Poles of Karlsruhe-Helsinki KH80 and KA84 solutions extracted by using the Laurent-Pietarinen method

Poles of partial wave scattering matrices in hadron spectroscopy have recently been established as a sole link between experiment and QCD theories and models. Karlsruhe-Helsinki (KH) partial wave analyses have been “above the line” in the Review of Particle Physics (RPP) for over three decades. The RPP compiles Breit-Wigner (BW) parameters from local BW fits, but give only a limited number of pole positions using speed plots (SP). In the KH method only Mandelstam analyticity is used as a theoretical constraint, so these partial wave solutions are as model independent as possible. They are a valuable source of information. It is unsatisfactory that BW parameters given in the RPP have been obtained from the KH80 solution, while pole parameters have been obtained from the KA84 version. To remedy this, we have used a newly developed Laurent + Pietarinen expansion method to obtain pole positions for all partial waves for KH80 and KA84 solutions. We show that differences from pole parameters are, with a few exceptions, negligible for most partial waves. We give a full set of pole parameters for both solutions.

Figure 1

L + P fit for $I=1/2$ solutions. (a) Fit to KA84, (b) fit to KH80.

Figure 2

L + P fit for I = 1/2 solutions. (a) Fit to KA84, (b) fit to KH80.

Figure 3

L + P fit for $I=3/2$ solutions. (a) Fit to KA84, (b) fit to KH80.

Figure 4

L + P fit for $I=3/2$ solutions. (a) Fit to KA84, (b) fit to KH80.