Model-independent resonance parameter extraction from the trace of K and T matrices

Abstract

A model-independent method for the determination of Breit-Wigner resonance parameters is presented. The method is based on eliminating the dependence on the choice of channel basis by analyzing the trace of the K and T matrices in the coupled-channel formalism, rather than individual matrix elements of the multichannel scattering matrix.of Particle Physics [1] by the Particle Data Group (PDG). Each resonance in the Review has been parametrized in two ways. First, there are Breit-Wigner parameters, i.e. the resonance mass M R , decay width Γ R , and branching ratios x a (the ratio between the partial width into channel a and the total width). Alternatively, T -matrix complex poles (Re W p and −2 Im W p ), as well as complex residues (moduli |r|, and phases θ) are given in [1]. Breit-Wigner parameters obtained in various partial-wave analyses vary quite substantially, partly because details of those analyses are different; i.e. the number and character of the included channels, different parameterization schemes, analyticity constraints for scattering amplitudes, the choice of background models, and the method of unitarization (if at all) of the S matrix. However, it is also the case that the methods for extracting resonance parameters are different: Argand-plot fits [2], Breit-Wigner fits with background [3], direct fits of analysis parameters [4,5], or model specific schemes which extract T matrix poles [6,7,8].In this Letter we present a model-independent

Parameterization dependence ofT-matrix poles and eigenphases from a fit toπNelastic scattering data

“…As has been noted previously [17], resonances may be associated with a single eigenphase crossing 90 degrees, and this will result in a K-matrix pole. However, a more robust measure (if a set of amplitudes is available) is given by the time-delay matrix [18], which is proportional to the sum of energy derivatives of all eigenphases.…”

Strong decay of low-lyingS11andD13nucleon resonances to pseudoscalar mesons and octet baryons

“…Results of a K-matrix approach [26] for πN and ηN final states provide realistic values for all considered partial widths, except for Γ S 11 (1650)→ηN .…”

P -wave excited baryons from pion- and photo-induced hyperon production

“…The physics at MAMI (among other data) has been closely followed by the MAID group of Drechsel and Tiator [131,132,133,134,135,136,137,138]. Smaller groups at Zagreb [139,140,141,142], Gent [143,144,145,146] and KVI made significant contributions to the field [147,148,149,150,151]. A few further papers are to be mentioned [152,153,154,155,156].…”