Spin forces in mesons made up of quarks of different mass

With the help of a variational method we apply the standard Coulomb + Linear potential to the analysis of mesons constructed from quarks of different mass. Fine and hyperfine splittings are discussed, with particular emphasis on their asymptotic behaviour. Striking differences in this behaviour are predicted to occur compared with the case of mesons built up from equal mass quarks, with the spin-orbit mixing force playing here a fundamental role. Such predictions may be tested within the bottom ((bbar u)) meson family. Our considerations are also extended to the strange and charmed mesons. Our model favours ak(O⁺) below theK ^* (1.430), and predicts a partial inversion in the ordering of theP-wave states of the charmed mesons ((cbar u)) .