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

Švarc, Alfred; Hadžimehmedović, M.; Osmanović, H.; Stahov, J.; Tiator, L.; Workman, R. L.

doi:10.1103/physrevc.88.035206

Cited by 42 publications

(87 citation statements)

References 23 publications

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“…It was later used by a number of authors for solving various problems in scattering and field theory [25], but not applied to the pole search prior to our recent study [13]. A more detailed discussion of the use of conformal mapping, and this method in particular, can be found in Refs.…”

Section: B Pietarinen Seriesmentioning

confidence: 99%

“…In our principal paper [13] we have tested the validity of the model on a number of well known πN amplitudes, and concluded that the method is very robust and stable. However, in that paper we did not present an error analysis, deferring it to the forthcoming paper.…”

Section: B Error Analysismentioning

confidence: 99%

“…A more detailed discussion of the use of conformal mapping, and this method in particular, can be found in Refs. [13,20].…”

Section: B Pietarinen Seriesmentioning

confidence: 99%

“…The starting point of our method is a generalization of the Laurent expansion, applied to multipoles, using the Mittag-Leffler theorem [13,20], a theorem expressing a function in terms of its k first order poles and an entire function:…”

Section: A Laurent (Mittag-leffler) Expansionmentioning

confidence: 99%

“…[13] we have presented 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 have represented this using a convergent series of Pietarinen functions.…”

Section: Introductionmentioning

confidence: 99%

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Pole positions and residues from pion photoproduction using the Laurent-Pietarinen expansion method

et al. 2014

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We have applied a new approach to determine the pole positions and residues from pion photoproduction multipoles. The method is based on a Laurent expansion of the partial wave T-matrices, with a Pietarinen series representing the regular part of energy-dependent and single-energy photoproduction solutions. The method has been applied to multipole fits generated by the MAID and GWU/SAID groups. We show that the number and properties of poles extracted from photoproduction data correspond very well to results from πN elastic data and values cited by Particle Data Group (PDG). The photoproduction residues provide new information for the electromagnetic current at the pole position, which are independent of background parameterizations, as opposed to the Breit-Wigner representation. Finally, we present the photo-decay amplitudes from the current MAID and SAID solutions at the pole, for all four-star nucleon resonances below W = 2 GeV.

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Section: B Pietarinen Seriesmentioning

confidence: 99%

Section: B Error Analysismentioning

confidence: 99%

“…A more detailed discussion of the use of conformal mapping, and this method in particular, can be found in Refs. [13,20].…”

Section: B Pietarinen Seriesmentioning

confidence: 99%

Section: A Laurent (Mittag-leffler) Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pole positions and residues from pion photoproduction using the Laurent-Pietarinen expansion method

et al. 2014

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Different manifestations of S-matrix poles

Jiménez

Kelkar

2018

Annals of Physics

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Making use of the analytical properties of the S-matrix and a theorem of Mittag-Leffler, model independent non-relativistic expressions for cross sections in single channel elastic scattering, scattering phase shifts and survival probabilities of resonances are derived. Provided certain conditions are satisfied by the poles, the residues can also be estimated analytically. Considerations of the low energy behaviour of the S-matrix and cross sections reveal additional conditions on the residues of the poles appearing in the Mittag-Leffler expansions. The exact expressions for the resonant cross section and phase shift are shown to reduce to the commonly used Breit-Wigner formula plus corrections. The latter is shown to approach the exact result with the example of a meson and a baryon resonance. Finally, a comparison of the exact expressions with some realistic examples is presented. The calculations of survival probabilities in particular reveal the reason behind the non-observability of non-exponential decay.

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Generalization of the model-independent Laurent–Pietarinen single-channel pole-extraction formalism to multiple channels

et al. 2016

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A method to extract resonance pole information from single-channel partial-wave amplitudes based on a Laurent (Mittag-Leffler) expansion and conformal mapping techniques has recently been developed. This method has been applied to a number of reactions and provides a model-independent extraction procedure which is particularly useful in cases where a set of amplitudes is available only at descrete energies. This method has been generalized and applied to the case of a multi-channel fit, where several sets of amplitudes are analysed simultaneously. The importance of unitarity constraints is discussed. The final result provides a powerful, modelindependent tool for analyzing partial-wave amplitudes of coupled or connected channels based entirely on the concepts of analyticity and unitarity.

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

Cited by 42 publications

References 23 publications

Pole positions and residues from pion photoproduction using the Laurent-Pietarinen expansion method

Pole positions and residues from pion photoproduction using the Laurent-Pietarinen expansion method

Different manifestations of S-matrix poles

Generalization of the model-independent Laurent–Pietarinen single-channel pole-extraction formalism to multiple channels

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