Finite volume effects in pion-kaon scattering and reconstruction of the kappa(800) resonance

Abstract

Simulating the kappa(800) on the lattice is a challenging task that starts to become feasible due to the rapid progress in recent-years lattice QCD calculations. As the resonance is broad, special attention to finite-volume effects has to be paid, because no sharp resonance signal as from avoided level crossing can be expected. In the present article, we investigate the finite volume effects in the framework of unitarized chiral perturbation theory using next-to-leading order terms. After a fit to meson-meson partial wave data, lattice levels for piK scattering are predicted. In addition, levels are shown for the quantum numbers in which the sigma(600), f_0(980), a_0(980), phi(1020), K*(892), and rho(770) appear, as well as the repulsive channels. Methods to extract the kappa(800) signal from the lattice spectrum are presented. Using pseudo-data, we estimate the precision that lattice data should have to allow for a clear-cut extraction of this resonance. To put the results into context, in particular the required high precision on the lattice data, the sigma(600), the P-wave resonances K*(892) and rho(770), and the repulsive piK, pipi phases are analyzed as well.

31 pages, 14 figures

References in corpus (24)

• Ab-initio Determination of Light Hadron Masses
• Toward the excited meson spectrum of dynamical QCD
• Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks
• First results from 2+1 dynamical quark flavors on an anisotropic lattice: light-hadron spectroscopy and setting the strange-quark mass
• Isoscalar meson spectroscopy from lattice QCD
• Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Scalar mesons in a finite volume
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Identification of a Scalar Glueball
• Isolating the Λ(1405) in Lattice QCD
• The reaction pi+ p --> K+ Sigma+ in a unitary coupled-channels model
• The phase-shift of isospin-2 pi-pi scattering from lattice QCD
• The $KD$, $\eta D_s$ interaction in finite volume and the nature of the $D_{s^{\ast }0}(2317)$ resonance
• Dynamical coupled-channel approaches on a momentum lattice
• Hadron Spectroscopy with Dynamical Chirally Improved Fermions
• Matching Chiral Perturbation Theory and the Dispersive Representation of the Scalar Kpi Form Factor
• Non-relativistic bound states in a finite volume
• The Delta-resonance in a finite volume
• Chiral dynamics with strange quarks in the light of recent lattice simulations
• The mass of the Delta resonance in a finite volume: fourth-order calculation
• Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory
• The preliminary lattice QCD calculation of $\kappa$ meson decay width
• Mass dependence of pion-pion phase shifts within standard and unitarized ChPT versus Lattice results

Cited by in corpus (55)

• Hadronic molecules
• The $XYZ$ states: experimental and theoretical status and perspectives
• Scattering processes and resonances from lattice QCD
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Coupled-channel dynamics in the reactions piN --> piN, etaN, KLambda, KSigma
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Three-body Unitarity in the Finite Volume
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• Wave functions of composite hadron states and relationship to couplings of scattering amplitudes for general partial waves
• QCD with Two Light Dynamical Chirally Improved Quarks: Baryons
• Scalar mesons moving in a finite volume and the role of partial wave mixing
• Photocouplings at the Pole from Pion Photoproduction
• K pi scattering for isospin 1/2 and 3/2 in lattice QCD
• A framework for the calculation of the $\Delta N{\gamma }^{\ast }$ transition form factors on the lattice
• K pi scattering and the K* decay width from lattice QCD
• Dynamical coupled-channel approaches on a momentum lattice
• A finite-volume matrix Hamiltonian model for a Delta -> nucleon-pion system
• Matrix elements of unstable states
• Finite-volume Hamiltonian method for coupled channel interactions in lattice QCD
• The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD
• Determination of $s$- and $p$-wave $I=1/2$ $K\pi$ scattering amplitudes in $N_{\mathrm{f}}=2+1$ lattice QCD
• The quark-mass dependence of elastic $\pi K$ scattering from QCD
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Chiral study of the $a_0(980)$ resonance and $\pi \eta$ scattering phase shifts in light of a recent lattice simulation
• The pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• A cross-channel study of pion scattering from lattice QCD
• Chiral Dynamics and S-wave Contributions in Semileptonic B decays
• Scattering of unstable particles in a finite volume: the case of pi rho scattering and the a1(1260) resonance
• Two-flavor Simulations of the $\rho (770)$ and the Role of the $K\bar{K}$ Channel
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• Model Selection for Pion Photoproduction
• The Optical Potential on the Lattice
• Strategy to find the two $\Lambda (1405)$ states from lattice QCD simulations
• The pion-pion Interaction in the rho Channel in Finite Volume
• Hidden charm molecules in finite volume
• Finite volume treatment of pi pi scattering and limits to phase shifts extraction from lattice QCD
• $I=1/2$ $S$-wave and $P$-wave $K\pi$ scattering and the $\kappa$ and $K^{\ast }$ resonances from lattice QCD
• Study of decuplet baryon resonances from lattice QCD
• QCD with two light dynamical chirally improved quarks: Mesons
• Fermion-dimer scattering using an impurity lattice Monte Carlo approach and the adiabatic projection method
• $I=0$ $\pi \pi$ $s$-wave scattering length from lattice QCD
• Nucleon resonance structure in the finite volume of lattice QCD
• The composite nature of the $\Lambda (1520)$ resonance
• Preliminary lattice study of $\sigma$ meson decay width
• Strange Hadron Spectroscopy with Secondary KL Beam in Hall D
• The $DN$, $\pi {\Sigma }_c$ interaction in finite volume and the ${\Lambda }_c(2595)$ resonance
• K-pi interaction in finite volume and the K* resonance
• Cross sections for inelastic meson-meson scattering
• Cross sections for 2-to-1 meson-meson scattering
• Cross Sections for Inelastic 2-to-2 Meson-Meson Scattering in Hadronic Matter
• Baryon resonances and hadronic interactions in a finite volume
• Cross sections for 2-to-3 meson-meson scattering
• From QCD to Physical Resonances
• Potential dangers when phase shifts are used as a link between experiment and QCD