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Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology

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abstract

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 $\lambda$ 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 $2499 \times 2499$ anomalous dimension matrix. We discuss how the renormalization of the dimension-six operators, and the additional renormalization of the dimension $d \le 4$ 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 $gg \to h$, $h \to \gamma \gamma$ and $h \to Z \gamma$, 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 $h \rightarrow Z \, \ell^+ \, \ell^-$ 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 $C_{e\gamma}$ which contributes to $\mu \to e \gamma$ and to the muon and electron magnetic and electric dipole moments.

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Exploring the SMEFT landscape: Bayesian Model Selection for indirect discovery

hep-ph · 2026-05-20 · unverdicted · novelty 7.0

Bayesian model selection over SMEFT operator subsets using a genetic algorithm and BIC approximation is applied to electroweak, Higgs, top and diboson data, finding no evidence for new physics and improved Wilson coefficient posteriors compared to global fits.

When Two Loops Matter: Electroweak Precision in the SMEFT

hep-ph · 2026-04-29 · unverdicted · novelty 7.0

A modification to the top-Higgs Yukawa coupling in SMEFT induces a two-loop shift in the W mass through a large anomalous dimension, providing a new indirect probe via electroweak precision observables.

The effect of the two-loop SMEFT RGEs at future colliders

hep-ph · 2026-04-17 · conditional · novelty 7.0

Two-loop SMEFT RGEs induce non-negligible effects on the evolution of Wilson coefficients, leading to percent-level shifts in projected sensitivities for four-quark, top Yukawa, and Higgs-gluon operators in collider fits.

The KSVZ Atlas: A Unified SMEFT-ALP Framework

hep-ph · 2026-06-10 · unverdicted · novelty 6.0

A matching framework from arbitrary KSVZ UV completions to SMEFT and ALP EFT yields robust operator bounds from global fits that often dominate direct ALP searches except when mass mixing occurs.

Revisiting $\mu$-$e$ conversion in $R$-parity violating SUSY

hep-ph · 2026-01-26 · unverdicted · novelty 4.0

RG running changes limits on certain RPV SUSY λ and λ' couplings by up to 80 percent, with upcoming μ-e conversion experiments expected to set stronger bounds than μ→eγ or μ→eee decays.

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