Anomalous Scaling Under the Influence of Helicity and Finite-Time Correlations in the Kazantsev-Kraichnan Model of Fully Developed Kinematic Magnetohydrodynamic Turbulence

The influence of the spatial parity violation (helicity) of a conductive turbulent environment on the anomalous scaling of the weak magnetic field in the Kazantsev-Kraichnan model with finite-time correlations of the velocity field and in the presence of a large-scale anisotropy is investigated using the field theoretic renormalization group approach together with the operator product expansion in the second-order (two-loop) approximation of the corresponding perturbation theory. The relevant leading composite operators that drive the anomalous scaling of the correlation functions are analyzed. The two-loop expressions for the anomalous dimensions of the leading composite operators are found as functions of the parameter that control the amount of the helicity in the studied turbulent system. The combined effects of the helicity and finite-time correlations of the velocity field on the anomalous scaling and critical dimensions of the leading composite operators are discussed.