We discuss unitarity constraints on the dynamics of a system of three interacting particles. We show how the short-range interaction that describes three-body resonances can be separated from the long-range exchange processes, in particular the one-pion-exchange process. It is demonstrated that unitarity demands a specific functional form of the amplitude with a clear interpretation: the bare three-particle resonances are dressed by the initial- and final-state interaction, in a way that is consistent with the considered long-range forces. We postulate that the resonance kernel admits a factorization in the energy variables of the initial- and the final-state particles. The factorization assumption leads to an algebraic form for the unitarity equations, which is reminiscent of the well-known two-body-unitarity condition and approaches it in the limit of the narrow-resonance approximation.

In the search for exotic mesons, the GlueX Collaboration will soon extract moments of the $\eta {\pi }^0$ angular distribution. In the perspective of these results, we generalize the formalism of moment extraction to the case in which the two mesons are produced with a linearly polarized beam and build a model for the reaction $\overrightarrow{\gamma }p\to \eta {\pi }^{0}p$. The model includes resonant $S$, $P$, and $D$ waves in $\eta {\pi }^0$, produced by natural exchanges. Moments of the $\eta {\pi }^0$ angular distribution are computed with and without the $P$ wave, to illustrate the sensitivity to exotic resonances. Although little sensitivity to the $P$ wave is found in moments of even angular momentum, moments of odd angular momentum are proportional to the interference between the $P$ wave and the dominant $S$ and $D$ waves. We also generalize the definition of the beam asymmetry for two mesons photoproduction and show that, when the meson momenta are perpendicular to the reaction plane, the beam asymmetry enhances the sensitivity to the exotic $P$ wave.

We study tensor meson photoproduction outside of the resonance region, at beam energies of a few GeVs. We build a model based on Regge theory that includes the leading vector and axial exchanges. We consider two determinations of the unknown helicity couplings and fit to the recent $a_2$ photoproduction data from CLAS. Both choices give a similar description of the $a_2$ cross section but result in different predictions for the parity asymmetries and the $f_2$ photoproduction cross section. We conclude that new measurements of $f_2$ photoproduction in the forward region are needed to pin down the correct production mechanism. We also extend our predictions to the 8.5 GeV beam energy, where current experiments are running.

The formalism devoted to the production of two pseudoscalar mesons with a linearly polarized photon beam has been detailed and illustrated in Phys. Rev. D100 (2019) 054017. This document reports the necessary formulas, without proof, to perform an analysis of the angular distribution of two mesons photoproduction. The relations to extract moments of the angular distribution are provided, as well as the relations between moments and partial waves for a system involving $S$, $P$ and $D$ waves. The expressions of the integrated beam asymmetry and the beam asymmetry along the $y$ axis in term of moments are mentioned.

In the search for exotic mesons, the GlueX collaboration will soon extract moments of the $\eta\pi^0$ angular distribution. In the perspective of these results, we generalize the formalism of moment extraction to the case in which the two mesons are produced with a linearly polarized beam, and build a model for the reaction $\vec \gamma p \to \eta \pi^0 p$. The model includes resonant $S$-, $P$-, $D$-waves in $\eta\pi^0$, produced by natural exchanges. Moments of the $\eta\pi^0$ angular distribution are computed with and without the $P$-wave, to illustrate the sensitivity to exotic resonances. Although little sensitivity to the $P$-wave is found in moments of even angular momentum, moments of odd angular momentum are proportional to the interference between the $P$-wave and the dominant $S$- and $D$-waves. We also generalize the definition of the beam asymmetry for two mesons photoproduction and show that, when the meson momenta are perpendicular to the reaction plane, the beam asymmetry enhances the sensitivity to the exotic $P$-wave.

We study tensor meson photoproduction outside of the resonance region, at beam energies of few GeVs. We build a model based on Regge theory that includes the leading vector and axial exchanges. We consider two determinations of the unknown helicity couplings, and fit to the recent a2 photoproduction data from CLAS. Both choices give a similar description of the a2 cross section, but result in different predictions for the parity asymmetries and the f2 photoproduction cross section. We conclude that new measurements of f2 photoproduction in the forward region are needed to pin down the correct production mechanism. We also extend our predictions to the 8.5 GeV beam energy, where current experiments are running.