Chiral symmetry constraints on resonant amplitudes

Abstract

We discuss the impact of chiral symmetry constraints on the quark-mass dependence of meson resonance pole positions, which are encoded in non-perturbative parametrizations of meson scattering amplitudes. Model-independent conditions on such parametrizations are derived, which are shown to guarantee the correct functional form of the leading quark-mass corrections to the resonance pole positions. Some model amplitudes for $\pi \pi$ scattering, widely used for the determination of $\rho$ and $\sigma$ resonance properties from results of lattice simulations, are tested explicitly with respect to these conditions.

arXiv commentVersion accepted by Phys. Lett. B. Supplemental material include additional proofs

References in corpus (34)

• ππscattering
• Meson-Meson interaction in a non-perturbative chiral approach
• Elastic $\pi \pi$ scattering to two loops
• Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD
• Coupled $\pi \pi ,K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• 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
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Bethe-Salpeter Approach for Meson-Meson Scattering in Chiral Perturbation Theory
• Chiral Perturbation Theory for Vector Mesons
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
• Rho resonance parameters from lattice QCD
• Strange and non-strange quark mass dependence of elastic light resonances from SU(3) Unitarized Chiral Perturbation Theory to one loop
• $\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$
• Infrared regularization for spin-1 fields
• Chiral Behaviour of the Rho Meson in Lattice QCD
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
• Pion-Kaon Scattering near the Threshold in Chiral SU(2) Perturbation Theory
• Power counting in baryon chiral perturbation theory including vector mesons
• Complex-mass renormalization in chiral effective field theory
• Two-flavor Simulations of the $\rho (770)$ and the Role of the $K\bar{K}$ Channel
• Vector Meson Masses in Chiral Perturbation Theory
• Connecting physical resonant amplitudes and lattice QCD
• Chiral Extrapolations of the $\mathbf{\rho }(770)$ Meson in ${\mathbf{N}}_{\mathbf{f}}=2+1$ Lattice QCD Simulations
• The magnetic moment of the ρ-meson
• Feynman-Hellmann theorem for resonances and the quest for QCD exotica
• Chiral behavior of vector meson self energies
• When hadrons become unstable: a novel type of non-analyticity in chiral extrapolations
• Chiral Extrapolation of the Sigma Resonance
• On the sigma sigma term
• Isospin-0 $\pi \pi$ scattering from twisted mass lattice QCD

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• Quark-mass dependence in $\omega \to 3\pi$ decays