论文部分内容阅读
The vacuum condensate is known to play the essential role for characterizing the nonperturbative aspect of the QCD vacuum. In fact, the gauge invariant vacuum condensates such as the chiral quark condensate, the two gluon condensate and the mixed quark gluon condensate are well known examples studied extensively so far. Meanwhile susceptibilities of vacuum are also important quantities of strong interaction physics. They directly enter in the determination of hadron properties in the QCD sum rule external field approach.In particular, the strong and parity-violating pion-nucleon coupling depends crucially upon xπ, the π susceptibility. Tensor susceptibilities of the vacuum are relevant for the determination of tensor charges of the nucleon. To study the property of the vacuum susceptibility, we have to know the quark 2-point function first. The Dyson-Schwinger equations provides us a good tools. Solving these equations provides a solution of the theory. In this thesis, I give an brief introduction to the DSE. DSE for a given n-point function involving at least one m＞n-point function, so we have to truncate the equations.By some truncation scheme, we get the rainbow DSE.In the second sections, we study the vacuum condensate using the rainbow DSE, and models for the gluon propagator. And by using an adequate subtraction mechanism which is consistent with the definition of vacuum condensate in QCD sum rule, we calculate pion vacuum susceptibility. Within this approach the pion vacuum susceptibility is free of UV divergence. In the third section,we calculate vector vacuum susceptibility. Other than previous approach, we calculate the vector vacuum susceptibility using the complete vertex Γv instead of using the “bare”vertex γv. The GCM models are not renormalizable. Therefore, the scale at which the pion and tensor vacuum susceptibility is defined in these models is not clear. So, We also study the vacuum suceptibility in the framework of the renormalized DSEs in the last section.