Solving the octant degeneracy with the Silver channel

We study the potential of the combination of the golden ($\nu_e \to \nu_\mu$) and silver ($\nu_e \to \nu_\tau$) channels to solve the octant degeneracy affecting the measurement of $\theta_{13}$ and $\delta$ at future neutrino factories. To search for $\tau$ leptons produced in $\nu_\tau$ charged-current interactions, we consider two different detectors: the Emulsion Cloud Chamber detector (ECC) and the Liquid Argon Time Projection Chamber (LAr TPC). We show that, when using similar detector masses, the upgraded version of the ECC detector (sensitive also to hadronic $\tau$ decay modes) and the LAr TPC detector have comparable sensitivities to the octant of $\theta_{23}$, being able to discriminate the two solutions for $\sin^2 (2\theta_{13}) \gtrsim 10^{-3}$ at 3$\sigma$ level if $\theta_{23}=40^\circ$. We also show that the same setups are able to see deviation from maximal mixing as small as $\sim$ (4-6)% (at 3$\sigma$) if $\theta_{13}$ is close to its upper bound.