From Experimental Data to Pole Parameters in a Model Independent Way (Fixed-t Single-Energy Partial Wave Analysis (SE PWA) and Laurent + Pietarinen Model (L+P) for Pole Extraction)

As it has been shown in the invited talk at the NSTAR-2017 conference [1] it is in principle possible to extract pole parameters directly from experiment with minimal model dependence, and in this contribution one way to achieve it in practice by fixed-t analyticity has been demonstrated. Namely, unconstrained partial- wave amplitudes obtained at discrete energies from fits even to complete sets of independent observables which are required to uniquely reconstruct reaction amplitudes do not vary smoothly with energy, and are in prin ciple non-unique. We have demonstrated that this behavior can be ascribed to the continuum ambiguity. We have applied continuum ambiguity invariance to pseudo-scalar meson photoproduction and showed that for a complete set of pseudo-data the non-uniqueness effect can be removed through a phase rotation generating “up-to-a-phase” unique set of single energy partial wave amplitudes. Now we show that for real data this method does not work, but another approach - fixed-t analyticity solves the problem. We present the final results for the η and π0 -photoproduction [2, 3]. Extracting pole positions from partial wave amplitudes is the next step, and we summarize the essence of the new, Laurent + Pietarinen expansion method applicable for continuous and discrete data. It is based on applying the Laurent decomposition of partial wave amplitude, and expanding the non-resonant background into a power series of a conformal-mapping-generated, quickly converging power series obtaining the simplest analytic function with well-defined partial wave analytic properties which fits the input. Unifying both methods in succession, one constructs a model independent procedure to extract pole parameters directly from experimental data without referring to any theoretical model.