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arXiv · 1912.08339

Can the hyperfine mass splitting formula in heavy quarkonia be applied to the $B_c$ system?

Lei Chang·Muyang Chen·Xue-qian Li·Yu-xin Liu·Khépani Raya
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Abstract

The mass relation ${M_{0^{+}}+3M_{1^{+\prime}}+5M_{2^{+}}= 9M_{1^{+}}}$ miraculously holds for the $P$-wave charmonium $(c\bar{c})$ and bottomonium $(b\bar{b})$ 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 $M_{0^{+}}+5M_{2^{+}}=3(M_{1^{+\prime}}+M_{1^{+}})$ as an extension to the $P$-wave $B_{c}$ case. In order to test its applicability, we employ a variety of Quark Model predictions for the $B_c$ mass spectrum. Our numerical analysis confirms such formula is accurate up to very small deviations.

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Lei Chang, Muyang Chen, Xue-qian Li, Yu-xin Liu, Khépani Raya. 2019-12-18. Can the hyperfine mass splitting formula in heavy quarkonia be applied to the $B_c$ system?. https://doi.org/10.1007/s00601-020-01586-w

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