Strong P invariance, neutron EDM and minimal Left-Right parity at LHC

In the minimal Left-Right model the choice of left-right symmetry is twofold: either generalized parity $\mathcal P$ or charge conjugation $\mathcal C$. In the minimal model with spontaneously broken strict $\mathcal P$, a large tree-level contribution to strong CP violation can be computed in terms of the spontaneous phase $\alpha$. Searches for the neutron electric dipole moments then constrain the size of $\alpha$. Following the latest update on indirect CP violation in the kaon sector, a bound on $W_R$ mass at $20 \text{TeV}$ is set. Possible ways out of this bound, either by an additional relaxation mechanism or explicit breaking of $\mathcal P$ are considered. To this end, the chiral loop of the neutron electric dipole moment at next-to-leading order is re-computed and provides an estimate of the weak contribution. Combining this constraint with other CP violating observables in the kaon sector allows for $M_{W_R} \gtrsim 3 \text{TeV}$. On the other hand, $\mathcal C$-symmetry is free from such constraints, leaving the right-handed scale within the experimental reach.
Comment: 9 pages, 3 figures, two-columns. Added references and an additional discussion on UV counter-terms, matches the version accepted by PRD