Abnormal solutions of Bethe--Salpeter equation with massless and massive exchanges

• URL: http://arxiv.org/abs/2404.12182v1
• Date: Thu, 18 Apr 2024 13:41:14 GMT
• Title: Abnormal solutions of Bethe--Salpeter equation with massless and massive exchanges
• Authors: Jaume Carbonell1, Vladimir Karmanov, Ekaterina Kupriyanova, Hagop Sazdjian,
• Abstract summary: We present the main properties of the so called ''abnormal solutions'' of the Wick-Cutkosky model. These solutions do not exist in the non-relativistic limit, in spite of having very small binding energies. We determine under which conditions is it possible to obtain such peculiar solutions without spoiling the model by tachyonic states.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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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