No ambiguities in the partial wave analysis for hybrids

The extraction of partial waves from experimental cross sections can be plagued by mathematical ambiguities, that is by the fact that different sets of partial waves can lead to the very same physical observables. This fact was originally studied in the spinless case, and it is known as Barrelet zeroes. When particles carry spin, the presence of additional polarization observables can help resolving those ambiguities. While there is no general solution to this problem, it is important to focus on the practical cases that are useful for the detection of hybrids at GlueX. A work by the JPAC collaboration, led by Wyatt Smith (IU graduate student), Vincent Mathieu (Barcelona U.), and Derek Glazier (Glasgow U.), studied the ambiguities in the partial wave analysis of double scalar meson photoproduction (say $\eta\pi$) with a linearly polarized beam. A new formalism that makes special use of beam asymmetries shows that, for most reasonable wave sets of a single reflectivity, the information available is sufficiently constraining, so that we different partial wave sets can always be disambiguated, thus ruling out the possibility of discrete ambiguities in this type of analysis.

Papers: Phys. Rev. D 108 (2023), 076001