Elliptical polarization in partial wave analysis of two spinless meson photoproduction

Mathematical ambiguities in partial-wave analysis present a significant challenge to the extraction of resonance properties in hadronic reactions. Recent work has shown that while linear photon polarization can resolve continuous ambiguities in the photoproduction of two pseudoscalar mesons, a final complex conjugate ambiguity remains. In this work, we extend the partial-wave formalism to include circular and elliptical photon polarization. We demonstrate that the additional constraints provided by circularly polarized observables, which are sensitive to the imaginary parts of bilinear amplitude products, are sufficient to remove remaining mathematical ambiguities, yielding an improved partial-wave solution. Furthermore, we show that the resulting overconstrained system allows for a novel application: using the reaction dynamics themselves as a polarimeter. Using recent high-statistics data on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>ρ</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>770</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> photoproduction from the GlueX experiment, we illustrate the viability of this technique in determining the degrees of beam polarization from the data. These results will benefit the next generation of photoproduction experiments at facilities such as Jefferson Lab and the future ilectron-Ion collider.