  We study the frequency-dependent structure of electronic self-energy in the
pseudogap and superconducting states of the two-dimensional Hubbard model. We
present the self-energy calculated with the cellular dynamical mean-field
theory systematically in the space of temperature, electron density, and
interaction strength. We show that the low-frequency part of the self-energy is
well represented by a simple equation, which describes the transitions of an
electron to and from a hidden fermionic state. By fitting the numerical data
with this simple equation, we determine the parameters characterizing the
hidden fermion and discuss its identity. The simple expression of the
self-energy offers a way to organize numerical data of this uncomprehended
superconducting and pseudogap states, as well as a useful tool to analyze
spectroscopic experimental results. The successful description by the simple
two-component fermion model supports the idea of "dark" and "bright" fermions
emerging from a bare electron as bistable excitations in doped Mott insulators.
