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Can the Hyperfine Mass Splitting Formula in Heavy Quarkonia be Applied to the \(B_c\) System?

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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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Acknowledgements

We acknowledge helpful conversations with Dr. Xian-hui Zhong. This work is supported by: the National Natural Science Foundation of China under contracts Nos. 11435001, and 11775041, the National Key Basic Research Program of China under contract No. 2015CB856900.

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Authors and Affiliations

  1. School of Physics, Nankai University, Tianjin, 300071, China

    Lei Chang, Muyang Chen, Xue-qian Li & Khépani Raya

  2. Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, 100871, China

    Yu-xin Liu

  3. Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China

    Yu-xin Liu

  4. Center for High Energy Physics, Peking University, Beijing, 100871, China

    Yu-xin Liu

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  1. Lei Chang
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Correspondence to Lei Chang.

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Chang, L., Chen, M., Li, Xq. et al. Can the Hyperfine Mass Splitting Formula in Heavy Quarkonia be Applied to the \(B_c\) System?. Few-Body Syst 62, 4 (2021). https://doi.org/10.1007/s00601-020-01586-w

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