0000000000949876
AUTHOR
Y. Wunderlich
Towards an understanding of discrete ambiguities in truncated partial wave analyses
It is well known that the observables in a single-channel scattering problem remain invariant once the amplitude is multiplied by an overall energy- and angle-dependent phase. This invariance is called the continuum ambiguity and acts on the infinite partial wave set. It has also long been known that, in the case of a truncated partial wave set, another invariance exists, originating from the replacement of the roots of partial wave amplitudes with their complex conjugate values. This discrete ambiguity is also known as the Omelaenko-Gersten-type ambiguity. In this paper, we show that for scalar particles, discrete ambiguities are just a subset of continuum ambiguities with a specific phase…
The complete experiment for photoproduction of pseudoscalar mesons in a truncated partial wave analysis
The complete experiment problem in the truncated partial wave analysis of pseudoscalar meson photoproduction with suppressed t-channel exchanges is investigated. The focus is set to ambiguities of the group S observables with the unpolarized differential cross section, $\sigma_0$, and the three single-spin observables, $\Sigma$, $T$ and $P$. For this purpose, the approach and formalism already worked out by Omelaenko in 1981 is revisited in this work. A numerical study using multipoles of the PWA solution MAID2007 shows how only one additional double polarization observable can resolve all ambiguities. Therefore, the possibility emerges to perform a complete experiment with only five observ…
Amplitude- and truncated partial-wave analyses combined: A single-channel method for extracting photoproduction multipoles directly from measured data
Amplitude- and truncated partial-wave analyses are combined into a single-channel method for extracting multipoles directly from measured data. In practice, we have created a two-step procedure which is fit to the same database: in the first step we perform an energy-independent amplitude analysis where continuity is achieved by constraining the amplitude phase, and the result of this first step is then taken as a constraint for the second step where a constrained, energy-independent, truncated partial-wave analysis is done. The method is tested on the world collection of data for $\ensuremath{\eta}$ photoproduction, and the obtained fit results are very good. The sensitivity to different p…