Infinite Towers of Metastable Vacua in Supersymmetric Field Theories
• Solving reaction dynamics with quantum computing algorithms
• General aspects of effective field theories and few-body applications
• Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content
• Universal behavior of $p$-wave proton-proton fusion near threshold
• Electric structure of shallow D-wave states in Halo EFT
• P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED
• Removing the Wigner bound in non-perturbative effective field theory
• Large-$N_c$ constraints for elastic dark matter-light nucleus scattering in pionless effective field theory
• Subleading contributions to $N$-boson systems inside the universal window
• Effective Field Theory for Nuclear Physics
• Halo structure of ${}^{17}$C
• Precision neutron interferometric measurements of the n-p, n-d, and n-3He zero-energy coherent neutron scattering amplitudes
• Universal physics of the few-body system of two neutrons and one flavored meson
• Short-range interactions and narrow resonances in effective field theory
• What hath Weinberg wrought? Reflections on what Weinberg's papers on 'Nuclear Forces from Chiral Lagrangians' did and did not accomplish
• Spectrum of light nuclei in a finite volume
• Pion-only, chiral light-front model of the deuteron
• A Vision for the Science of Rare Isotopes
• ${}^7$H ground state as a ${}^3$H+4n resonance
• Towards a unified treatment of $\Delta S=0$ parity violation in low-energy nuclear processes
• New fixed points of the renormalisation group for two-body scattering
• Thermodynamic contacts and breathing mode physics of 1D p-wave Fermi gases in the high temperature limit
• Dimensional crossover in non-relativistic effective field theory
• B${}_{\Lambda }$(${}_{\Lambda }^5$He) from short range effective field theory
• Causality bounds for neutron-proton scattering
• Asymmetric regularization of the ground and excited state of the helium-4 nucleus
• $NN$ scattering in ${}^3{S}_1{-}^3{D}_1$ channels of EFT ($/\pi$)
• Effective field theory for one-dimensional nonrelativistic particles with contact interaction
• Ultracold spin-balanced fermionic quantum liquids with renormalized $P$-wave interactions
• Finite-Size Effects in Heavy Halo Nuclei from Effective Field Theory
• A Padé-aided analysis of nonperturbative $NN$ scattering in ${}^1{S}_0$ channel
• Reexamining the perturbative renormalizability of the coupled triplets
• Large-$N_c$ and renormalization group constraints on parity-violating low-energy coefficients for three-derivative operators in pionless effective field theory
• A note on nonperturbative renormalization of effective field theory
• Effective Field Theory for Nuclear Physics
• Emergent four-body parameter in universal two-species bosonic systems
• Matching effective few-nucleon theories to QCD
• Toward precision Fermi liquid theory in two dimensions
• Neutrinoless double-beta decay in a finite volume from relativistic effective field theory
• Les Houches Lectures on Effective Field Theories for Nuclear and (some) Atomic Physics
• Nucleon-nucleon scattering with perturbative pions: The uncoupled $P$-wave channels
• The Four-Boson First-Excited State Near Two-Body Unitarity
• Feasibility of perturbative generation of bound-states from resonances or virtual states
• Effective range expansion in various scenarios of EFT($\notpi$)
• Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions
• Perturbative application of next-to-leading order pionless EFT for $A\le 3$ nuclei in a finite volume
• Short-range force between two Higgs bosons
• Tracing the evolution of nuclear forces under the similarity renormalization group
• Radiative Corrections and the Renormalization Group for the Two-Nucleon Interaction in Effective Field Theory
• Recent progress on hypernuclei
• Renormalisation-group analysis of electromagnetic couplings in the pionless effective field theory
• Cold atoms beyond atomic physics
• Residual cut-off dependence and power counting: the deuteron as a case study
• Contact interactions, self-adjoint extensions, and low-energy scattering
• Investigation of ${\Xi }^{-}nn$ ($S=-2$) Hypernucleus in Low-energy Pionless Halo Effective Theory
• New Photodisintegration Model of GEANT4 for the $d\gamma \to np$ Reaction with a Dibaryon Effective Field Theory
• ${}_{\Lambda \Lambda }^5$H and ${}_{\Lambda \Lambda }^5$He Hypernuclei reexamined in Halo/Cluster Effective Theory
• Renormalization group analysis of electromagnetic properties of the deuteron
• Exact evaluation of large-charge correlation functions in non-relativistic conformal field theory
• One- and two-neutron halos in effective field theory
• Quantum Simulation of Nuclear Dynamics in First Quantization
• Short-distance production of three particles with large scattering length
• Retardation effects from quark confinement on low-energy nucleon dynamics
• Auxiliary counterterms and their role in effective field theory
• Improved Actions for Nuclear Effective Field Theories
• Anomalous mapping between pionfull and pionless EFT's
• UV/IR symmetries of the $S$-matrix and RG flow
• Halo EFT calculation of charge form factor for two-neutron ${}^6\text{He}$ halo nucleus: two-body resonant P-wave interaction
• Symmetries of the nucleon-nucleon $S$-matrix and effective field theory expansions
• Trapped two-nucleon system in energy-dependent effective field theory
• Effective Field Theory and the Nuclear Many Body Problem
• Neutron-neutron distribution of the triton from pionless EFT
• The ${}^9$Be photodisintegration cross section within Cluster Effective Field Theory