  Deviations from the standard Higgs sector generated by some new (nonstandard)
physics at an energy scale \Lambda could be described by an effective SU(3)_c x
SU(2)_L x U(1) invariant non-renormalizable Lagrangian terms of dimension six.
The set of dimension-six operators involving the Higgs field is chosen in such
a way that the form of gauge bosons kinetic terms remains untouched, preserving
all high-precision electroweak constraints. A systematic study of effects in
various Higgs boson production channels (\gamma \gamma, ZZ, WW, bb-bar, \tau
\tau-bar) caused by effecive operators is carried out beyond the {production x
decay} approximation (or infinitely small width approximation). Statistical
methods are used to establish consistency of the standard Higgs sector with the
available LHC data. A global fit in the two-parametric anomalous coupling space
indicating to possible deviations from the standard Higgs-fermion and
Higgs-gauge boson couplings is performed, using post-Moriond 2012 data and more
precise LC 2013 data. We find that the standard Higgs sector is consistent with
the current CMS and ATLAS experimental results both in the infinitely small
width approximantion and the calculation with complete gauge invariant sets of
diagrams. However, visible difference of the exclusion contours is found for
some combinations of production and decay channels, although minor for the
global fits for all possible channels. Updates of the signal strength and the
signal strength error reported at LC 2013 result in a significant improvements
of the allowed regions in the anomalous coupling space, which are recalculated
also at complete tree level.
