Scaling of P -wave excitation energies in heavy-quark systems

A simple regularity in anticipating P-wave excitation energies of states with heavy quarks is noted. It can apply to systems such as the negative-parity Σ𝑐, Σ𝑏, and Ω𝑐, ¯ 𝑄 ⁢𝑄 quarkonia, and the bottom-charmed meson 𝐵𝑐. When one subtracts a term accounting for phenomenological energies of heavy quarks binding with one another in S-waves, the residual excitation energies display an approximately linear behavior in the reduced mass of constituents, all the way from the Λ to the ϒ.