Two distinct sets of properties are used to describe short-lived particles: the pole and the Breit-Wigner parameters. There is an ongoing decades-old debate on which of them is fundamental. All resonances, from excited hydrogen nuclei hit by ultra-high energy gamma rays in deep space, to new particles produced in Large Hadron Collider, should be described by the same fundamental physical quantities. In this study of nucleon resonances we discover an intricate interplay of the parameters from the both sets, and realize that neither set is fundamental on its own.

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.

We present a new approach to quantifying pole parameters of single-channel processes based on a Laurent expansion of partial-wave T-matrices in the vicinity of the real axis. Instead of using the conventional power-series description of the non-singular part of the Laurent expansion, we represent this part by a convergent series of Pietarinen functions. As the analytic structure of the non-singular part is usually very well known (physical cuts with branch points at inelastic thresholds, and unphysical cuts in the negative energy plane), we find that one Pietarinen series per cut represents the analytic structure fairly reliably. The number of terms in each Pietarinen series is determined by the quality of the fit. The method is tested in two ways: on a toy model constructed from two known poles, various background terms, and two physical cuts, and on several ∞

The mini-proceedings of the Workshop on PWA tools in Hadronic Spectroscopy held in Mainz from February 18th to 20th, 2013.

We present a new approach to quantifying pole parameters of single-channel processes based on Laurent expansion of partial wave T-matrices. Instead of guessing the analytical form of non-singular part of Laurent expansion as it is usually done, we represent it by the convergent series of Pietarinen functions. As the analytic structure of non-singular term is usually very well known (physical cuts with branhcpoints at inelastic thresholds, and unphysical cuts in the negative energy plane), we show that we need one Pietarinen series per cut, and the number of terms in each Pietarinen series is automatically determined by the quality of the t. The method is tested on a toy model constructed from two known poles, various background terms, and two physical cuts, and shown to be robust and condent up to three Pietarinen series. We also apply this method to Zagreb CMB amplitudes for the N(1535) 1/2- resonance, and conrm the full success of the method on realistic data. This formalism can also be used for tting experimental data, and the procedure is very similar as when

In Hadzimehmedovicet al.[Phys. Rev. C 84, 035204 (2011)] we have used the Zagreb realization of Carnegie-Melon-Berkeley coupled-channel, unitary model as a tool for extracting pole positions from the world collection of partial-wave data, with the aim of eliminating model dependence in pole-search procedures. In order that the method is sensible, we in this paper discuss the stability of the method with respect to the strong variation of different model ingredients. We show that the Zagreb CMB procedure is very stable with strong variation of the model assumptions and that it can reliably predict the pole positions of the fitted partial-wave amplitudes.

The dispersion relations are used to perform an analytical continuation of the πN scattering amplitude D + to the Cheng-Dashen point and to calculate the πN sigma term. The dispersion relations were evaluated along two different families of dispersion curves passing through different kinematical regions in the s-channel physical region. The obtained results for the sigma term are still within the error bars of the previous Karlsruhe result.

Dispersion relations along interior hyperbolas and a set of hyperbolas passing through the Cheng-Dashen point are used to calculate the pion-nucleon sigma term. The t-channel input is updated using the recent GWU partial wave solution and ππ phase shifts from calculations based on Roy equations. Obtained values for the sigma term are still within the error bars of the previous Karlsruhe result.