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We highlight Hermiticity issues in bound-state equations whose kernels aresubject to a highly asymmetric mass and momentum distribution and whoseeigenvalue spectrum becomes complex for radially excited states. We trace backthe presence of imaginary components in the eigenvalues and wave functions totruncation artifacts and suggest how they can be eliminated in the case ofcharmed mesons. The solutions of the gap equation in the complex plane, whichplay a crucial role in the analytic structure of the Bethe-Salpeter kernel, arediscussed for several interaction models and qualitatively and quantitativelycompared to analytic continuations by means of complex-conjugate pole modelsfitted to real solutions.

Excited hadrons and the analytical structure of bound-state interaction kernels