The protophobic $X$-boson coupled to quantum electrodynamics

Abstract

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.