Derivation of a Semi-Empirical Relation Between the Electron Mass, Proton Mass, and the Fine-Structure Constant

Essay in the subject Physics - Other, , language: English, abstract: The origin of fermion mass hierarchies remains one of the unresolved problems in fundamental physics. While the Standard Model successfully parameterizes particle masses through Yukawa couplings, it does not predict their numerical values. In this work, we present a semi-empirical relation connecting the electron rest mass to the proton mass and the fine-structure constant . The proposed relation involves a leading scaling with a small corrective term proportional to . Using CODATA 2022 recommended values, the expression reproduces the experimentally measured electron mass within relative deviation of order . The relation is not derived from first principles but is motivated by known mass-ratio regularities involving powers of . Possible interpretations, limitations, and directions for theoretical justification are discussed.