Speaker
Description
We present an analysis of elastic $P$-wave $\pi\pi$ phase shifts and inelasticities up to $2$ GeV, in order to identify the corresponding $J^{PC}=1^{--}$ excited $\rho$ resonances and focusing on the $\rho(1250)$ vs.\ $\rho(1450)$ controversy. In our approach we employed an improved parametrization in terms of a manifestly unitary and analytic three-channel $S$-matrix with its complex-energy pole positions. The included channels were $\pi\pi$, $\rho2\pi$, and $\rho\rho$. The improvement with respect to prior work amounts to the enforcement of maximum crossing symmetry through once-subtracted dispersion relations called GKPY equations. A clear picture emerges from this analyses, identifying five vector $\rho$ states below 2~GeV which are $\rho(770)$, $\rho(1250)$, $\rho(1450)$, $\rho(1600)$, and $\rho(1800)$, with $\rho(1250)$ being indisputably the most important excited $\rho$ resonance.
