基于狄拉克夸克哈密顿量和数值方法的π介子与K介子质量的类氢模型
A Hydrogen-Like Model for Pion and Kaon Masses Based on Dirac Quark-Hamiltonians and Numerical Methods
AI总结：
该研究提出一种基于狄拉克夸克哈密顿量的类氢介子质量模型，用单一禁闭电荷替代三色电荷，拟合31个π介子和K介子质量，误差约18%，确定了夸克相互作用的基本长度。
AI中文摘要：
我们考虑一种用于介子质量谱的相对论性类氢模型，该模型基于具有新的广义杨-米尔斯对称性的拉格朗日量。强相互作用包含一个四阶场方程，可产生线性禁闭势。值得注意的是，该介子质量模型要求夸克仅携带单一的“禁闭电荷”$f_c$，而非三种色电荷。我们将介子质量谱按同位旋、G宇称、总角动量和宇称划分为子谱。通过将数值求解器应用于狄拉克哈密顿量（包含两个短程禁闭势），我们得到了自然单位下的能量本征值。该模型有三个耦合常数和一个参数，可在约18%的相对百分比误差内对31个π介子和K介子质量（从约140 MeV到约2300 MeV）进行稳健拟合。该模型表明，禁闭电荷$f_c=0.045/MeV=8.87$ fm在夸克相互作用中起到基本长度的作用。
英文摘要：
We consider a relativistic hydrogen-like model for meson mass spectra. The model is based on a Lagrangian with a new general Yang-Mills symmetry. The strong interactions involve a fourth-order field equation that generates a linear confining potential. Notably, this model for meson masses requires quarks to carry only a single `confining charge' $f_c$ rather than three color charges. We classify meson mass spectra into sub-spectra defined by isospin, G-parity, total angular momentum and parity. By applying a numerical solver to the Dirac Hamiltonians--incorporating two short-range confining potentials, we obtain energy eigenvalues in natural units. The model has three coupling constants and one parameter. It provides a robust fit of 31 pions and kaons masses (from $\approx 140 MeV$ to $\approx 2,300 MeV$) to within $\approx 18\%$ of relative percentage error. The model suggests that the confining charge $f_c$=0.045/MeV = 8.87 fm plays the role of the basic length in the quark interactions.
