  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.
