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arXiv · hep-ph/0305012

Spin-Orbit and Tensor Forces in Heavy-quark Light-quark Mesons: Implications of the New Ds state at 2.32 GeV

Robert N. Cahn·J. David Jackson
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Abstract

We consider the spectroscopy of heavy-quark light-quark mesons with a simple model based on the non-relativistic 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 $1/m_1m_2$ 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 $J^P=1^+$ 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.

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Robert N. Cahn, J. David Jackson. 2003-05-02. Spin-Orbit and Tensor Forces in Heavy-quark Light-quark Mesons: Implications of the New Ds state at 2.32 GeV. https://doi.org/10.1103/physrevd.68.037502

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