A New Method to Predict Meson Masses

The Feynman--Hellmann theorem is used to show that vector meson energy eigenvalues are monotonically decreasing functions of the reduced masses of their constituent quarks. The experimental meson masses are used to put constraints on the values of quark masses and to predict the masses of some as yet undiscovered mesons. The mass of the $B_c^*$ meson is predicted to be $6320\pm 10$ MeV, and, with less precision, the masses of a number of excited vector mesons are also predicted.