Determining the dominant partial wave contributions from angular distributions of single- and double-polarization observables in pseudoscalar meson photoproduction

TL;DR

This paper introduces a straightforward method to identify significant partial wave contributions in pseudoscalar meson photoproduction by analyzing angular distributions and polarization data, aiding the detection of high-spin resonances.

Contribution

It presents a new approach to determine the maximum orbital angular momentum needed for fitting angular distributions and applies it to recent polarization measurements.

Findings

High-precision, large angular coverage data are essential for detecting high-spin resonances.

The method successfully projects high-spin partial wave contributions to observables.

Identification of specific resonances like N(1680)5/2+ and Δ(1950)7/2+ in the analysis.

Abstract

This work presents a simple method to determine the significant partial wave contributions to experimentally determined observables in pseudoscalar meson photoproduction. First, fits to angular distributions are presented and the maximum orbital angular momentum $\text{L}_{\mathrm{max}}$ needed to achieve a good fit is determined. Then, recent polarization measurements for $\gamma p \rightarrow \pi^{0} p$ from ELSA, GRAAL, JLab and MAMI are investigated according to the proposed method. This method allows us to project high-spin partial wave contributions to any observable as long as the measurement has the necessary statistical accuracy. We show, that high precision and large angular coverage in the polarization data are needed in order to be sensitive to high-spin resonance-states and thereby also for the finding of small resonance contributions. This task can be achieved via interference of these resonances with the well-known states. For the channel $\gamma p \rightarrow \pi^{0} p$, those are the $N(1680)\frac{5}{2}^{+}$ and $\Delta(1950)\frac{7}{2}^{+}$, contributing to the $F$-waves.