Regularization of Breit Potential and Splitting of η_c-J/ψ

Abstract: The study of the splittings between the masses of mesons with different spin and orbit quantum numbers is important for checking the quark potential model. In the previous calculations with quark potential models, the splitting between ηc and J/ψ is however too small to the experimental result. In this paper the mass splitting of ηcJ/ψ and the splitting between the new
meson ηb and Υ(1s) are investigated with the complete Breit quark potential regularized by applying the form factor μ2/(q2+μ2) one time in momentum space. In addition, because the complete Breit potential includes the spinorbit interaction, it can be used to investigate the splittings among χc0, χc1
and χc2. The investigated results indicate that the screen mass μ in the form factor of regularization is related to the reduced mass of meson.
The splittings of η_c-J/ψ, ηbΥ, and χc0χc1χc2 can reproduce the experimental results with high accuracy when the screen mass is expanded to the thirdorder polynomial of meson reduced mass.