T-violation in flavour oscillations as a test for relativity principles at a neutrino factory

We study the effects of violation of the equivalence principle (VEP) or violation of Lorentz invariance (LIV) in the neutrino sector on the asymmetry between T-conjugate oscillation probabilities, $Delta P_T equiv P( u_{alpha} to u_{beta}) - P( u_{beta} to u_{alpha})$, in a three-flavour framework. We find that additional mixing due to these mechanisms, while obeying all present bounds, can lead to an observable enhancement, suppression, and/or sign change in $Delta P_T$ for the preferred energies and baselines of a neutrino factory. The measurement of this asymmetry can be used to establish a new upper limit of order $10^{-26}$ on VEP or LIV in the $( u_e, u_mu)$ and $( u_e, u_tau)$ sectors.