Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states

Abstract

We derive analytic expansions for the finite-volume energies of weakly-interacting two-particle systems, using the general relations between scattering amplitudes and energies derived by Lüscher and others. The relations hold for ground and excited states with both zero and non-zero total momentum in the finite-volume frame. A number of instructive aspects arise in the derivation, including the role of accidental degeneracies and the importance of defining a power-counting scheme in the expansions. The results give intuition concerning the imprint of weakly-interacting systems on the energy spectrum, while also providing a useful basis for the analogous results concerning three-particle excited states, to appear.

arXiv comment34 pages, 2 figures, 9 tables, CERN-TH-2021-133

References in corpus (52)

• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Weak transition matrix elements from finite-volume correlation functions
• Scattering processes and resonances from lattice QCD
• Multiple-channel generalization of Lellouch-Luscher formula
• A relativistic, model-independent, three-particle quantization condition
• Two-particle multichannel systems in a finite volume with arbitrary spin
• Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Vector Correlators in Lattice QCD: methods and applications
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• Three particles in a finite volume
• Three-particle scattering amplitudes from a finite volume formalism
• Two Particle States and the $S$-matrix Elements in Multi-channel Scattering
• A method to measure the antikaon-nucleon scattering length in lattice QCD
• Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Three-body Unitarity in the Finite Volume
• The coupled-channel scattering on a torus
• Scalar mesons in a finite volume
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• Lattice QCD and Three-particle Decays of Resonances
• Rummukainen-Gottlieb's formula on two-particle system with different mass
• Lattice QCD and the Timelike Pion Form Factor
• Three-particle systems with resonant subprocesses in a finite volume
• From deep inelastic scattering to heavy-flavor semi-leptonic decays: Total rates into multi-hadron final states from lattice QCD
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• On the extraction of spectral densities from lattice correlators
• Implementing the three-particle quantization condition including higher partial waves
• Generalizing the relativistic quantization condition to include all three-pion isospin channels
• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• Extracting Scattering Phase-Shifts in Higher Partial-Waves from Lattice QCD Calculations
• Numerical study of the relativistic three-body quantization condition in the isotropic approximation
• On the Equivalence of Three-Particle Scattering Formalisms
• Inclusive semi-leptonic decays from lattice QCD
• Energy shift of the three-particle system in a finite volume
• Hadrons and Nuclei
• Lattice QCD and baryon-baryon interactions: HAL QCD method
• Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
• Scattering amplitudes from finite-volume spectral functions
• Relativistic three-particle quantization condition for nondegenerate scalars
• Alternative derivation of the relativistic three-particle quantization condition
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Equivalence of relativistic three-particle quantization conditions
• Perturbative results for two and three particle threshold energies in finite volume
• Finite-volume energy shift of the three-pion ground state
• Relativistic $N$-particle energy shift in finite volume
• Finite-volume effects in $(g-2{)}_{\mu }^{\text{HVP,LO}}$
• Finite-volume and thermal effects in the leading-HVP contribution to muonic $(g-2)$
• Variations on the Maiani-Testa approach and the inverse problem
• Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states
• Meson-Nucleon Scattering Amplitudes from Lattice QCD

Cited by in corpus (2)

• Three-body resonances in the ${\phi }^4$ theory
• Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states