Containing Of Quark Ring Effect Study Of The Gluon Propagator

Dyson-Schwinger(DS)Equation is an effective method to study the nonperturbative quantum chromodynamics(NPQCD)phenomena:color confinement, dynamical chiral symmetry breaking,and other hadronic problems.Because DS equations(DSEs)are infinite tower of coupled integral equations relating the Green's functions,the rainbow-ladder approximation is used to simplify the equations. Through solving this simplification of DSEs,we can study the related physical problems strictly.Over the past few years,considerable success has been made in the so-called rainbow-ladder approximation of the DSEs[21,22].The rainbow-ladder approximation was also employed to study dressed gluon propagator containing quack loop effect in DS approach.From the gluon DSEs we clearly know that quark loops are contained in the dressed gluon propagator.However,in the previous studies this effect is often neglected.Recently,based on the global color symmetry model(GCM),we developed a method for obtaining the quark-loop effects on the dressed gluon propagator in GCM theoretically[23].It is a general approach to calculate the quark-loop effects on the dressed gluon propagator.This approach can also be used to calculate the current quark mass and chemical potential dependence of the dressed gluon propagator.Through the above expressions,the dressed gluon propagator containing quack loop effect in the chiral limit can be obtained numerically, and the dressed quark self function can be calculated on the base of the gluon propagator obtained previously.The influences of quack loop effect on the motions of gluon propagator can be well-illustrated by comparing the figures of dressed quark self-energy function under our condition with the figures obtained through traditional method(quack loop effect was not involved in the calculation of dressed gluon propagator).As a result,the quack loop effect cannot be neglected in the calculation of the gluon propagator.