Heavy Quark Mesons: Mass Spectrum and Mass Relations

We derive an assumption-free mass relation that connects heavy-quark mesons (c (c) over bar, b (b) over bar band B-c mesons) with different quantum numbers, but same orbital angular momentum. The obtained formula is exact, provided the hyperfine mass splitting, delta(hf), and delta(xi) := M(n(1)L(l))/M(n(3)L(l)) - 1 are determined independently. For completeness, we obtain the heavy-quark mesons spectrum following a Schrodinger wave equation (SWE) approach. The Song-Lin potential is employed along with the corresponding relativistic corrections, namely: spin-spin, spin-orbit and tensor interactions. Our numerical strategy is based upon the Numerov method, which enables us to cast our SWE approach into a matrix eigenvalue problem, for which high numerical accuracy can be achieved. Notably, only a single set of parameters is required to produce the known spectrum of the heavy-quark mesons.