Chiral solitons in the spectral quark model

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Chiral solitons with baryon number one are investigated in the spectral quark model. In this model the quark propagator is a superposition of complex-mass propagators weighted with a suitable spectral function. This technique is a method of regularizing the effective quark theory in a way preserving many desired features crucial in analysis of solitons. We review the model in the vacuum sector, stressing the feature of the absence of poles in the quark propagator. We also investigate in detail the analytic structure of meson two-point functions. We provide an appropriate prescription for constructing valence states in the spectral approach. The valence state in the baryonic soliton is identified with a saddle point of the Dirac eigenvalue treated as a function of the spectral mass. Because of this feature the valence quarks never become unbound nor dive into the negative spectrum, hence providing stable solitons as absolute minima of the action. This is a manifestation of the absence of poles in the quark propagator. Self-consistent mean-field hedgehog solutions are found numerically and some of their properties are determined and compared to previous chiral soliton models. Our analysis constitutes an involved example of a treatment of a relativistic complex-mass system.