Renormalization group evolution of the standard model dimension six operators. I: formalism and λ dependence

We calculate the order lambda, lambda(2) and lambda y(2) terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where lambda and 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.