RI′/SMOM scheme amplitudes for quark currents at two loops

We determine the two loop corrections to the Green’s function of a quark current inserted in a quark 2-point function at the symmetric subtraction point. The amplitudes for the scalar, vector and tensor currents are presented in both the and RI′/SMOM renormalization schemes. The RI′/SMOM scheme two loop renormalization for the scalar and tensor cases agree with previous work. The vector current renormalization requires special treatment as it must be consistent with the Slavnov–Taylor identity which we demonstrate. We also discuss the possibility of an alternative definition of the RI′/SMOM scheme in the case of the tensor current.