  We formulate a generalization of Higgs effective field theory (HEFT)
including arbitrary number of extra neutral and charged Higgs bosons
(generalized HEFT, GHEFT) to describe non-minimal electroweak symmetry breaking
models. Using the geometrical form of the GHEFT Lagrangian, which can be
regarded as a nonlinear sigma model on a scalar manifold, it is shown that the
scalar boson scattering amplitudes are described in terms of the Riemann
curvature tensor (geometry) of the scalar manifold and the covariant
derivatives of the potential. The coefficients of the one-loop divergent terms
in the oblique correction parameters S and U can also be written in terms of
the Killing vectors (symmetry) and the Riemann curvature tensor (geometry). It
is found that perturbative unitarity of the scattering amplitudes involving the
Higgs bosons and the longitudinal gauge bosons demands the flatness of the
scalar manifold. The relationship between the finiteness of the electroweak
oblique corrections and perturbative unitarity of the scattering amplitudes is
also clarified in this language: we verify that once the tree-level unitarity
is ensured, then the one-loop finiteness of the oblique correction parameters S
and U is automatically guaranteed.
