The Study Of The Two-loop Correction To The Chiral Magnetic Conductivity With NJL Model

The high order correction of chiral current in the quark gluon plasma has been a hot reasearch topic in the theoretical circle,and the chiral magnetic effect induced by the chiral imbalance of quark system and the background magnetic field is of which the reserach object to be disscussed in this paper.Since the general structure of field theory,the people has usually believe that there absence of the high order correction related to CME due to the protection from the triangle anomaly and the topological mass term of Chern-Simons.As we known,however,the Feynman triangle diagrams linked to the CME current may bring bout the infrared singularity due to the injected momentun on the axial vertex.Indeed,the high order triangle diagrams we discuss is the linear order of the axial chemical potential according to the expansion with current-current correlation.Therefore,we do not need to consider the infrared problem on the axial vertex.Then there are difference from the traditional triangle Feynman diagrams.It is considered that the CME current in the classical formula is the product of the chiral magnetic conductivity and the magnetic field.A general framework based on the finite temperature theory,we derive the current-current correlation and the ChernSimons term.Hence,the calculation of all the high order diagrams has been involved in the current-current correlation with the QCD and electromagnetic effect.Under the static limit,we introduce the NJL model instead of non-Abelian gauge field to evaluate the triagle diagrams at two-loop level,which shows that the current-current correlation receive no contribution.This means that the CME current may not need to consider the renormalization from the higher order.