Single-energy partial wave analysis for pion photoproduction with fixed-t analyticity

TL;DR

This paper presents a model-minimal, single-energy partial wave analysis of pion photoproduction data across four reaction channels, enforcing unitarity and fixed-t analyticity to extract electromagnetic multipoles with minimal initial assumptions.

Contribution

It introduces a novel iterative method that minimizes model dependence in partial wave analysis by combining experimental data with fixed-t analyticity constraints.

Findings

Partial wave amplitudes show minimal dependence on initial models.

Watson theorem is fulfilled up to W≈1.6 GeV in many partial waves.

Electromagnetic multipoles for multiple waves are provided and discussed.

Abstract

Experimental data for pion photoproduction including differential cross sections and various polarization observables from four reaction channels, $\gamma p \to \pi^0 p$, $\gamma p \to \pi^+n$, $\gamma n \to \pi^- p$ and $\gamma n \to \pi^0 n$ from threshold up to $W=2.2$ GeV have been used in order to perform a single-energy partial wave analysis with minimal model dependence by imposing constraints from unitarity and fixed-$t$ analyticity in an iterative procedure. Reaction models were only used as starting point in the very first iteration. We demonstrate that with this procedure partial wave amplitudes can be obtained which show only a minimal dependence on the initial model assumptions. The analysis has been obtained in full isospin, and the Watson theorem is enforced for energies below $W=1.3$ GeV but is even fulfilled up to $W\approx 1.6$ GeV in many partial waves. Electromagnetic multipoles $E_{\ell\pm}$ and $M_{\ell\pm}$ are presented and discussed for $S,P,D$ and $F$-waves.