Recent progress in the partial-wave analysis of the diffractively produced ${\pi }^{-}{\pi }^{+}{\pi }^{-}$ final state at COMPASS

The COMPASS spectrometer at CERN has collected a large data set for diffractive three-pion production of $46\times {10}^6$ exclusive events. Based on previous conventional Partial-Wave Analyses (PWA), we performed a `freed-isobar PWA’ on the same data, removing model assumptions on the dynamic isobar amplitudes for dominating waves. In this analysis, we encountered continuous mathematical ambiguities, which we were able to identify and resolve. This analysis gives an unprecedented insight in the interplay of $2\pi$ and $3\pi$ dynamics in the process. As an example we show results for a spin-exotic wave $J_{X^{-}}^{PC}=1^{-+}$ wave.