  Probing the properties of the discovered Higgs boson may tell us whether or
not it is the same particle as the one predicted by the Standard Model. To this
aim we parametrize deviations of the Higgs couplings to matter from the
Standard Model by using the Higgs Effective Field Theory framework. Starting
with a general dimension-6 effective Lagrangian including both CP-even and
CP-odd operators, and requiring that the operators do not introduce power
divergences in the oblique parameters, we reduce the number of independent
effective couplings of the theory. This framework is then used to put updated
constraints on the effective couplings, using the latest Higgs rates data from
the Run-I of the ATLAS and CMS experiments, and electroweak precision data from
LEP, SLC and Tevatron. We show that the current data is able to significantly
constrain the CP-even and some CP-odd operators of the effective Lagrangian.
