Spin dependence of the potential

Although the static quarkonium potential is flavour independent to a good approximation, nevertheless, the potential does contain flavour dependence in its non-static parts. These include both spin-dependent and spin-independent terms. We shall focus mainly on the spin-dependent corrections, as these are directly testable by measvirements of the fine and hyperfine splittings in quarkoniimi. 

To order v /c, the one-gluon-exchange contributions to the non-static potential are known as the Fermi-Breit terms. These Fermi-Breit terms include a spin-spin interaction, a spin-orbit interaction, and a tensor interaction. They go inversely as the square of one or the other of the quark masses or inversely as their product. 

The existence of spin-spin, spin-orbit, and tensor interactions is well established by the quarkonium data. The heavier the quarks, the smaller the corrections arising from these non-static terms, but the splitting of energy levels arising from these terms is significant even in bottomonium. 

The spin-dependent Fermi-Breit terms can give information about the Lorentz transformation properties of the potential. Most attention has 

In terms of V and 5, the generalized Fermi-Breit spin-spin, spin-orbit, and tensor potentials are given by (for the equal-mass case) 

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