engleski

Introducing the Pietarinen expansion method into the single-channel pole extraction problem

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 nonsingular part of the Laurent expansion, we represent this part by a convergent series of Pietarinen functions. As the analytic structure of the nonsingular 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 sets of realistic πN elastic energy-dependent partial-wave amplitudes (GWU/SAID [Arndt et al., Phys. Rev. C 74, 045205 (2006) ; Workman et al., Phys. Rev. C 86, 035202 (2012)], and Dubna-Mainz-Taipei [Chen et al., Phys. Rev. C 76, 035206 (2007) ; Tiator et al., Phys. Rev. C 82, 055203 (2010)]).We show that the method is robust and confident using up to three Pietarinen series, and is particularly convenient in fits to amplitudes, such as single-energy solutions, coming more directly from experiment: cases where the analytic structure of the regular part is a priori unknown.

nucleon resonances; poles; new pole extraction method

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