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

Abstract

Abstract.A new generation of complete experiments in pseudoscalar meson photo-production is being pursued at several laboratories. While new data are emerging, there is some confusion regarding definitions of asymmetries and the conventions used in partial wave analyses (PWA). We present expressions for constructing asymmetries as coordinate-system independent ratios of cross sections, along with the names used for these ratios by different PWA groups. (This update reflects a recent change in the definition of an asymmetry as used by one group.)

Extraction of reaction amplitudes from complete photo-production experiments

“…However, each of these observables enters the general form of the cross section scaled by two terms containing different combinations of beam, target and recoil spins [3]. This leads to two distinct ways to measure each observable.…”

“…Expressions for the photo-production asymmetries as coordinate-system independent ratios of cross sections, along with the names used for these ratios by different PWA groups, can be found in ref [4]. Examples of the explicit measurements needed to construct all of the observables are given in the appendices to ref [3].…”

“…While the beam and target polarization are under experimental control, the recoil polarization is rather a byproduct of the entrance channel angular momentum and the reaction physics. As such, the recoil polarization can be written in terms of various combinations of different spin asymmetries [3]. This can lead to a particularly fruitful arena in which different components of the recoiling baryon's polarization determine various spin observables.…”

“…An explicit decomposition of all 16 into the 4 CGLN F i amplitudes is given in [3]. However, the four amplitudes in each of these representations are angle dependent.…”

“…Extracting them directly from experiment would require separate fits at each angle, which greatly limits the data that can be used and requires some model-dependent scheme to constrain an arbitrary phase that could be angle-dependent. The solution to this intractable situation is a Wigner-Echart style factorization into reduced matrix elements, multipoles, and simple angle-dependent coefficients from angular momentum algebra [3,5]. One can then fit the multipoles directly, which both facilitates the search for resonance behavior and allows the use of full angular distribution data at a fixed energy to constrain angle-independent quantities.…”