# The protophobic $X$-boson coupled to quantum electrodynamics

## TL;DR

This paper investigates a hypothetical 17 MeV X-boson interacting with leptons via a U(1) x U'(1) symmetry, analyzing its theoretical properties, radiative corrections, and potential implications for physics beyond the Standard Model.

## Contribution

It introduces a renormalizable QFT model for the X-boson with kinetic mixing, calculates radiative corrections, and explores its phenomenological implications.

## Key findings

- Calculated the X-boson propagator correction at one loop.
- Confirmed the X-boson's effect on electron's anomalous magnetic moment.
- Explored the X-boson mass and coupling via renormalization group analysis.

## 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.