Strong P invariance, neutron electric dipole moment, and minimal left-right parity at LHC

In the minimal left-right model the choice of left-right symmetry is twofold: either generalized parity P or charge conjugation C. In the minimal model with spontaneously broken strict 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 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-WR greater than or similar to 3 TeV. On the other hand, C symmetry is free from such constraints, leaving the right-handed scale within the experimental reach.