Improved pion mean fields and masses of singly heavy baryons

A singly heavy baryon can be viewed as $N_c-1$ ($N_c$ being the number of colors) light valence quarks bound by the pion mean fields that are created by the presence of the $N_c-1$ valence quarks self-consistently, while the heavy quark inside a singly heavy baryon is regarded as a static color source. We investigate how the pion mean fields are created by the presence of $N_c$, $N_c-1$, and $N_c-2$ light valence quarks, which correspond to the systems of light baryons, singly heavy baryons, and doubly heavy baryons. As the number of colors decreases from $N_c$ to $N_c-1$, the pion mean fields undergo changes. As a result, the valence quark contributions to the moments of inertia of the soliton become larger than for $N_c$ valence quarks, whereas the sea quark contributions decrease systematically. On the other hand, the presence of the $N_c-2$ valence quarks is not enough to produce the strong pion mean fields, which leads to the classical soliton not being formed. This indicates that the pion mean-field approach is not suitable to describe doubly heavy baryons. We show that the mass spectra of the singly heavy baryons are better described by the improved pion mean fields, compared with the previous work in which the pion mean fields are assumed to be intact with $N_c$ varied.