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Excited Hadrons and the Analytical Structure of Bound-State Interaction Kernels

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Abstract

We highlight Hermiticity issues in bound-state equations whose kernels are subject to a highly asymmetric mass and momentum distribution and whose eigenvalue spectrum becomes complex for radially excited states. We trace back the presence of imaginary parts in the eigenvalues and wave functions to truncation artifacts and suggest how they can be eliminated in the case of charmed mesons. The solutions of the gap equation in the complex plane, which play a crucial role in the analytic structure of the Bethe–Salpeter kernel, are discussed for several interaction models and qualitatively and quantitatively compared to analytic continuations by means of complex-conjugate pole models fitted to real solutions.

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Acknowledgments

B. E. thanks the organizers of the ECT* workshop “Nucleon Resonances From Photoproduction to High Photon Virtualities” for their kind invitation and local support. The work mentioned in this contribution was made possible by: FAPESP Grant Nos. 2013/01907-0 and 2013/16088-4 (São Paulo State); CNPq Grant Nos. 305894/2009-9, 458371/2014-9 and 305852/2014-0 (Brazil). E. R. acknowledges support by Patrimonio Autónomo Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación, Francisco José de Caldas and by Sostenibilidad-UDEA 2014–2015 (Colombia).

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Authors and Affiliations

  1. Laboratório de Física Teórica e Computacional, Universidade Cruzeiro do Sul, Rua Galvão Bueno 868, São Paulo, SP, 01506-000, Brazil

    Bruno El-Bennich

  2. Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271 – Bloco II, São Paulo, SP, 01140-070, Brazil

    Gastão Krein & Fernando E. Serna

  3. Instituto de Física, Universidad de Antioquia, Calle 70, no. 52-21, Medellín, Colombia

    Eduardo Rojas

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  1. Bruno El-Bennich
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  2. Gastão Krein
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  4. Fernando E. Serna
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Correspondence to Bruno El-Bennich.

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This article belongs to the special issue “Nucleon Resonances”.

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El-Bennich, B., Krein, G., Rojas, E. et al. Excited Hadrons and the Analytical Structure of Bound-State Interaction Kernels . Few-Body Syst 57, 955–963 (2016). https://doi.org/10.1007/s00601-016-1133-x

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