Unitary coupled-channel analysis of diffractive production of theA1resonance

Employing unitary coupled-channel $J^{\mathrm{PC}}=1^{++}$ partial-wave amplitudes for the $\rho \pi$ and $K^{*}\overline{K}$ systems, we show that the mass dependence and phase variations of the diffractive data on $\pi p\to \left(\rho \pi \right)p$ are indicative of the presence of an $A_1$ resonance whose mass and width we determine to be roughly 1.3±0.15 GeV and 400±100 MeV, respectively. Our unitary amplitudes incorporate the Deck backgrounds explicitly. The fits to the data are excellent. We point out some interesting quantities to be measured in the future in order to resolve remaining uncertainties.