  Beyond standard model (BSM) particles should be included in effective field
theory in order to compute the scattering amplitudes involving these extra
particles. We formulate an extension of Higgs effective field theory which
contains arbitrary number of scalar and fermion fields with arbitrary electric
and chromoelectric charges. The BSM Higgs sector is described by using the
non-linear sigma model in a manner consistent with the spontaneous electroweak
symmetry breaking. The chiral order counting rule is arranged consistently with
the loop expansion. The leading order Lagrangian is organized in accord with
the chiral order counting rule. We use a geometrical language to describe the
particle interactions. The parametrization redundancy in the effective
Lagrangian is resolved by describing the on-shell scattering amplitudes only
with the covariant quantities in the scalar/fermion field space. We introduce a
useful coordinate (normal coordinate), which simplifies the computations of the
on-shell amplitudes significantly. We show the high energy behaviors of the
scattering amplitudes determine the "curvature tensors" in the scalar/fermion
field space. The massive spinor-wavefunction formalism is shown to be useful in
the computations of on-shell helicity amplitudes.
