- Article
We investigate dark photon emission from the final state leptons in the rare decay
within a point-like description of the parent transition. The physical electron mass and exact three-body kinematics are retained throughout the complete phase space for each dark photon mass in the interval
. By normalizing the radiative width to the corresponding non-radiative width, we obtain dimensionless radiation factors that are independent of the unknown normalization of the effective amplitude. This formulation allows the mass dependence, polarization content, and spectral shape to be studied without fixing the poorly constrained kinetic mixing parameter. A covariant decomposition separates the transverse and longitudinal dark photon contributions, while normalized dilepton invariant mass spectra describe the event kinematics. Across the scanned mass interval, the mixing-independent pseudoscalar radiation factor decreases by more than nine orders of magnitude and approaches zero at the kinematic endpoint. The transverse modes dominate throughout the scanned interval, while the longitudinal fraction remains approximately to . The normalized dilepton invariant mass spectrum shifts toward lower masses as increases. After normalization, the scalar and pseudoscalar radiation factors differ only through finite electron mass effects. These results provide a quantitative polarization-resolved benchmark for the point-like lepton final-state radiation component and can serve as baseline input for more complete phenomenological studies of rare charm decays.
Particles
19 September 2026




