Fixed- t analyticity as a constraint in single-energy partial-wave analyses of meson photoproduction reactions

Abstract

Partial wave amplitudes of meson photoproduction reactions are an important source of information in baryon spectroscopy. We investigate a new approach in single-energy partial wave analyses of these reactions. Instead of using a constraint to theoretical models in order to achieve solutions which are continuous in energy, we enforce the analyticity of the amplitudes at fixed values of the Mandelstam variable t. We present an iterative procedure with successive fixed-t amplitude analyses which constrain the single-energy partial wave analyses and apply this method to the γp → ηp reaction. We use pseudo data, generated by the EtaMAID model, to test the method and to analyze ambiguities. Finally, we present an analytically constrained partial wave analysis using experimental data for four polarization observables recently measured at MAMI and GRAAL in the energy range from threshold to √ s = 1.85 GeV.

Single-energy partial wave analysis for π0 photoproduction on the proton with fixed- t analyticity imposed

“…In this paper, we apply the fixed-t analyticity constraining method for single-energy partial wave analysis (SE PWA) in pion photoproduction. The method was developed previously and applied in η photoproduction on the proton [10]. Later on, the method was applied in SE PWA of π 0 photoproduction on the proton, considering π 0 as a "light η meson" [11].…”

“…Φ trunc makes a soft cutoff of higher partial waves and is effective at low energies, for details see Ref. [10]. According to unitarity (Watson's theorem [14]), phases of multipoles in pion photoproduction are equal to corresponding phases of πN partial waves up to nπ:…”

“…Therefore some interpolation between measurements at different energies and angles is necessary. We have used a spline smoothing method [60] which was similarly applied in the Karlsruhe-Helsinki analysis KH80 [13] and in our previous analysis of η production [10]. The uncertainties of interpolated data points are taken to be equal to the errors of nearest measured data points.…”

“…Further details about the iterative procedure can be found in our earlier PWA for η photoproduction, Ref. [10].…”

“…In Refs. [10,11] we developed a method to impose analyticity of the reactions amplitudes in the Mandelstam variable s at a fixed value of the variable t in an iterative procedure. A reaction model is only necessary as a starting point in the very first iteration.…”