  We investigate the properties of attractive polaron formed by a single
impurity dressed with the particle-hole excitations in a three-dimensional (3D)
doped (extrinsic) parabolic system. %at zero-temperature limit. Base on the
single particle-hole variational ansatz, we study the pair propagator,
self-energy, and the non-self-consistent medium $T$-matrix. The
non-self-consistent $T$-matrix discussed in this paper contains only the open
channel since we don't consider the shift of center-of-mass due to the
resonance (e.g., induced by the magnetic field). Besides, since we focus on the
low-density regime of the majority particles, the effective Fermi wave vector
is small. The scattering form factor is discussed in detail for the chiral case
and compared to the non-chiral one. The effects of the bare coupling strength,
which is momentum-cutoff-dependent, are also discussed. %within the pair
propagator due to the scattering %with a certain scattering angle. We found
that the pair propagator and the related quantities, like the self-energy,
spectral function, induced effective mass, and residue (spectral weight), all
exhibit different features in the low-momentum regime and the high one, which
also related to the polaronic instabilities as well as the many-body
fluctuation and nonadiabatic/adiabatic dynamics. The pair-propagator and the
energy relaxation time at finite temperature are also explored.
