Abstract
We use a hybrid constituent-quark model for the microscopic description of \(\pi N N\), \(\pi N \Delta \) and \(\pi \Delta \Delta \) vertices. In this model quarks are confined by an instantaneous potential and are allowed to emit and absorb a pion, which is also treated as dynamical degree of freedom. The point form of relativistic quantum mechanics is employed to achieve a relativistically invariant description of this system. Starting with an SU(6) spin-flavor symmetric wave function for \(N_0\) and \(\Delta _0\), i.e. the eigenstates of the pure confinement problem, we calculate the strength of the \(\pi N_0 N_0\), \(\pi N_0 \Delta _0\) and \(\pi \Delta _0 \Delta _0\) couplings and the corresponding vertex form factors. Interestingly the ratios of the resulting couplings resemble strongly those needed in purely hadronic coupled-channel models, but deviate significantly from the ratios following from SU(6) spin-flavor symmetry in the non-relativistic constituent-quark model.
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This article belongs to the Topical Collection “The 23rd European Conference on Few-Body Problems in Physics”.
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Jung, JH., Schweiger, W. On the Microscopic Structure of \({\varvec{\pi }}\) NN, \({\varvec{\pi }}\) N \({\varvec{\Delta }}\) and \({\varvec{{\pi }\Delta \Delta }}\) Vertices. Few-Body Syst 58, 73 (2017). https://doi.org/10.1007/s00601-017-1234-1
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DOI: https://doi.org/10.1007/s00601-017-1234-1