From QCD to Physical Resonances

Abstract

In this talk, we present the first chiral extrapolation of a resonant scattering amplitude obtained from lattice QCD. Finite-volume spectra, determined by the Hadron Spectrum Collaboration at $m_{\pi }=236$ MeV, for the isotriplet $\pi \pi$ channel are analyzed using the Lüscher method to determine the infinite-volume scattering amplitude. Unitarized Chiral Perturbation Theory is then used to extrapolate the scattering amplitude to the physical light quark masses. The viability of this procedure is demonstrated by its agreement with the experimentally determined scattering phase shift up to center-of-mass energies of 1.2 GeV. Finally, we analytically continue the amplitude to the complex plane to obtain the $\rho$-pole at $\left[755(2)(1)\left({}_{02}^{20}\right)-\frac{i}{2}129(3)(1)\left({}_1^7\right)\right]$ MeV.

Parallel talk at the XVI International Conference on Hadron Spectroscopy (HADRON 2015), September 13-18, 2015, Newport News. Submitted to AIP Conference Proceedings

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• Scalar mesons moving in a finite volume and the role of partial wave mixing
• Timelike pion form factor in lattice QCD
• $\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
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• Perturbative results for two and three particle threshold energies in finite volume
• Connecting physical resonant amplitudes and lattice QCD
• Nuclear Reactions from Lattice QCD
• Chiral extrapolation of the sigma and rho mesons from dispersion relations and Chiral Perturbation Theory
• Hadron Structure and Spectrum from the Lattice
• Pion-pion scattering and the timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD simulations using the stochastic LapH method
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