Pion-nucleon partial-wave analysis

Abstract

We have carried out a partial-wave analysis of arnalganialcd pion-nucieon scattering data at 35 momenta in the range 0.429-1.995 GeV/c. At each momenturn, a large srt of fits was obtained, with the amplitude represented as the sum of a fixed background and the fitted terms of an accelerated convergence expansion. The effects of discrete and continuum ambiguities were separated by special statistical and numerical techniques which sort the fits into clusters. Dispersion relations on selected curves within the kinematical region for physical scattering were used to resolve the ambiguities arid to derive constraints. These constraints, which ensure that the fitted amplitudes have a relatively smooth energy dependence consistent with analyticity, were used iteratively to arrive at a unique set of amplitudes which fit the scattering data throughout the energy region studied.

2πproduction in the Giessen coupled-channels model

“…The KSU approach is based on multichannel parameterization of the scattering matrix in the form S = (1 + iK)/(1 − iK) within K-matrix formalism [30] whereas the calculations [31] utilize CMB ansatz of Cutkosky et al [32]. While both approaches are able to maintain at least two-body unitarity their PWA amplitudes are fitted to the single energy solutions from [10] which are obtained by neglecting this constraint.…”

Resonance model for πN scattering and η-meson production in the S11 channel

“…We employ the solutions obtained by Höhler and the Karlsruhe-Helsinki group [11] and by Cutkosky and the CMU-LBL group [12].…”

“…energies below √ s =1.8 GeV involves two N * resonances [11,12]. The lower one, the S 11 (1535) resonance, decays into πN, ηN and ππN with the branching ratios 35-55 %, 30-50 % and 5-20 %, respectively [13].…”

Poles as the only true resonant-state signals extracted from a worldwide collection of partial-wave amplitudes using only one, well controlled pole-extraction method

“…[5,6] energy dependent width is related to the resonant part of the S-matrix. In a method proposed in ref [7] and applied in refs. [8,9] width is deffined from the function consisting of a background term and Breit-Wigner shape term.…”

“…The second one is to allow the Breit-Wigner parameters to become energy dependent. That is predominantly done by modeling the Breit-Wigner width [4][5][6][7][8][9].…”