Charge-Sign-Dependent Dark Gauge Coupling: A C-Violating Extension of the Dark Photon Framework

We propose an extension of the dark photon framework in which the hidden U (1) D gauge boson couples to matter and antimatter with different strengths. The model introduces a C-violating split where the C-symmetric coupling (epsilonₛ) and C-antisymmetric coupling (epsilonₐ) allow charge-sign-dependent interaction. This framework preserves CPT symmetry while introducing C-violation in the dark sector. We derive two quantitative constraints from existing data: |epsilonₛ times epsilonₐ| < 1. 85e-9 (95% CL) from Van Dyck et al. 1987 electron/positron g-2, and |epsilonₛ times epsilonₐ| < 7e-13 (95% CL, dark photon mass below 4 keV) from the 2025 ALPHA 1S-2S antihydrogen measurement (Baker et al. , Nat. Phys. 21, 201-207). The model predicts null results in positronium, consistent with J-PET, and makes testable predictions for CERN ALPHA-3.