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 TeV is set. Possible ways out of this bound require a further hypothesis, either a relaxation mechanism or explicit breaking of $\mathcal{P}$. To this end, the chiral loop of the neutron electric dipole moment at next-to-leading order is recomputed and provides an estimate of the weak contribution. Combining this constraint with other $CP$-violating observables in the kaon sector allows for $M_{W_R}\gtrsim 3\mathrm{TeV}$. On the other hand, $\mathcal{C}$ symmetry is free from such constraints, leaving the right-handed scale within the experimental reach.

• Received 24 July 2014

DOI:https://doi.org/10.1103/PhysRevD.90.095002