The possible origin of an (X)-boson having a mass value around 17 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 simplest (X)-boson model unified to the Standard Model is based on an (\mathrm {SU}{c}(3) \times \mathrm {SU}{L}(2) \times \mathrm {U}{Y}(1) \times \mathrm {U}(1){B-L}) symmetry, where the group (\mathrm {U}(1){B-L}) is attached to the (X)-boson, with a kinetic mixing with the gauge field of (\mathrm {U}{Y}(1)). The Higgs sector was revisited to generate the mass for the new boson. Thus, the mass of 17 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 (R_{\xi })-gauge, and we analyze 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 the 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 running (X)-boson mass and its coupling constant with the leptons of the Standard Model.