Reflecting on chirality: CP-violating extensions of the single scalar-leptoquark solutions for the $(g-2)_{e,\mu}$ puzzles and their implications for lepton EDMs

We study the two scalar leptoquarks capable of generating chirally-enhanced, sign-dependent contributions to lepton magnetic dipole moments (MDMs) and electric dipole moments (EDMs), $R_2\sim (\mathbf{3}, \mathbf{2}, 7/6)$ and $S_1\sim (\mathbf{3}, \mathbf{1}, -1/3)$. We consider the case in which the electron and muon sectors are decoupled, and leptoquark couplings are assigned complex values. Adopting the coupling ansatz that the electron dipole operator is generated by charm-containing loops, and muon dipole operator by top-containing loops, we find that both minimal leptoquark models remain viable solutions for reconciling anomalies in the muon and electron MDMs, accounting for either of the two current (disparate) electron MDM results from Cs and Rb interferometry experiments. We also examine the correlated corrections to the muon and electron masses generated by these models, and argue that to minimise fine-tuning this introduces an upper bound on viable leptoquark ($\phi$) masses, $m_{\phi}<\mathcal{O}(4)$ TeV. Similar arguments allow us to make a prediction for the upper bound of the muon EDM generated by these models, $|d_\mu|< \mathcal{O}(10^{-22})\; e$ cm, which could be within reach of upcoming experimental programs, including Muon g$-$2 at Fermilab (FNAL), and muEDM at Paul Scherrer Institute (PSI).