Study Of The Static And Homogeneous Limit Of The In Homogeneous Chiral Chemical Potential In Chiral Magnetic Effect

In heavy ion collision experiments,hadron matter will undergo a phase transition to produce quark gluon plasma.When heavy ions collide noncentrically,a very strong magnetic field will be generated along the angular momentum direction of the collision,which can reach the strong interaction energy scale,so it will have a significant impact on the dynamics of quark gluons.It is predicted that the sphaleron effect is obvious in the high temperature and high density quark gluon plasma,and the gluon field will undergo topological transition,resulting in the unequal number of left and righthanded quarks.When there are magnetic field and unequal number of left and right-handed quarks in quark-gluon plasma,an electric current will be induced along the magnetic field,which is called chiral magnetic effect,the induced electric current is called chiral magnetic current.The chiral magnetic current is proportional to the magnetic field,and the proportional coefficient is called CME conductivity.When calculating the CME conductivity produced by uniform magnetic field in finite-temperature and consider constant chiral chemical potential,we need to take the limit when the energy and space momentum of magnetic field approach to zero respectively.Lorentz covariance in finite temperature field theory is destroyed.In principle,when calculating the limit of energy and space momentum approaching zero,we need to calculate two kinds of limits: the limit of taking energy as zero first and then taking space momentum as zero,and the limit of taking space momentum as zero first and then taking energy as zero.The results show that the calculation results of the two limits are different,that is,the order of the infrared limits of the magnetic field is noncommucativity.There are articles pointed out that there is damping effect in the quark gluon plasma,which is reflected in the non-zero imaginary part of the quark propagator,will eliminate this noncommucativity.The magnetic field and chiral chemical potential are both inhomogeneous in the heavy ion collision experiment,there are noncommutativity issue of different orders of zero energy-momentum limit pertaining to the chiral chemical potential in the chiral magnetic effect when consider finite-temperature and inhomogeneous chiral chemical potential.We study that the the noncommutativity issue cannot be removed by introducing damping term to the quark progator.We compute the one-loop triangle diagram in finite-temperature to show that this noncommutativity issue originates from the pinching singularity of fermion propagator.This pinching singularity can be removed by introducing a damping term to the fermion progator,but modifying the fermion propagator along would violate the axialvector Ward identity,a modification of the axial-vector vertex is required(longitudinal component).Although the longitudinal component of vector vertex function does not contribute to the chiral magnetic effect,the longitudinal component of axis vector vertex function contributes to the chiral magnetic effect.Therefore,it is necessary to modify the vertex functions of quark propagator and axis vector when considering the damping effect in the triangle diagram.The pinching singularity with fermion propagator was taken over by the singularity stemming from the dressed axial-vector vertex,the noncommutativity issue still exist,we show this mechanism by a concrete example.Moreover,we proved in general the chiral magnetic current would vanish in the limit with zero energy taken first for a external magnetic field with zero energy and small special momentum.For the opposite limit with zero special momentum taken first,the nonvanishing chiral magnetic current was a consequence of the nonrenormalizability of chiral anomaly for an arbitrary external magnetic field.