  We introduce a new class of higgs type complex-valued scalar fields $U$ with
Feynman propagator $\sim 1/p^4$ and consider the matching to the traditional
fields with propagator $\sim 1/p^2$ in the viewpoint of effective potentials at
tree level. With some particular postulations on the convergence and the
causality, there are a wealth of potential forms generated by the fields $U$,
such as the linear, logarithmic, and Coulomb potentials, which might serve as
sources of effects such as the confinement, dark energy, dark matter,
electromagnetism and gravitation. Moreover, in some limit cases, we get some
deductions, such as: a nonlinear Klein-Gordon equation, a linear QED, a mass
spectrum with generation structure and a seesaw mechanism on gauge symmetry and
flavor symmetry; and, the propagator $\sim 1/p^4$ would provide a possible way
to construct a renormalizable gravitation theory and to solve the
non-perturbative problems.
