The COMPASS collaboration has collected the currently largest data set on diffractively produced $pi^-pi^-pi^+$ final states using a negative pion beam of 190 GeV/c momentum impinging on a stationary proton target. This data set allows for a systematic partial-wave analysis in 100 bins of three-pion mass, $0.5 < m_{3pi} < 2.5$ GeV/c$^2$ , and in 11 bins of the reduced four-momentum transfer squared, $0.1 < t < 1.0$ (GeV/c)$^2$ . This two-dimensional analysis offers sensitivity to genuine one-step resonance production, i.e. the production of a state followed by its decay, as well as to more complex dynamical effects in nonresonant $3pi$ production. In this paper, we present detailed studies on selected $3pi$ partial waves with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{-+}$, $2^{++}$, and $4^{++}$. In these waves, we observe the well-known ground-state mesons as well as a new narrow axial-vector meson $a_1(1420)$ decaying into $f_0(980) pi$. In addition, we present the results of a novel method to extract the amplitude of the $pi^-pi^+$ subsystem with $I^{G}J^{PC} = 0^+ 0^{++}$ in various partial waves from the $pi^-pi^-pi^+$ data. Evidence is found for correlation of the $f_0(980)$ and $f_0(1500)$ appearing as intermediate $pi^- pi^+$ isobars in the decay of the known $pi(1800)$ and $pi_2(1880)$.
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