Causality and the effective range expansion

Abstract

We derive the generalization of Wigner's causality bounds and Bethe's integral formula for the effective range parameter to arbitrary dimension and arbitrary angular momentum. We also discuss the impact of these constraints on the separation of low- and high-momentum scales and universality in low-energy scattering. Some of our results were summarized earlier in a letter publication. In this work, we present full derivations and several detailed examples.

27 pages, 5 figures, explicit examples added, typos corrected, final version

References in corpus (10)

• Theory of ultracold Fermi gases
• Quantum Monte Carlo calculations of neutron-alpha scattering
• Universal Properties of the Four-Body System with Large Scattering Length
• p-wave Feshbach molecules
• Three fully polarized fermions close to a p-wave Feshbach resonance
• Universal Properties of Two-Dimensional Boson Droplets
• Strongly-resonant p-wave superfluids
• Analytic description of atomic interaction at ultracold temperatures: the case of a single channel
• Efimov effect from functional renormalization
• Prediction of Feshbach resonances from three input parameters

Cited by in corpus (63)

• Efimov Physics: a review
• Effective field theory description of halo nuclei
• Remarks on pole trajectories for resonances
• Volume Dependence of N-Body Bound States
• Radiative Neutron Capture on Lithium-7
• Universal high-momentum asymptote and thermodynamic relations in a spinless Fermi gas with a resonant $p$-wave interaction
• Effective range expansion for narrow near-threshold resonances
• Renormalization in the Three-body Problem with Resonant P-wave Interactions
• Non-relativistic bound states in a finite volume
• Impossibility of the Efimov effect for p-wave interactions
• Causality constraints for charged particles
• Hadron mass scaling near the s-wave threshold
• Quantum-defect theory for $-1/r^4$ type of interactions
• Strongly Interacting p-wave Fermi Gas in Two-Dimensions: Universal Relations and Breathing Mode
• Large-momentum distribution of a polarized Fermi gas and p-wave contacts
• Resonance Contribution to Radiative Neutron Capture on Lithium-7
• Geometry and entanglement in the scattering matrix
• Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction
• Dissecting reaction calculations using Halo EFT and ab initio input
• Ab initio calculations of low-energy nuclear scattering using confining potential traps
• The proton-deuteron system in pionless EFT revisited
• Bayesian analysis of capture reactions ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$
• Super Efimov effect for mass-imbalanced systems
• The renormalisation group and nuclear forces
• Probing open- and closed-channel p-wave resonances
• Resonant three-body physics in two spatial dimensions
• Few-body bound states and resonances in finite volume
• Unitary $p$-wave Fermi gas in one dimension
• Quantum Monte Carlo simulations of two-dimensional repulsive Fermi gases with population imbalance
• Non-Hermitian topological Fermi superfluid near the $p$-wave unitary limit
• Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion
• Effective field theory for shallow P-wave states
• Three-body bound states in atomic mixtures with resonant p-wave interaction
• Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries
• Multi-channel analog of the effective-range expansion
• Quantum Monte Carlo study of the role of p-wave interactions in ultracold repulsive Fermi gases
• Generalized Crossover in Interacting Fermions within the Low-Energy Expansion
• Optical spin transport theory of spin-1/2 topological Fermi superfluids
• Three-Body Scattering Hypervolume of Particles with Unequal Masses
• P-wave contacts of quantum gases in quasi-one-dimensional and quasi-two-dimensional traps
• Scattering Hypervolume of Spin-Polarized Fermions
• Universality in s-wave and higher partial wave Feshbach resonances: an illustration with a single atom near two scattering centers
• Removing the Wigner bound in non-perturbative effective field theory
• Universal relations for a spin-polarized Fermi gas in two dimensions
• Scattering Hypervolume of Fermions in Two Dimensions
• Universality of isolated $N$-body resonances at large scattering length
• Quantum Monte Carlo and perturbative study of two-dimensional Bose-Fermi mixtures
• Causality and dimensionality in geometric scattering
• Causality bounds for neutron-proton scattering
• Effective field theory with resonant P-wave interaction
• B${}_{\Lambda }$(${}_{\Lambda }^5$He) from short range effective field theory
• Causality, universality, and effective field theory for van der Waals interactions
• Renormalization of a Contact Interaction on a Lattice
• Toward precision Fermi liquid theory in two dimensions
• Non-Hermitian $p$-wave superfluid and effects of the inelastic three-body loss in a one-dimensional spin-polarized Fermi gas
• Contact interactions, self-adjoint extensions, and low-energy scattering
• Effective theory for strongly attractive one-dimensional fermions
• Shallow Trimers of Two Identical Fermions and One Particle in Resonant Regimes
• Symmetries of the nucleon-nucleon $S$-matrix and effective field theory expansions
• Low Energy Continuum and Lattice Effective Field Theories
• Two particles interacting via a contact interaction on $S^2$
• Halo EFT for ${}^{31}$Ne in a spherical formalism
• Reliability of the Born-Oppenheimer approximation in noninteger dimensions