  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.
