From QCD to Physical Resonances

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 L"uscher 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 $\left[755(2)(1)\left({}^{20}_{02}\right) - \frac{i}{2} 129(3)(1)\left({}^7_1\right)\right]$ MeV.