Vacuum Susceptibility Of QCD In The Dyson-Schwinger Approach

The dynamical chiral symmetry breaking is the genuine effect of non-perturbative Quantum Chromodynamics (NPQCD). To study the effects, non-perturbative methods are required. Recently the Dyson-Schwinger (DS) approach has been a useful tool to study the effects. It has been proven to be successful in developing a hadron phenomenology which interpolates smoothly between the infrared (non-perturbative) and the ultraviolet (perturbative) regime.In this paper, we firstly introduce briefly the DS equation (DSE) formalism under laudan gauge, then apply the DS approach to the caculation of non-perturbative problem. In studying the linear response of the dressed quark propagator in the presence of the variable external field, we derive a general expression for the vacuum susceptibility, based on the two-point external field formula in the Quantum Chromodynamical (QCD) sum rule. The expressions we have derived for the calculation of vacuum susceptibility are model independent. Then we use the expressions to calculate the renormalised axial vector, vector and tensor vacuum susceptibilities. To get the numerical results, the rainbow-ladder approximation of the DS approach is used to get the quark propagator. However, the dreesed effects of the non-perturbative vertices was taken into consideration when calculating the vacuum susceptibility. To extract the effect of nonperturbation and eliminate the divergence, the mechanism of subtraction is used. A comparison with the results of the previous approach is given. We show that the differences between the results of our approach and the previous for the axial vector and vector vacuum susceptibilities are large, while that for the tensor vacuum susceptibility is small. The differences come from the dressed effects of the non-perturbative vertices, additionally, we also extended our discussion to the scalar susceptibilities.