Padé approximants and resonance poles

Regular Article - Theoretical Physics

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.

Keywords

Pole Position Pole Mass Production Threshold Resonance Pole Riemann Sheet 

Notes

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 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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Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Institut für KernphysikJohannes Gutenberg-UniversitätMainzGermany
  2. 2.Departamento de Física Teórica and Instituto de Física TeóricaIFT-UAM/CSIC Universidad Autónoma de MadridMadridSpain

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