Spin-orbit and tensor forces in heavy-quark light-quark mesons: Implications of the newDsstate at 2.32 GeV

Abstract

We consider the spectroscopy of heavy-quark light-quark mesons with a simple model based on the nonrelativistic reduction of vector and scalar exchange between fermions. Four forces are induced: the spin-orbit forces on the light and heavy quark spins, the tensor force, and a spin-spin force. If the vector force is Coulombic, the spin-spin force is a contact interaction, and the tensor force and spin-orbit force on the heavy quark to order ${1/m}_1{m}_2$ are directly proportional. As a result, just two independent parameters characterize these perturbations. The measurement of the masses of three p-wave states suffices to predict the mass of the fourth. This technique is applied to the $D_s$ system, where the newly discovered state at 2.32 GeV provides the third measured level, and to the D system. The mixing of the two $J^P{=1\mathrm{}}^{+}$ p-wave states is reflected in their widths and provides additional constraints. The resulting picture is at odds with previous expectations and raises new puzzles.