Higher order quantization conditions for two-body scattering with spin

Abstract

We examine the Lüscher quantization condition to high order for the scattering of a spinless particle and a spin-1/2 particle in a periodic box. First, we derive the quantization conditions in a non-relativistic framework up to total angular momentum $J=11/2$ in both cubic and elongated geometries, and for both rest and moving frames. Then, we introduce a method to transparently cross-check their convergence, using both quantized energy levels in the box and infinite-volume phase shifts for the same potential. We clarify how to incorporate spin-orbit coupling into the formalism and show in detail how the quantization conditions converge order by order in the various irreducible representations. In all, we validated 19 quantization conditions (12 in cubic box, 7 in elongated box). This is a necessary step in applying the method in precision studies of systems in finite volume with half-integer spin, such as meson-baryon scattering.

53 pages, 3 figures, 26 tables, 1 supplement. Updated to match the version published in PRD

References in corpus (48)

• Nuclear Force from Lattice QCD
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Multiple-channel generalization of Lellouch-Luscher formula
• Hadron-Hadron Interactions from Imaginary-time Nambu-Bethe-Salpeter Wave Function on the Lattice
• Two-particle multichannel systems in a finite volume with arbitrary spin
• Scattering phases for meson and baryon resonances on general moving-frame lattices
• Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion
• Unitarized Chiral Perturbation Theory in a finite volume: scalar meson sector
• Resonance Parameters of the rho-Meson from Lattice QCD
• Coupled channel analysis of the rho meson decay in lattice QCD
• The coupled-channel scattering on a torus
• Lattice QCD Calculation of the $\rho$ Meson Decay Width
• Scattering phase shifts for two particles of different mass and non-zero total momentum in lattice QCD
• Resonance properties from the finite-volume energy spectrum
• An $a_0$ resonance in strongly coupled $\pi \eta$, $K\overline{K}$ scattering from lattice QCD
• Rummukainen-Gottlieb's formula on two-particle system with different mass
• Multi-Pion Systems in Lattice QCD and the Three-Pion Interaction
• $\rho$ Meson Decay in 2+1 Flavor Lattice QCD
• Scalar mesons moving in a finite volume and the role of partial wave mixing
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD
• Rho resonance parameters from lattice QCD
• Implementing the three-particle quantization condition including higher partial waves
• Two Particle States in an Asymmetric Box and the Elastic Scattering Phases
• 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
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
• $\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$
• Two Particle States in a Box and the $s$-Matrix in Multi-Channel Scattering
• Estimating the two-particle $K$-matrix for multiple partial waves and decay channels from finite-volume energies
• Finite-volume energy spectrum of the $K^{-}{K}^{-}{K}^{-}$ system
• Generalized Lüscher Formula in Multi-channel Baryon-Meson Scattering
• Systematics of the HAL QCD Potential at Low Energies in Lattice QCD
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• A cross-channel study of pion scattering from lattice QCD
• Lattice baryon spectroscopy with multi-particle interpolators
• Lattice QCD study of $\pi \Sigma -\bar{K}N$ scattering and the $\Lambda (1405)$ resonance
• Elastic nucleon-pion scattering at $m_{\pi }=200\mathrm{MeV}$ from lattice QCD
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• $\omega$ meson from lattice QCD
• Partial Wave Mixing in Hamiltonian Effective Field Theory
• A lattice model of heavy-light three-body system
• Scattering phaseshift formulas for mesons and baryons in elongated boxes
• Hamiltonian effective field theory in elongated or moving finite volume
• Elastic Nucleon-Pion scattering amplitudes in the $\Delta$ channel at physical pion mass from Lattice QCD
• Higher order finite volume quantization conditions for two spinless particles
• The 3D entangled structure of the proton; transverse degrees of freedom in QCD, momenta, spins and more
• The odd-parity strange baryons $\Sigma ({\frac{1}{2}}^{-})$ below 1.8 GeV with Hamiltonian effective field theory