A singly heavy baryon can be viewed as $N_c-1$ ($N_c$ as 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 color 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 the case of the $N_c$ 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 fact that the classical soliton can not be formed. It 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.

中文翻译：

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改进的π平均场和单重重子质量

单重重子可以被视为 $N_c-1$（$N_c$ 作为颜色的数量）受介子约束的轻价夸克平均场由 $N_c-1$ 价夸克的存在自洽产生，而单重重子内的重夸克被视为静态色源。我们研究了 pion 平均场是如何通过 $N_c$、$N_c-1$ 和 $N_c-2$ 轻价夸克的存在产生的，它们对应于轻重子、单重重子和双重重子系统. 随着颜色数量从 $N_c$ 减少到 $N_c-1$，pion 平均场发生变化。结果，价夸克对孤子惯性矩的贡献变得比$N_c$价夸克的情况大，而海夸克的贡献系统地减少。另一方面，$N_c-2$价夸克的存在不足以产生强π介子平均场，导致经典孤子无法形成。这表明pion平均场方法不适用于描述双重重子。我们表明单重重子的质谱可以通过改进的 pion 平均场更好地描述，与之前的工作相比，pion 平均场被假定为完整的，而 $N_c$ 变化。