Proton driver optimization for new generation neutrino superbeams to search for sub-leading numu->nue oscillations ($\theta_{13}$ angle)

We perform a systematic study of particle production and neutrino yields for different incident proton energies $E_p$ and baselines $L$, with the aim of optimizing the parameters of a neutrino beam for the investigation of $\theta_{13}$-driven neutrino oscillations in the $\Delta m^2$ range allowed by Superkamiokande results. We study the neutrino energy spectra in the ``relevant'' region of the first maximum of the oscillation at a given baseline $L$. We find that to each baseline $L$ corresponds an ``optimal'' proton energy $E_p$ which minimizes the required integrated proton intensity needed to observe a fixed number of oscillated events. In addition, we find that the neutrino event rate in the relevant region scales approximately linearly with the proton energy. Hence, baselines $L$ and proton energies $E_p$ can be adjusted and the performance for neutrino oscillation searches will remain approximately unchanged provided that the product of the proton energy times the number of protons on target remains constant. We apply these ideas to the specific cases of 2.2, 4.4, 20, 50 and 400 GeV protons. We simulate focusing systems that are designed to best capture the secondary pions of the ``optimal'' energy. We compute the expected sensitivities to $\sin^22\theta_{13}$ for the various configurations by assuming the existence of new generation accelerators able to deliver integrated proton intensities on target times the proton energy of the order of ${\cal O}(5\times 10^{23})\rm\ GeV\times\rm pot/year$.