Higgs windows to new physics through d=6 operators: constraints and one-loop anomalous dimensions

The leading contributions from heavy new physics to Higgs processes can be captured in a model-independent way by dimension-six operators in an effective Lagrangian approach. We present a complete analysis of how these contributions affect Higgs couplings. Under certain well-motivated assumptions, we find that 8 CP-even plus 3 CP-odd Wilson coefficients parametrize the main impact in Higgs physics, as all other coefficients are constrained by non-Higgs SM measurements. We calculate the most relevant anomalous dimensions for these Wilson coefficients, which describe operator mixing from the heavy scale down to the electroweak scale. This allows us to find the leading-log corrections to the predictions for the Higgs couplings in specific models, such as the MSSM or composite Higgs, which we find to be significant in certain cases.