The mass relation $${M_{0^{+}}+3M_{1^{+\prime }}+5M_{2^{+}}= 9M_{1^{+}}}$$ M 0 + + 3 M 1 + ′ + 5 M 2 + = 9 M 1 + miraculously holds for the P -wave charmonium $$(c\bar{c})$$ ( c c ¯ ) and bottomonium $$(b\bar{b})$$ ( b b ¯ ) systems with soaring precision. The origin of such relation can be addressed from Quark Models, and have been confirmed experimentally in a limited number of cases. In this connection, we propose $$M_{0^{+}}+5M_{2^{+}}=3(M_{1^{+\prime }}+M_{1^{+}})$$ M 0 + + 5 M 2 + = 3 ( M 1 + ′ + M 1 + ) as an extension to the P -wave $$B_{c}$$ B c case. In order to test its applicability, we employ a variety of Quark Model predictions for the $$B_c$$ B c mass spectrum. Our numerical analysis confirms such formula is accurate up to very small deviations.

中文翻译：

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重夸克尼亚中的超精细质量分裂公式能否应用于 $$B_c$$ 系统？

质量关系 $${M_{0^{+}}+3M_{1^{+\prime }}+5M_{2^{+}}= 9M_{1^{+}}}$$ M 0 + + 3 M 1 + ′ + 5 M 2 + = 9 M 1 + 奇迹般地适用于 P 波charmonium $$(c\bar{c})$$ ( cc ¯ ) 和bottomonium $$(b\bar{b} )$$ ( bb ¯ ) 系统精度飙升。这种关系的起源可以从夸克模型中得到解决，并且已经在有限数量的案例中得到了实验证实。在这方面，我们建议 $$M_{0^{+}}+5M_{2^{+}}=3(M_{1^{+\prime }}+M_{1^{+}})$$ M 0 + + 5 M 2 + = 3 ( M 1 + ′ + M 1 + ) 作为 P 波 $$B_{c}$$ B c 情况的扩展。为了测试其适用性，我们对 $$B_c$$ B c 质谱采用了各种夸克模型预测。我们的数值分析证实，这种公式在非常小的偏差下都是准确的。