Spectroscopy of atomlike mesonsQq¯in a semirelativistic theory

A semirelativistic theory of an atomlike meson, a bound state of a heavy quark Q and a light antiquark q¯, is developed on the basis of the equation introduced by Fermi and Yang in their composite model of a pion. As for the Qq¯ potential, a vector ‘‘Coulomb’’ plus scalar linear potential is chosen as an example and the transverse interaction of the gluon exchange is also taken into account. The spin-dependent forces are introduced automatically by applying the Foldy transformation to the heavy quark Q. Furthermore, the transverse gluon term generates additional spin-dependent forces. This model reproduces the mass levels of D ($D^{\mathrm{*}}$), $D_s$ ($D_s^{\mathrm{*}}$), and B ($B^{\mathrm{*}}$) mesons well. $D^{\mathrm{*}\mathrm{*}}$(2420) is likely one of the $1^1$ $P_1$, $1^3$ $P_1$, or $1^3$ $P_2$ states.