  We provide a detailed investigation of single-photon production processes in
$e^+e^-$ collisions with missing momenta carried by neutrinos or neutralinos.
The transition amplitudes for both processes can be organized into a generic
simplified, factorized form; each neutral V$\pm$A vector current of missing
energy carriers is factorized out and all the characteristics of the reaction
is solely included in the electron vector current. Firstly, we apply the
generic form to give a unified description of a single-photon production with a
Dirac-type or Majorana-type neutrino-pair and to confirm their identical
characteristics as suggested by the so-called Practical Dirac-Majorana
Confusion Theorem. Secondly, we show that the generic amplitude form is
maintained with the anomalous P- and C-invariant WW$\gamma$ couplings in the
neutrino-associated process and it enables us to easily understand large
contributions of the anomalous WW$\gamma$ couplings at higher energies and, in
particular, at the points away from the Z-resonance peak. Finally, the
neutralino-associated process, which receives modifications in both the
left-handed and right-handed electron currents due to the exchanges of the
left-handed and right-handed selectrons, can be differentiated from the
neutrino-associated ones through the left-right asymmetries and/or the circular
polarization of the outgoing photon.
