Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD

Abstract

We present for the first time a determination of the energy dependence of the isoscalar $\pi \pi$ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the $S$-wave phase-shift up to the $K\overline{K}$ threshold. Calculations are performed at two values of the $u,d$ quark mass corresponding to $m_{\pi }=236,391$ MeV and the resulting amplitudes are described in terms of a $\sigma$ meson which evolves from a bound-state below $\pi \pi$ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.

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Cited by in corpus (21)

• Three-body Unitarity in the Finite Volume
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• Tetraquark operators in lattice QCD and exotic flavour states in the charm sector
• Extending Chiral Perturbation Theory with an Isosinglet Scalar
• Chiral study of the $a_0(980)$ resonance and $\pi \eta$ scattering phase shifts in light of a recent lattice simulation
• Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions
• Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states
• Feynman-Hellmann theorem for resonances and the quest for QCD exotica
• Excited $J^{--}$ meson resonances at the SU(3) flavor point from lattice QCD
• Resonance enhancement of Charm CP
• Scrutinizing $\pi \pi$ scattering in light of recent lattice phase shifts
• Chiral symmetry constraints on resonant amplitudes
• Chiral Extrapolation of the Sigma Resonance
• Examining the Low Energy Dynamics of Walking Gauge Theory
• Strong correlation of the neutron star core-crust transition density with the $\sigma$-meson mass via vacuum polarization
• Exploring S-Wave Threshold Effects in QCD: A Heavy-Light Approach
• The reactions $\pi \pi \to \pi \pi$ and $\gamma \gamma \to \pi \pi$ in $\chi$PT with an isosinglet scalar resonance
• Constraints on Disconnected Contributions in $\pi \pi$ Scattering
• $N_C$ evolution of the light meson resonances
• Studies of Conformal Behavior in Strongly Interacting Quantum Field Theories
• Unitary model analysis of $f_0(500)$ pole positions by continuously varying $m_{\pi }$: comparison with discrete lattice predictions