Amplitude reconstruction from complete experiments and truncated partial-wave expansions

Amplitude reconstruction from complete electroproduction experiments and truncated partial-wave expansions

We compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the electroproduction of pseudoscalar mesons. We give examples which show, in detail, how the amplitude reconstruction (observables measured at a single energy and angle) is related to a truncated partial-wave analysis (observables measured at a single energy and a number of angles). A connection is made to existing data.

Amplitude- and truncated partial-wave analyses combined: A novel, almost theory-independent single-channel method for extracting photoproduction multipoles directly from measured data

Amplitude- and truncated partial-wave analyses are combined into a single procedure and a novel, almost theory-independent single-channel method for extracting multipoles directly from measured data is developed. In practice, we have created a two-step procedure which is fitted to the same data base: 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 do…

A Truncated partial wave analysis of a complete experiment for photoproduction of two pseudoscalar mesons on a nucleon

A truncated partial wave analysis for the photoproduction of two pseudoscalar mesons on a nucleon is discussed with respect to the determination of a complete set of observables. For the selection of such a set we have applied a criterion previously developed for photo- and electrodisintegration of a deuteron, which allows one to find a 'minimal' set of observables for determining the partial wave amplitudes up to possible discrete ambiguities. The question of resolving the remaining ambiguities by invoking additional observables is discussed for the simplest case, when the partial wave expans…

基于贝叶斯统计的η光生可观测数截断分波分析

Truncated Partial-Wave Analysis for $η$-photoproduction observables via Bayesian Statistics

本研究首次结合贝叶斯统计与截断分波分析，针对η光生过程的极化可观测数开展研究，分析不同能量箱的截断阶数、歧义结构，并预测未测可观测数以指导未来实验消除剩余数学歧义。

Complete experiment problem for photoproduction of two pseudoscalar mesons on a nucleon in a truncated partial-wave analysis

It is shown that within a truncated partial wave analysis for photoproduction of two pseudoscalar mesons, it is possible to halve the number of independent partial amplitudes by taking into account parity conservation. In addition, within the framework of the proposed formalism, one can rather easily resolve the double discrete ambiguity arising from the symmetry under complex conjugation of the helicity amplitudes. This leads to essential simplifications of the complete experiment problem, at least as far as mathematical aspects are concerned.

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 scal…