Resolution of the multichannel anomaly in the extraction of S-matrix resonance-pole parameters

Abstract

Inspired by anomalies which the standard scattering matrix pole-extraction procedures have produced in a mathematically well defined coupled-channel model, we have developed a new method based solely on the assumption of partial-wave analyticity. The new method is simple and applicable not only to theoretical predictions but to the empirical partial-wave data as well. Since the standard pole-extraction procedures turn out to be the lowest-order term of the proposed method the anomalies are understood and resolved. 11.55.Fv, 14.20.Gk, 25.40.Ny. Introduction. The determination of the scattering matrix (S-matrix) is considered to be the major objective of both, scattering theory and energy-dependent analysis of scattering data. The collection of S-matrix poles in the "unphysical" Riemann sheet is related to resonance mass spectrum [1, 2] so obtaining them is the crucial goal of any partial-wave analysis. There is, however, a long lasting (and yet unresolved) controversy on the resonances' physical properties. It is not clear whether physical mass and decay width of a resonance are given by the "conventional" resonance parameters like Breit-Wigner mass and the decay width, or by resonance pole parameters-real part and −2× imaginary part of pole [3,4]. In the case of baryon resonances, the compromise is achieved in a way that all the conventional, as well as pole parameters are collected in the Review of Particle Physics (RPP) [5].The motivation for this work came from the fact that pole parameters we extracted from our coupled-channel partial waves [6] by a standard model-independent pole searching method (speed plot [3]) were not unique. The obtained pole positions varied from one reaction to another. The time-delay [7], another method of choice for resonance pole extraction was employed, but with similar outcome. This anomalous behavior challenged common sense and the conclusion was drawn that either our partial-wave analysis or the applied pole extraction methods were incorrect. The extraction methods were carefully examined, and those methods were determined to be at fault. This effort resulted in a new model-independent extraction method free from this anomaly. In addition, we calculated elastic pole residues, and the obtained values were in quite good agreement with others published in the RPP [5]. Since there are no RPP estimates for elastic residues yet, this result lends support to provide them.It is important to draw a distinction between the timedelay signal as resonance's "smoking gun", and utilization of the time-delay (or speed plot) for the extraction

Pole structure from energy-dependent and single-energy fits to GWU-SAIDπNelastic scattering data

“…In principle, there are two ways to extract pole parameters from experimental data: (i) construct theoretical single or multichannel models, solve them, fit the obtained analytic solutions to the data, and extract the pole parameters of obtained solutions through an analytic continuation of the model functions into the complex energy plane; or (ii) make a local expansion of the partial-wave T matrix in the vicinity of a pole. At present, poles are usually extracted using the first method [2][3][4][5][6], but considerable effort has been put into the development of alternate approaches, such as the speed plot [7], time delay [8], N/D method [9], regularization procedure [10], or Pade approximation [11],…”

Introducing the Pietarinen expansion method into the single-channel pole extraction problem

“…Simple procedures for pole extraction exist, but are not reliable in all cases. At present, poles are usually extracted from theoretical single or multi-channel models, fitted to the data, using an array of standard pole extraction methods: analytic continuation of the model * alfred.svarc@irb.hr functions into the complex energy plane [7][8][9][10][11], speed plot [12], time delay [13], N/D method [14], regularization procedure [15], etc. However, this typically requires solving an involved single/coupled-channel model and analyzing the obtained analytic solution, which implicitly contains both parts: singular and background.…”

Extraction of resonances from meson-nucleon reactions

“…We also want to mention here that an improved SP method using higher order derivatives of the amplitudes was proposed in Ref. [35]. It may be interesting to compare this method with the TD method.…”