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 ${\rm Y}$.

Comments: 10 pages, 1 figure, discussion of B_s added, to be submitted to Phys. Rev. D. Third paragraph of last section modified