Fifth Force and Hyperfine Splitting in Muonic Atoms

The potential existence of a fifth fundamental force, mediated by the X17 boson, has generated significant interest. This force can manifest itself as either a vector or pseudoscalar particle. In order to gain insight into the effective potentials produced by the X17 boson for hyperfine interactions in muonic systems, we conduct calculations for both the pseudoscalar and vector hypotheses. Our study reveals that, for muonic atoms with nuclear charge numbers ranging from 10 to 15, the energy shift associated with the fifth force can be as high as 0.61 eV. These effects have the potential to be detected through the utilization of high-precision X-ray detectors that are used to analyze the energy spectrum of muonic characteristic X-rays.