First determination of vector and tensor couplings from polarized $\pi\Delta$ photoproduction

Coupling constants encode the underlying dynamics of the interacting hadrons and their determination forms a central goal of hadron physics. Many such couplings cannot be extracted from decay widths because the corresponding decays are kinematically forbidden.
Of these, the coupling of $N\Delta$ to mesons are of special interest due to their applications in a wide variety of studies. High-energy polarized photoproduction offers an alternative route, where these couplings appear as residues of Regge poles exchanged in the $t$-channel.

This work, carried out by Vanamali Shastry (Indiana U., ExoHad postdoc), Lukasz Bibrzycki (AGH Krakow), Vincent Mathieu (Barcelona U., co-PI), Gloria Montana (Barcelona U., ExoHad postdoc), Alessandro Pilloni (Messina U. & INFN Catania, co-PI), Cesar Fernandez-Ramirez (UNED, co-PI), Robert J. Perry (MIT, ExoHad postdoc), Arkaitz Rodas (ODU & JLab, co-PI), Adam P. Szczepaniak (Indiana U. & JLab), and Daniel Winney (UNAM, co-PI), presents a systematic Regge exchange framework for the amplitude analysis of $\gamma p \to \pi^- \Delta^{++}$ incorporating $\pi$, $\rho$, $b_1$, and $a_2$ trajectories. The model is fit simultaneously to spin-density matrix elements measured by GlueX at $E_\gamma = 8.2$--$8.8$~GeV and to SLAC differential cross-section data. The inclusion of SDME data constrains not only the magnitudes but also the relative phases of the helicity amplitudes. Coupling constants are then extracted by analytically continuing the $s$-channel amplitudes to the $t$-channel and isolating the dynamical residues at each meson pole.

The extracted $\pi N\Delta$ coupling is consistent with the value from the $\Delta(1232)$ decay width, validating the method. For the $\rho N\Delta$, $b_1 N\Delta$, and $a_2 N\Delta$ vertices, these are the first extractions from scattering data. These results are essential inputs for amplitude analyses of exotic meson searches at GlueX, where $\pi\Delta$ photoproduction constitutes a significant hadronic background.

Papers: arXiv:2606.07917; arXiv:2604.22719