Fano theory for hadronic resonances: the rho meson and the pionic continuum

We develop a model-independent analysis of hadronic scattering data in the resonance region, where the resonance shape follows from the matrix elements of a Hamiltonian. We investigate the rho meson in the tau decay. We demonstrate that the rho meson resonance in the two-pion decay of the tau lepton is described well through the coupling of a bare rho meson to the two-pion and the four-pion continuum. Furthermore, this four-pion continuum corresponds with the data of the four-pion decay channel of the tau lepton at energies up to 1.1 GeV.