Abstract
We deliver a new scheme to compute the quark propagator and the quark-gluon interaction vertex through the coupled Dyson-Schwinger equations (DSEs) of QCD. We take the three-gluon vertex into account in our calculations, and implement the gluon propagator and the running coupling function fitted by the solutions of their respective DSEs. We obtain the momentum and current mass dependence of the quark propagator and the quark-gluon vertex, and the chiral quark condensate which agrees with previous results excellently. We also compute the quark-photon vertex within this scheme and give the anomalous chromo- and electro-magnetic moment of quark. The obtained results also agree with previous ones very well. These applications manifest that the new scheme is realistic and then practical for explaining the QCD-related phenomena.
Highlights
People have made a lot of effort to study the nonperturbative phenomena of QCD, such as the dynamical chiral symmetry breaking (DCSB), confinement, and lowlying hadron spectra
When solving the Dyson-Schwinger equations (DSEs) of the quark propagator and the quark-gluon interaction vertex, we choose the following form as the input of the three-gluon vertex, Γ3νσgτðp − k; k − qÞ 1⁄4 Gðl2Þ1⁄2ðq þ k − 2pÞτδνσ þ ðp þ q − 2kÞνδστ þ ðk þ p − 2qÞσδντ; ð29Þ
These results reveal that our presently obtained quark-gluon interaction vertex carries more DCSB effect than the CLRQ model and the RL approximation, even though the DCSB effect demonstrated by the quark propagator, i.e., quark condensate, is similar
Summary
People have made a lot of effort to study the nonperturbative phenomena of QCD, such as the dynamical chiral symmetry breaking (DCSB), confinement, and lowlying hadron spectra. [3,6,7,10,29,30,32,36,37,38,54,55,56,57,58,59,60]) because of the simplicity and the systematization [people can define a self-consistent truncation with bare vertex for the quark-quark scattering kernel in the Bethe-Salpeter equation (BSE) [2,3,6,7,12,36,37,38,61,62], which is called the ladder approximation]. Our obtained result of the quark condensate is consistent with those from other computations, and the result for the vertex is consistent with the CLRQ vertex qualitatively Since this scheme is systematically derived from the QCD Lagrangian, it is easy to be generalized to construct the quark-quark scattering kernel, which is useful for formalizing the Bethe-Salpeter equations beyond RL approximation and constructing a realistic scheme for computing hadron properties.
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