Connecting physical resonant amplitudes and lattice QCD

Abstract

We present a determination of the isovector, $P$-wave $\pi \pi$ scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using $m_{\pi }=236$ MeV. The finite volume spectra are described using extensions of Lüscher's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at $m_{\pi }=140$ MeV. The scattering phase shift is found to be in good agreement with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude to the complex plane yields a $\rho$-resonance pole at $E_{\rho }=\left[755(2)(1){(}_{02}^{20})-\frac{i}{2}129(3)(1){(}_1^7)\right]\mathrm{MeV}$. The techniques presented illustrate a possible pathway towards connecting lattice QCD observables of few-body, strongly interacting systems to experimentally accessible quantities.

8 pages, 6 figures, equivalent to published version, added two appendices and a figure

References in corpus (22)

• Big-Bang Nucleosynthesis
• Ab initio calculation of the neutron-proton mass difference
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• A relativistic, model-independent, three-particle quantization condition
• First results from 2+1 dynamical quark flavors on an anisotropic lattice: light-hadron spectroscopy and setting the strange-quark mass
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Coupled $\pi \pi ,K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Isoscalar meson spectroscopy from lattice QCD
• Resonances in coupled πK,ηK scattering from quantum chromodynamics
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• Scalar mesons moving in a finite volume and the role of partial wave mixing
• The Inverse Amplitude Method and Adler Zeros
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
• The phase-shift of isospin-2 pi-pi scattering from lattice QCD
• The resonant ${\pi }^{+}\gamma \to {\pi }^{+}{\pi }^0$ amplitude from Quantum Chromodynamics
• Precise determination of resonance pole parameters through Padé approximants
• Nuclear Reactions from Lattice QCD
• Decay constants of the pion and its excitations on the lattice
• Chiral extrapolation of the sigma and rho mesons from dispersion relations and Chiral Perturbation Theory

Cited by in corpus (32)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Scattering processes and resonances from lattice QCD
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Three-body Unitarity in the Finite Volume
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• Relativistic, model-independent, multichannel $2\to 2$ transition amplitudes in a finite volume
• Extraction of isoscalar $\pi \pi$ phase-shifts from lattice QCD
• Determination of $s$- and $p$-wave $I=1/2$ $K\pi$ scattering amplitudes in $N_{\mathrm{f}}=2+1$ lattice 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
• Variational approach to $N$-body interactions in finite volume
• A cross-channel study of pion scattering from lattice QCD
• Two- and three-body interactions in ${\phi }^4$ theory from lattice simulations
• Novel approaches in Hadron Spectroscopy
• Two-flavor Simulations of the $\rho (770)$ and the Role of the $K\bar{K}$ Channel
• Pion scattering in the isospin I=2 channel from elongated lattices
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• The Optical Potential on the Lattice
• Elastic nucleon-pion scattering at $m_{\pi }=200\mathrm{MeV}$ from lattice QCD
• Chiral Extrapolations of the $\mathbf{\rho }(770)$ Meson in ${\mathbf{N}}_{\mathbf{f}}=2+1$ Lattice QCD Simulations
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• Low energy scattering phase shifts for meson-baryon systems
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
• Scalar and tensor charmonium resonances in coupled-channel scattering from QCD
• Charmonium ${\chi }_{c0}$ and ${\chi }_{c2}$ resonances in coupled-channel scattering from lattice QCD
• Axial-vector $D_1$ hadrons in $D^{\ast }\pi$ scattering from QCD
• Chiral symmetry constraints on resonant amplitudes
• Chiral Extrapolation of the Sigma Resonance
• Physical-mass calculation of $\rho (770)$ and $K^{\ast }(892)$ resonance parameters via $\pi \pi$ and $K\pi$ scattering amplitudes from lattice QCD
• Hadron Structure and Spectrum from the Lattice
• From QCD to Physical Resonances