Abstract
We present first results for the excited nucleon spectrum in the framework of Poincaré-covariant three-body Bethe-Salpeter equations using the Rainbow-Ladder truncation of the interaction kernel. As expected, this truncation does not provide the mechanisms for a correct description of the spectrum. We also comment on possible steps beyond Rainbow-Ladder.
Highlights
The continuum approach to hadron physics based on solutions of Dyson-Schwinger (DSE) and Bethe-Salpeter (BSE) equations has as one of its main goals the description of hadron properties using the elementary degrees of freedom of QCD
Assuming the identification of these solutions with physical states is correct, we have studied the dependence of the results with the interaction width ω
We have performed the first calculation of excited nucleon masses in a three-body covariant Bethe-Salpeter framework
Summary
The continuum approach to hadron physics based on solutions of Dyson-Schwinger (DSE) and Bethe-Salpeter (BSE) equations (see e.g. Ref. and references therein) has as one of its main goals the description of hadron properties using the elementary degrees of freedom of QCD. The complications inherent to this enterprise have led to simplify this problem using the so-called Rainbow-Ladder (RL) truncation for the interaction kernels and vertices This truncation is the simplest possible one preserving covariance and chiral symmetry. Fischer reasonably well a number of hadron observables, namely pseudoscalar ground-state meson masses and decay constants,[1,2,3] ground-state baryon masses[4,5] and form factors.[6,7,8,9,10] The limitations of this very simple truncation have, been observed for example in the description of scalar and vector mesons, mesonic excited states[11] or in the low-Q behavior of baryon electromagnetic form factors.[8,9,10] In this work we report on the failure of the RL truncation to describe the excited-state spectrum of nucleons
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