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

TL;DR

This paper investigates the Hermiticity issues in bound-state equations with asymmetric kernels, identifies truncation artifacts causing complex eigenvalues, and proposes methods to eliminate these issues, especially for charmed mesons.

Contribution

It analyzes the origin of complex eigenvalues in bound-state equations and offers solutions to mitigate truncation artifacts affecting the analytic structure of hadronic models.

Findings

Imaginary components linked to truncation artifacts.

Methods to eliminate artifacts in charmed meson calculations.

Comparison of complex solutions with pole models.

Abstract

We highlight Hermiticity issues in bound-state equations whose kernels are subject to a highly asymmetric mass and momentum distribution and whose eigenvalue spectrum becomes complex for radially excited states. We trace back the presence of imaginary components in the eigenvalues and wave functions to truncation artifacts and suggest how they can be eliminated in the case of charmed mesons. The solutions of the gap equation in the complex plane, which play a crucial role in the analytic structure of the Bethe-Salpeter kernel, are discussed for several interaction models and qualitatively and quantitatively compared to analytic continuations by means of complex-conjugate pole models fitted to real solutions.