  The complete effective chiral Lagrangian for a dynamical Higgs is presented
and constrained by means of a global analysis including electroweak precision
data together with Higgs and triple gauge boson coupling data from the LHC
Run~I. The operators' basis up to next-to-leading order in the expansion
consists of 148 (188 considering right-handed neutrinos) flavour universal
terms and it is presented here making explicit the custodial nature of the
operators. This effective Lagrangian provides the most general description of
the physical Higgs couplings once the electroweak symmetry is assumed, and it
allows for deviations from the $SU(2)_L$ doublet nature of the Standard Model
Higgs. The comparison with the effective linear Lagrangian constructed with an
exact $SU(2)_L$ doublet Higgs and considering operators with at most canonical
dimension six is presented. A promising strategy to disentangle the two
descriptions consists in analysing i) anomalous signals present only in the
chiral Lagrangian and not expected in the linear one, that are potentially
relevant for LHC searches, and ii) decorrelation effects between observables
that are predicted to be correlated in the linear case and not in the chiral
one. The global analysis presented here, that includes several kinematic
distributions, is crucial for reducing the allowed parameter space and for
controlling the correlations between parameters. This improves previous studies
aimed at investigating the Higgs Nature and the origin of the electroweak
symmetry breaking.
