Five loop anomalous dimension of non-singlet quark currents in the RI ^' scheme

We construct the five loop anomalous dimensions of the basic fields in Quantum Chromodynamics in a linear covariant gauge in the modified Regularization Invariant ( RI^' ) scheme. Using these core results we also compute the four loop Green’s function where the quark mass operator and vector current are separately inserted in a quark 2-point function. These are necessary for measurements of the same quantities on the lattice. The Green’s functions are provided in both the modified Minimal Subtraction ( MS ) and RI^' schemes. All the results are available for a general Lie group.