Flavor mixing and solution structures in Dyson–Schwinger equations for a two-flavor system  

作　　者：Xue-ao Chao Yu-xin Liu 

机构地区：[1]Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,Beijing 100871,China [2]Collaborative Innovation Center of Quantum Matter,Beijing 100871,China [3]Center for High Energy Physics,Peking University,Beijing 100871,China

出　　处：《Communications in Theoretical Physics》2024年第10期62-75,共14页理论物理通讯（英文版）

基　　金：supported by the National Natural Science Foundation of China under Contract Nos.11435001 and 11775041;the National Science Foundation of China under Grants No.12175007 and No.12247107。

摘　　要：We solved the Dyson–Schwinger(DS)equations for a two-flavor system with symmetry to study its flavor mixing effects.Initially,we employed the point interaction model and bare vertex approximation to reveal the structure of the solutions.Using the point interaction model,the DS equations can be solved analytically,and we found that these solutions can be classified into three groups,each forming an ellipse.These solutions exhibit SO(2)symmetry,while the original SU(2)symmetry at the Lagrangian level is dynamically broken to SO(2),corresponding to the emergence of flavor mixing effects.However,this flavor mixing effect does not manifest in the final physical state.By utilizing the system's SO(2)symmetry,we can diagonalize the propagators of the DS equations,eliminating the flavor mixing effect but causing the originally degenerate masses at the Lagrangian level to split.These mass eigenstates have identical quantum numbers but different masses.If we can correspond these to quark particles of different generations,we can explain why the three generations of quarks have different masses and obtain the corresponding quark mass spectrum.Finally,we provide the corresponding numerical results using a more realistic interaction model.

关 键 词：Dyson–Schwinger equation flavor change mass splitting dynamic symmetry breaking 

分 类 号：O572.33[理学—粒子物理与原子核物理]