Global parametrizations of $\pi \pi$ scattering with dispersive constraints: Beyond the S0 wave

Abstract

We provide new global parametrizations of $\pi \pi \to \pi \pi$ scattering for the S2, P, D, F, and G partial waves up to at least 1.8 GeV, easy to implement for phenomenological use. With earlier S0-wave parametrizations, slightly updated here, they reproduce previous partial wave dispersion analyses up to the $\pi \omega$ threshold. In addition, these new parametrizations have improved their description of recent P-wave data, the inelasticity in various waves, and their fulfillment of Roy-like and forward dispersion relations. The latter now test very high partial waves and have an improved matching with the Regge regime, extending those with P-wave contributions up to 1.6 GeV. Above 1.6 GeV and up to 1.8 GeV, or sometimes somewhat beyond, the parametrizations are simple unconstrained fits to data.

arXiv comment37 pages, 20 figures. v2: matches published version in Phys. Rev. D

References in corpus (66)

• ππscattering
• Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons
• Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma ,f_0(980),a_0(980)$ scalar mesons
• Meson-Meson interaction in a non-perturbative chiral approach
• N/D Description of Two Meson Amplitudes and Chiral Symmetry
• Two-pion contribution to hadronic vacuum polarization
• Mass and width of the lowest resonance in QCD
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Roy equation analysis of pi pi scattering
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• The inverse amplitude method in Chiral Perturbation Theory
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• Roy-Steiner-equation analysis of pion-nucleon scattering
• The Status of Glueballs
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• Coupled $\pi \pi ,K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD
• Bethe-Salpeter Approach for Unitarized Chiral Perturbation Theory
• A global fit of $\pi \pi$ and $\pi K$ elastic scattering in ChPT with dispersion relations
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• Regge analysis of the pi pi scattering amplitude
• The pion-pion scattering amplitude
• Roy-Steiner equations for gamma gamma -> pi pi
• Light scalars as tetraquarks or two-meson states from large Nc and unitarized Chiral Perturbation Theory
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• Precision Determination of the Pion Form Factor and Calculation of the Muon $g-2$
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• Separation of S- wave pseudoscalar and pseudovector amplitudes in pi^- p---> pi^+ pi^- n reaction on polarized target
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
• Bootstrapping QCD: the Lake, the Peninsula and the Kink
• Analysis and interpretation of new low-energy Pi-Pi scattering data
• The $\kappa$ resonance in s wave $\pi K$ scatterings
• Couplings of light I=0 scalar mesons to simple operators in the complex plane
• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• Roy-Steiner equations for pion-nucleon scattering
• $\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$
• Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross section from threshold to 1.2 GeV with the CMD-3 detector
• The pole structure of the unitary, crossing symmetric low energy $\pi \pi$ scattering amplitudes
• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• Coupled-channel approach in hadron-hadron scattering
• $\pi \pi \to K\bar{K}$ scattering up to 1.47 GeV with hyperbolic dispersion relations
• Studying the $\rho$ resonance parameters with staggered fermions
• The pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV
• Elimination of ambiguities in pion-pion phase shifts using crossing symmetry
• Chiral Perturbation Theory, the $1/N_c$ expansion and Regge behaviour determine the structure of the lightest scalar meson
• Dispersion relations for ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \pi$: helicity amplitudes, subtractions, and anomalous thresholds
• A cross-channel study of pion scattering from lattice QCD
• Regge analysis of pion-pion (and pion-kaon) scattering for energy s^{1/2}>1.4 GeV
• Global parameterization of $\pi \pi$ scattering up to 2 GeV
• Large-$N_c$ naturalness in coupled-channel meson-meson scattering
• Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarisation
• The pion-pion scattering amplitude. II: Improved analysis above $\bar{K}K$ threshold
• 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 $K_0^{\ast }(700)$
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance
• On the precision of chiral-dispersive calculations of $\pi \pi$ scattering
• The $\rho$-resonance with physical pion mass from $N_f=2$ lattice QCD
• Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
• Quark mass dependence of $\pi \pi$ scattering in isospin 0, 1, and 2 from lattice QCD
• Self-consistent statistical error analysis of $\pi \pi$ scattering
• Determination of crossing-symmetric $\pi \pi$ scattering amplitudes and the quark mass evolution of the $\sigma$ constrained by lattice QCD
• Dispersion relations with crossing symmetry for pipi D and F wave amplitudes
• The f0(1370) controversy from dispersive meson-meson scattering data analyses
• Coarse graining $\pi \pi$ scattering

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