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

Abstract

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 $\Sigma_c$, $\Sigma_b$, and $\Omega_c$, $\bar Q Q$ quarkonia, and the bottom-charmed meson $B_c$. 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 $\Lambda$ to the $\Upsilon$.