A Partial Wave Formalism for High-Energy Meson Electroproduction

Abstract

We present a comprehensive partial-wave analysis formalism for meson electroproduction based on reflectivity amplitudes. By applying parity-based symmetries, we construct a fully diagonalized framework that relates complex production amplitudes to measurable spherical harmonic moments and Spin Density Matrix Elements. We demonstrate that, under the assumption of high-energy Regge factorization, longitudinal and transverse cross sections can be natively separated without requiring beam-energy-varying Rosenbluth separations. We validate this inversion methodology through numerical closure tests and apply it to existing unpolarized ${\rho }^0$ and $\omega$ electroproduction data from HERMES and COMPASS. The extracted amplitudes align with $s$-channel helicity conservation expectations for the ${\rho }^0$, while clearly isolating the large unnatural-parity pion exchange contribution in $\omega$ production without model-dependent background approximations. Finally, we systematically generalize the formalism to include initial target and recoil baryon polarization, establishing the rigorous observables required for complete amplitude extraction, no longer requiring any factorisation assumptions. This unified framework directly supports upcoming spectroscopy and nucleon structure programs at CLAS12, GlueX, and the future Electron-Ion Collider.

44 pages (31 excluding extra appendix figures), 19 figures, 5 tables, 7 main sections and 8 appendices