Can the Hyperfine Mass Splitting Formula in Heavy Quarkonia be Applied to the $$B_c$$ System?

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. origin of such can be addressed from Quark Models, have been confirmed experimentally in a limited number cases. In this connection, we propose $$M_{0^{+}}+5M_{2^{+}}=3(M_{1^{+\prime }}+M_{1^{+}})$$ as an extension to $$B_{c}$$ case. order test its applicability, employ variety Model predictions $$B_c$$ spectrum. Our numerical analysis confirms formula is accurate up very small deviations.