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Note on Anomalous Higgs-Boson Couplings in Effective Field Theory

We propose a parametrization of anomalous Higgs-boson couplings that is both systematic and practical. It is based on the electroweak chiral Lagrangian, including a light Higgs boson, as the effective field theory (EFT) at the electroweak scale $v$. This is the appropriate framework for the case of sizeable deviations in the Higgs couplings of order $10\%$ from the Standard Model, considered to be parametrically larger than new-physics effects in the sector of electroweak gauge interactions. The role of power counting in identifying the relevant parameters is emphasized. The three relevant scales, $v$, the scale of new Higgs dynamics $f$, and the cut-off $Λ=4πf$, admit expansions in $ξ=v^2/f^2$ and $f^2/Λ^2$. The former corresponds to an organization of operators by their canonical dimension, the latter by their loop order or chiral dimension. In full generality the EFT is thus organized as a double expansion. However, as long as $ξ\gg 1/16π^2$ the EFT systematics is closer to the chiral counting. The leading effects in the consistent approximation provided by the EFT, relevant for the presently most important processes of Higgs production and decay, are given by a few (typically six) couplings. These parameters allow us to describe the properties of the Higgs boson in a general and systematic way, and with a precision adequate for the measurements to be performed at the LHC. The framework can be systematically extended to include loop corrections and higher-order terms in the EFT.