Search for in a three-pion system at GlueX

The GlueX experiment in Hall D at Jefferson Lab enables studies of the light meson spectrum in $\gamma p$ interactions with a linearly polarized photon beam. GlueX aims in particular to search for hybrid mesons that have exotic quantum numbers and therefore cannot be classified as conventional hadrons. We present the search for the ${\pi }_1(1600)$ meson by means of a partial-wave analysis of the ${\pi }^{+}{\pi }^{-}{\pi }^{-}$ system produced off the ${\mathrm{\Delta }}^{++}$-baryon. Data with the selected three-pion final state are fitted in bins of $m_{3\pi }$ as coherent sums of partial-wave amplitudes defined in the reflectivity basis. The properties of $a_2^{-}(1320)$ production are investigated through the extracted signal in the $\rho {\pi }^{-}$ $D$-waves. In this analysis, the overall $m_{3\pi }$ lineshape will be extracted for each of the model contributions. The main interest lies in establishing the existence of a resonant $1^{-+}$ contribution in the $\rho {\pi }^{-}$ $P$-wave configuration.