StrongPinvariance, neutron electric dipole moment, and minimal left-right parity at LHC

Abstract

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 $\ensuremath{\alpha}$. Searches for the neutron electric dipole moments then constrain the size of $\ensuremath{\alpha}$. 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 ${M}_{{W}_{R}}\ensuremath{\gtrsim}3\text{ }\text{ }\mathrm{TeV}$. On the other hand, $\mathcal{C}$ symmetry is free from such constraints, leaving the right-handed scale within the experimental reach.