Light isovector resonances in $pi^- p to pi^-pi^-pi^+ p$ at 190 GeV/${it c}$

We have performed the most comprehensive resonance-model fit of $pi^-pi^-pi^+$ states using the results of our previously published partial-wave analysis (PWA) of a large data set of diffractive-dissociation events from the reaction $pi^- + p to pi^-pi^-pi^+ + p_text{recoil}$ with a 190 GeV/$c$ pion beam. The PWA results, which were obtained in 100 bins of three-pion mass, $0.5 < m_{3pi} < 2.5$ GeV/$c^2$, and simultaneously in 11 bins of the reduced four-momentum transfer squared, $0.1 < t < 1.0$ $($GeV$/c)^2$, are subjected to a resonance-model fit using Breit-Wigner amplitudes to simultaneously describe a subset of 14 selected waves using 11 isovector light-meson states with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{++}$, $2^{-+}$, $4^{++}$, and spin-exotic $1^{-+}$ quantum numbers. The model contains the well-known resonances $pi(1800)$, $a_1(1260)$, $a_2(1320)$, $pi_2(1670)$, $pi_2(1880)$, and $a_4(2040)$. In addition, it includes the disputed $pi_1(1600)$, the excited states $a_1(1640)$, $a_2(1700)$, and $pi_2(2005)$, as well as the resonancelike $a_1(1420)$. We measure the resonance parameters mass and width of these objects by combining the information from the PWA results obtained in the 11 $t$ bins. We extract the relative branching fractions of the $rho(770) pi$ and $f_2(1270) pi$ decays of $a_2(1320)$ and $a_4(2040)$, where the former one is measured for the first time. In a novel approach, we extract the $t$ dependence of the intensity of the resonances and of their phases. The $t$ dependence of the intensities of most resonances differs distinctly from the $t$ dependence of the nonresonant components. For the first time, we determine the $t$ dependence of the phases of the production amplitudes and confirm that the production mechanism of the Pomeron exchange is common to all resonances.