Vector-pseudoscalar mass splitting andϒ−ηbmass difference

For the vector-pseudoscalar mass difference, we propose a new unified empirical formula which works very well for almost all known mesons whether or not they contain one light quark. For heavy mesons, we predict $\Upsilon -{\eta }_b=55.0\mathrm{}\pm 5.0$ MeV and in particular ${\psi }^{\prime }-{\eta }_c^{\prime }=96.5\mathrm{}\pm 5.0$ MeV without any additional parameters. This new relation seems also valid for the radially excited states of mesons. The well-known approximate relation $M_V^2-M_P^2\simeq 0.56$ Ge${\mathrm{V}}^2$ can be reproduced as a special case for a narrow region of the reduced mass. A problem concerning the difference in the hyperfine splittings of self-conjugate mesons with zero isospin and in other mesons is solved.