$\eta’-\pi$ production and search for exotic mesons at COMPASS and JLab12

In the exclusive production of $\eta\pi$ and $\eta’\pi$ pairs with a 191 GeV/c pion beam at COMPASS resonance-like enhancement in the P-wave was observed. Such a resonance would carry exotic quantum numbers therefore, cannot be associated with the conventional quark-antiquark states. To examine the observed behavior we examine the properties of reaction amplitude using analyticity, unitarity and high-energy constraints. Following Regge prediction, for sufficiently large incident energy the five-particle amplitude for the reaction $p\pi\to p\pi\eta$ is proportional to the reggeon-particle scattering amplitude $R\pi\to\eta\pi$. In the resonance region, the reggeon-particle amplitudes are parametrized within N/D formalism supplemented by elastic unitarity constraints. At higher values of $\eta\pi$ invariant masse, the amplitude is reggeized similarly to normal four-particle amplitudes. Matching between the two parametrizations in the transition region is implemented via finite energy sum rules. To constrain the parameters of reggeon and decay vertices we employ the Regge factorization as well as SU(3) constraints and use data from other high-energy experiments. Finally, we consider the extension of the developed formalism for the photoproduction of $\eta\pi$ meson systems at GlueX.