Upper Limit on the Photoproduction Cross Section of the Spin-Exotic ${\pi }_1(1600)$

The spin-exotic hybrid meson ${\pi }_1(1600)$ is predicted to have a large decay rate to the $\omega \pi \pi$ final state. Using 76.6~pb${}^{-1}$ of data collected with the GlueX detector, we measure the cross sections for the reactions $\gamma p\to \omega {\pi }^{+}{\pi }^{-}p$, $\gamma p\to \omega {\pi }^0{\pi }^{0}p$, and $\gamma p\to \omega {\pi }^{-}{\pi }^0{\mathrm{\Delta }}^{++}$ in the range $E_{\gamma }=$ 8-10 GeV. Using isospin conservation, we set the first upper limits on the photoproduction cross sections of the ${\pi }_1^0(1600)$ and ${\pi }_1^{-}(1600)$. We combine these limits with lattice calculations of decay widths and find that photoproduction of ${\eta }^{\mathrm{\prime }}\pi$ is the most sensitive two-body system to search for the ${\pi }_1(1600)$.