We explore the potential of several Neutrino Factory (NF) setups to constrain, discover and measure new physics effects due to Non-Standard Interactions (NSI) in propagation through Earth matter. We first study the impact of NSI in the measurement of
$theta_{13}$: we find that these could be large due to strong correlations of $theta_{13}$ with NSI parameters in the golden channel, and the inclusion of a detector at the magic baseline is crucial in order to reduce them as much as possible. We present, then, the sensitivity of the considered NF setups to the NSI parameters, paying special attention to correlations arising between them and the standard oscillation parameters, when all NSI parameters are introduced at once. Off-diagonal NSI parameters could be tested down to the level of $10^{-3}$, whereas the diagonal combinations $(epsilon_{ee} - epsilon_{tautau})$ and $(epsilon_{mumu}-epsilon_{tautau})$ can be tested down to $10^{-1}$ and $10^{-2}$, respectively. The possibilities of observing CP violation in this context are also explored, by presenting a first scan of the CP discovery potential of the NF setups to the phases $phi_{emu}, phi_{etau}$ and $delta$. We study separately the case where CP violation comes only from non-standard sources, and the case where it is entangled with the standard source, $delta$. In case $delta$ turns out to be CP conserving, the interesting possibility of observing CP violation for reasonably small values of the NSI parameters emerges.
We study the potential of the CNGS beam in constraining the parameter space of a model with one sterile neutrino separated from three active ones by an $mathcal{O}(eVq)$ mass-squared difference, $Dmq_Sbl$. We perform our analysis using the OPERA dete
ctor as a reference (our analysis can be upgraded including a detailed simulation of the ICARUS detector). We point out that the channel with the largest potential to constrain the sterile neutrino parameter space at the CNGS beam is $ u_mu to u_tau$. The reason for that is twofold: first, the active-sterile mixing angle that governs this oscillation is the less constrained by present experiments; second, this is the signal for which both OPERA and ICARUS have been designed, and thus benefits from an extremely low background. In our analysis we also took into account $ u_mu to u_e$ oscillations. We find that the CNGS potential to look for sterile neutrinos is limited with nominal intensity of the beam, but it is significantly enhanced with a factor 2 to 10 increase in the neutrino flux. Data from both channels allow us, in this case, to constrain further the four-neutrino model parameter space. Our results hold for any value of $Dmq_Sbl gtrsim 0.1 eVq$, textit{i.e.} when oscillations driven by this mass-squared difference are averaged. We have also checked that the bound on $theta_{13}$ that can be put at the CNGS is not affected by the possible existence of sterile neutrinos.
