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Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence

We calculate the order λ, λ^2 and λy^2 terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where λand y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixing between operators for which no direct one-particle-irreducible diagram exists, due to operator replacements by the equations of motion.