摘要: 研究自旋和轨道量子数不同的介子之间的质量劈裂对检验夸克势模型非常重要。
在以往的夸克势模型计算中,η_c-J/ψ的质量劈裂都很难达到实验的值。 用正规化形状因子μ2/(q2+μ2)， 在对完整的动量空间中的Breit夸克势实施一次正规化下研究了η_c-J/ψ和新介子ηb与Υ(1s)之间的质量劈裂。 结果表明， 正规化形状因子中的屏蔽质量μ应与介子折合
质量有关， 当将其展开为介子折合质量的三阶多项式时， 上述介子质量劈裂可以精确重现实验的结果。另外， 由于完整的Breit势包含有自旋-轨道耦合相互作用的项，因而还可以研究χc0,χc1和χc2之间的质量劈裂。
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.