Mechanisms of high energy polarized photoproduction of $\pi^{-}\Delta^{++}$

Abstract

We present an amplitude analysis of high-energy polarized photoproduction of $\pi^-\Delta^{++}$ within a Regge exchange framework. A Regge amplitude model incorporating $\pi$, $\rho$, $b_1$, and $a_2$ trajectory exchanges is fit simultaneously to spin density matrix elements measured by the GlueX experiment at photon energies of $E_\gamma = 8.2$--$8.8$ GeV and differential cross section data from SLAC. By including SDME data, the fit constrains not only the magnitudes but also the relative phases of the helicity amplitudes. The results confirm the dominance of pion exchange at small momentum transfer, while natural parity exchanges become significant at larger $t$. We analytically continue the $s$-channel amplitude to the $t$-channel, taking care of the kinematical singularities, and isolate the dynamical residues at the meson poles. The extracted $\pi N\Delta$ coupling constant is found to be consistent with the value obtained from the decay width of the $\Delta(1232)$. For the $\rho N\Delta$, $b_1 N\Delta$, and $a_2 N\Delta$ vertices, first extractions of the relevant coupling constants are provided.