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Padé approximants and resonance poles

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Abstract

Based on the mathematically well defined Padé theory, a theoretically safe new procedure for the extraction of the pole mass and width of a resonance is proposed. In particular, thanks to the Montessus de Ballore theorem we are able to unfold the second Riemann sheet of an amplitude to search for the position of the resonance pole in the complex plane. The method is systematic and provides a model-independent treatment of the prediction and the corresponding errors of the approximation. Likewise, it can be used in combination with other well-established approaches to improve future determinations of resonance parameters.

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Notes

  1. R N (x 0,x 0)=1, without loss of generality.

  2. Notice that, however, scattering amplitude partial-wave projections in general generate a left-hand cut.

  3. See, for example, Eq. (3.1) in Ref. [28], Eqs. (4) and (8) in Ref. [29], and Eq. (6) in Ref. [30] that parameterize the ππ scattering and are then used to precisely determine the σ or f 0(500) meson pole [31, 32].

  4. We thank B. Moussallam for his help with the Kπ phase shift from Ref. [33] and its derivatives.

  5. Notice, however, that the fair determinations of the input derivatives originally stem from the Roy–Steiner analysis [33].

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Acknowledgements

We would like to thank L. Tiator and B. Moussallam for comments on the manuscript. We are also thankful with B. Moussallam for his help with the Kπ phase shift from Ref. [33]. S.C. would like to thank the University of Mainz for its hospitality. This work has been partially supported by the MICINN, Spain, under contract FPA2010-17747 and Consolider-Ingenio CPAN CSD2007-00042, by the Italian Miur PRIN 2009, the Universidad CEU Cardenal Herrera grant PRCEUUCH35/11, the MICINN-INFN fund AIC-D-2011-0818 and by the Deutsche Forschungsgemeinschaft DFG through the Collaborative Research Center “The Low-Energy Frontier of the Standard Model” (SFB 1044). We thank as well the Comunidad de Madrid through Proyecto HEPHACOS S2009/ESP-1473 and the Spanish MINECO Centro de excelencia Severo Ochoa Program under grant SEV-2012-0249.

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Authors and Affiliations

  1. Institut für Kernphysik, Johannes Gutenberg-Universität, 55099, Mainz, Germany

    Pere Masjuan

  2. Departamento de Física Teórica and Instituto de Física Teórica, IFT-UAM/CSIC Universidad Autónoma de Madrid, Cantoblanco, Madrid, Spain

    Juan José Sanz-Cillero

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  1. Pere Masjuan
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Correspondence to Pere Masjuan.

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Masjuan, P., Sanz-Cillero, J.J. Padé approximants and resonance poles. Eur. Phys. J. C 73, 2594 (2013). https://doi.org/10.1140/epjc/s10052-013-2594-4

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