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We calculate the gauge terms of the one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory (SM EFT). Combining these results with our previous results for the λ and Yukawa coupling terms completes the calculation of the one-loop anomalous dimension matrix for the dimension-six operators. There are 1350 CP -even and 1149 CP -odd parameters in the dimension-six Lagrangian for 3 generations, and our results give the entire 2499 × 2499 anomalous dimension matrix. We discuss how the renormalization of the dimension-six operators, and the additional renormalization of the dimension d ≤ 4 terms of the SM Lagrangian due to dimension-six operators, lays the groundwork for future precision studies of the SM EFT aimed at constraining the effects of new physics through precision measurements at the electroweak scale. As some sample applications, we discuss some aspects of the full RGE improved result for essential processes such as gg → h, h → γγ and h → Zγ, for Higgs couplings to fermions, for the precision electroweak parameters S and T , and for the operators that modify important processes in precision electroweak phenomenology, such as the three-body Higgs boson decay h → Z ℓ + ℓ − and triple gauge boson couplings. We discuss how the renormalization group improved results can be used to study the flavor problem in the SM EFT, and to test the minimal flavor violation (MFV) hypothesis. We briefly discuss the renormalization effects on the dipole coefficient C eγ which contributes to µ → eγ and to the muon and electron magnetic and electric dipole moments.

Abstract: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.

We calculate the order λ, λ 2 and λy 2 terms of the 59 × 59 one-loop anomalous dimension matrix of dimension-six operators, where λ 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.

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