Implications for Electric Dipole Moments of a Leptoquark Scenario for the $B$-Physics Anomalies

Vector leptoquarks can address the lepton flavor universality anomalies in decays associated with the $b\to c\mathrm{\ell }\nu$ and $b\to s\mathrm{\ell }\mathrm{\ell }$ transitions, as observed in recent years. Generically, these leptoquarks yield new sources of CP violation. In this paper, we explore constraints and discovery potential for electric dipole moments (EDMs) in leptonic and hadronic systems. We provide the most generic expressions for dipole moments induced by vector leptoquarks at one loop. We find that $O(1)$ CP-violating phases in tau and muon couplings can lead to corresponding EDMs within reach of next-generation EDM experiments, and that existing bounds on the electron EDM already put stringent constraints on CP-violating electron couplings.