Renormalization group evolution of the Standard Model dimension six operators II: Yukawa dependence

We calculate the complete order y 2 and y 4 terms of the 59 × 59 one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory, where y is a generic Yukawa coupling. These terms, together with the terms of order λ, λ 2 and λy 2 depending on the Standard Model Higgs self-coupling λ which were calculated in a previous work, yield the complete one-loop anomalous dimension matrix in the limit of vanishing gauge couplings. The Yukawa contributions result in non-trivial flavor mixing in the various operator sectors of the Standard Model effective theory.