Sterile neutrinos at the CNGS

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 detector 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.