  The possible origin of an $X$-boson having a mass value around $17 \,
\mbox{MeV}$ had motivated us to investigate its interaction with leptons of
QED. This new hypothetical particle can possibly be a candidate to describe the
so called fifth interaction, in a new physics scenario beyond the Standard
Model. The model of the $X$-boson interacting with QED is based on a $U(1)
\times U'(1)$ symmetry, where the group $U'(1)$ is attached to the $X$-boson,
with a kinetic mixing with the photon. The Higgs sector was revisited to
generate the mass for the new boson. Thus, the mass of $17 \, \mbox{MeV}$ fixes
a vacuum expected value scale. Thereby, we could estimate the mass of the
hidden Higgs field through both the VEV-scale and the Higgs' couplings. A model
of QFT was constructed in a renormalizable gauge, and we analyzed its
perturbative structure. After that, the radiative correction of the $X$-boson
propagator has been calculated at one loop approximation to yield the Yukawa
potential correction. The form factors associated with the QED-vertex
correction were calculated to confirm electron's anomalous magnetic moment
together with the computation of the interaction magnitude. The muon case was
discussed. Furthermore, we have introduced a renormalization group scheme to
explore the current $X$-boson mass and its coupling constant with the leptons
of the Standard Model.
