Determining pseudoscalar meson photoproduction amplitudes from complete experiments

Abstract

Abstract.A new generation of complete experiments is focused on a high precision extraction of pseudoscalar meson photo-production amplitudes. Here, we review the development of the most general analytic form of the cross section, dependent upon the three polarization vectors of the beam, target and recoil baryon, including all single, double and triple-polarization terms involving 16 spin-dependent observables. We examine the different conventions that have been used by different authors, and we present expressions that allow the direct numerical calculation of any pseudoscalar meson photo-production observables with arbitrary spin projections from the ChewGoldberger-Low-Nambu (CGLN) amplitudes. We use this numerical tool to clarify apparent sign differences that exist in the literature, in particular with the definitions of six double-polarization observables. We also present analytic expressions that determine the recoil baryon polarization, together with examples of their potential use with quasi-4π detectors to deduce observables. As an illustration of the use of the consistent machinery presented in this review, we carry out a multipole analysis of the γp → K + Λ reaction and examine the impact of recently published polarization measurements. When combining data from different experiments, we utilize the Fierz identities to fit a consistent set of scales. In fitting multipoles, we use a combined Monte Carlo sampling of the amplitude space, with gradient minimization, and find a shallow χ 2 valley pitted with a very large number of local minima. This results in broad bands of multipole solutions that are experimentally indistinguishable. While these bands have been noticeably narrowed by the inclusion of new polarization measurements, many of the multipoles remain very poorly determined, even in sign, despite the inclusion of data on 8 different observables. We have compared multipoles from recent PWA codes with our model-independent solution bands, and found that such comparisons provide useful consistency tests which clarify model interpretations. The potential accuracy of amplitudes that could be extracted from measurements of all 16 polarization observables has been studied with mock data using the statistical variations that are expected from ongoing experiments. We conclude that, while a mathematical solution to the problem of determining an amplitude free of ambiguities may require 8 observables, as has been pointed out in the literature, experiments with realistically achievable uncertainties will require a significantly larger number.

Polarisation observables for strangeness photoproduction on a frozen spin target with CLAS at Jefferson Lab

“…Additionally, polarisation information can be accessed with these probes, with the effects of polarisation on the reaction particles giving new insights into the properties of resonances, and more ways to find evidence of their existence [14].…”

“…Detailed investigations have demonstrated that measurement of the cross-section, σ 0 , and single polarisation observables Σ, T and P, as well as four appropriately chosen double polarisation observables (of which there are several examples) can determine the reaction amplitudes without ambiguities [19,20], however, the available data and associated uncertainties do not provide sufficient constraint to eliminate these ambiguities and more than eight measurements will be needed [14].…”

Polarization ObservablesTandFin singleπ0- andη-Photoproduction off quasi-free Nucleons

“…Following the notation of [7] the differential cross section for a circularly polarized photon beam and a transversally polarized target reads…”

A Rosetta Stone relating conventions in photo-meson partial wave analyses

“…To ensure data are correctly incorporated into partial wave arXiv:1108.5411v2 analyses, we encourage experimental groups to specify their sign convention relative to Table 1 1. Names for the coordinate-independent polarization ratios as used in the partial wave analyses of the groups from MAID [2], SAID [3], Bonn-Gatchina (BoGa) [4], Carnegie Mellon (CMU) [5] and JLab-EBAC [1]. MAID, SAID CMU SHKL-EBAC, BoGa R S " " "…”