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 one-loop divergences 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.
This talk is based on arXiv:1904.07618.