Kaon CP violation and neutron EDM in the minimal left-right symmetric model

Within the minimal Left-Right (LR) symmetric model we revisit the predictions for the kaon CP violating observables $\varepsilon$ and $\varepsilon'$ in correlation with the neutron electric dipole moment. We perform a complete study of the cross constraints on the model parameters, phases and the $M_{W_R}$ scale, considering the two cases of extended parity or charge conjugation as LR discrete symmetries, together with the possible presence of a Peccei-Quinn symmetry. We discuss in particular two scenarios: whether the Standard Model saturates the experimental value of $\varepsilon'/\varepsilon$ or whether new physics is needed, still an open issue after the recent lattice results on the QCD penguin matrix elements. Within the first scenario, we find no constraints on the LR scale in the charge-conjugation case while in the parity case we show that $M_{W_R}$ can be as low as 13 TeV. On the other side, the request that new physics contributes dominantly to $\varepsilon'$ implies strong correlations among the model parameters, with an upper bound of $M_{W_R}< 8-100$ TeV depending on $\tan\beta$ in the case of charge conjugation and a range of $M_{W_R}\simeq 7-45$ TeV in the parity setup. Both scenarios may be probed directly at future colliders and only indirectly at the LHC.