手征效应是QCD重要的非微扰效应之一，QGP是研究这种效应的理想介质。在非对心的核核碰撞中产生的强磁场和涡旋场会在QGP中的轴矢量流反常区域内诱导出宏观的流（包括电流、重子数流和手征流），我们称之为手征磁效应（CME）和手征涡旋效应（CVE）。现有文献中，格点和平均场方法的结果与经典结果有偏差，暗示CME可能存在高阶修正，但我们认为CME是一个不可重整的理论，不应该有高阶修正，本项目将用双圈费曼图检验这一矛盾，并与格点和平均场结果对比；Coleman-Hill在讨论手征效应的高阶修正中有重要的作用，但该定理是否能推广用于计算非矢量流-流关联还有待检验，本项目中我们先从具体例子CVE出发，然后尝试给出一个一般性的推广Coleman-Hill定理的方法，用来讨论更多的手征系数。讨论手征效应的高阶修正有助于人们进一步认识手征理论的结构，增加该理论的可靠性，并对实验上寻找手征信

Chiral effect is one of the important non-pertubative effects of QCD. QGP is an ideal medium to study such effcts. Strong magnetic field and/or vortical field produced in non-central nuclear-nuclear collision will induce macroscopic currents(including electric current, baryon current and chiral current) in the spots of QGP where there exists axial anomaly. In recent publications, results from Lattice QCD and mean-field approximation implied that the CME coefficient contrains higher-order corrections。 However, we think that the CME theory is non-renormalized with vanishing higher-order contribution. This project wil address this contradictory by computing two-loop Feymann diagrams in a real model and comparing the result with Lattice and mean field calculation. Coleman-Hill theorem plays an important role in discussing higher-order chiral effects. While whether it can be generalized to discuss non vector current-current correlation remains verification. We start from calculating higher-order CVE coefficient, then try to extend the Colemann-Hill theorem in a general way to discuss other chiral coefficients.The study on higher order corrections of chiral effect will help us to get deeper insight into the theoretic structures of CME and CVE, improve the reliability of such theory and play some positive significance on finding chiral signals in the experiment.