Breit夸克势的不同次正规化与ηc-J/ψ等的质量劈裂

用夸克势模型研究结构相同而自旋和轨道量子数不同的介子之间质量劈裂是检验势模型有效性的重要手段之一. 在以往的用各种夸克势模型计算质量劈裂工作中, 当轻介子和重介子一起计算时, π-ρ很容易劈裂, 而η_c-J/ψ等的劈裂都很 难达到实验值. 这里首先用正规化形状因子μ²/(q²+μ²), 对完整的动量空间中的Breit夸克势的第三项实施二次正规化, 除了第一项 库仑势和第七项常数项势, 对其余的项实施一次正规化, 然后用来计算 质量劈裂. 研究计算发现, 只有当屏蔽质量μ取为关于 折合质量μ_r=m_r m_j/(m_r+m_j) 的三阶多项式时, 轻介子π-ρ和重介子η_c-J/ψ, η_b-Υ(1s), 还有χ_c0-χ_c1-χ_c2 等的劈裂 精确达到实验值, 同时其他介子质量也都比以往得到较大的改善. 因此, 本文给出了一个有效的夸克势模型.

Different time regularization of the Breit quark potential and the mass splittings of ηc-J/ψ and other mesons

The study on the mass splittings of the mesons with the same structure but different spin-and orbit-quantum numbers is one of the important methods for checking the efficiency of potential models. In previous calculations for quark potential models, the splitting between π-ρ is easily obtained while that of the η_c-J/ψ is however too small to meet the experimental results. In this paper, the third term of the complete Breit quark potential in the momentum space is regularized twice by applying the form factor μ²/(q²+μ²), and the other terms except the first term of the Coulombic potential and the seventh term of the constant potential are regularized once. The mass splittings are calculated by using these values. Our results indicate that the mass splittings of light mesons π-ρ, heavy mesons η_c-J/ψ, η_b-Υ(1s), and χ_c0-χ_c1-χ_c2 can meet the experimental results with high accuracy only when the screen mass μ is expanded to the third-order polynomial with respect to the meson reduced mass μ_r=m_r m_j/(m_r+m_j), while the masses of other mesons are improved greatly. An efficient quark potential model is thus described in this paper.