Right-Handed Neutrinos and T-Violating, P-Conserving Interactions

We show that experimental probes of the P-conserving, T-violating triple correlation in polarized neutron or nuclear $\beta$-decay provide a unique probe of possible T-violation at the TeV scale in the presence of right-handed neutrinos. In contrast to other possible sources of semileptonic T-violation involving only left-handed neutrinos, those involving right-handed neutrinos are relatively unconstrained by present limits on the permanent electric dipole moments of the electron, neutral atoms, and the neutron. On the other hand, LHC results for $pp\to e+$ missing transverse energy imply that an order of magnitude of improvement in $D$-coefficient sensitivity would be needed for discovery. Finally, we discuss the interplay with the scale of neutrino mass and naturalness considerations.