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Abnormal Solutions of Bethe–Salpeter Equation with Massless and Massive Exchanges

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Abstract

We summarize the main properties of the so called “abnormal solutions” of the Wick–Cutkosky model, i.e. two massive scalar particles interacting via massless scalar exchange (“photons”), within the Bethe–Salpeter equation. These solutions do not exist in the non-relativistic limit, in spite of having very small binding energies. They present a genuine many-body character dominated by photons, with a norm of the valence constituent wave function (two-body norm) that vanishes in the limit of zero binding energy. We present new results concerning the massive-exchange case, in particular determine under which conditions is it possible to obtain such peculiar solutions without spoiling the model by tachyonic states (\(M^2<0\)).

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No datasets were generated or analysed during the current study.

Notes

  1. Note that there was a misprint in the integration limits over t in the original publication [6].

  2. since \({z-z'\over x} >z-z'\) and so \({z-z'\over x}+z'>z>-1\)

  3. We were solving at that time a generalized eigenvalue equation, formally writen as \(V_L\;g=V_R\; g\)

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Acknowledgements

J.C. thanks the financial support from FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) Grant 2022/10580-3. H.S. acknowledges financial support from the EU research and innovation programme Horizon 2020, under Grant Agreement No. 824093.

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Author notes

  1. Vladimir A. Karmanov, Ekaterina A. Kupriyanova and Hagop Sazdjian have contributed equally to this work.

Authors and Affiliations

  1. Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405, Orsay, France

    Jaume Carbonell & Hagop Sazdjian

  2. Lebedev Physical Institute, Leninsky prospect 53, 119991, Moscow, Russia

    Vladimir A. Karmanov & Ekaterina A. Kupriyanova

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  1. Jaume Carbonell
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  2. Vladimir A. Karmanov
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  3. Ekaterina A. Kupriyanova
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  4. Hagop Sazdjian
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Carbonell, J., Karmanov, V.A., Kupriyanova, E.A. et al. Abnormal Solutions of Bethe–Salpeter Equation with Massless and Massive Exchanges. Few-Body Syst 65, 56 (2024). https://doi.org/10.1007/s00601-024-01928-y

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