Muon Beam for Neutrino CP Violation: connecting energy and neutrino frontiers

We propose here a proposal to connect neutrino and energy frontiers, by exploiting collimated muon beams for neutrino oscillations, which generate symmetric neutrino and antineutrino sources: $\mu^+\rightarrow e^+\,\bar{\nu}_{\mu}\, \nu_{e}$ and $\mu^-\rightarrow e^-\, \nu_{\mu} \,\bar{\nu}_{e}$. Interfacing with long baseline neutrino detectors such as DUNE and T2K, this experiment can be applicable to measure tau neutrino properties, and also to probe neutrino CP phase, by measuring muon electron (anti-)neutrino mixing or tau (anti-)neutrino appearance, and differences between neutrino and antineutrino rates. There are several significant benefits leading to large neutrino flux and high sensitivity on CP phase, including 1) collimated and manipulable muon beams, which lead to a larger acceptance of neutrino sources in the far detector side; 2) symmetric $\mu^+$ and $\mu^-$ beams, and thus symmetric neutrino and antineutrino sources, which make this proposal ideally useful for measuring neutrino CP violation. More importantly, $\bar{\nu}_{e,\mu}\rightarrow\bar{\nu}_\tau$ and $\nu_{e,\mu}\rightarrow \nu_\tau$, and, $\bar{\nu}_{e}\rightarrow\bar{\nu}_\mu$ and $\nu_{e}\rightarrow \nu_\mu$ oscillation signals can be collected simultaneously, with no needs for separate specific runs for neutrinos or antineutrinos. Furthermore, it is possible to exchange $\mu^+$ and $\mu^-$ flying routes, thus further reducing possible bias or systematic uncertainties. In an optimistic way, we estimate $10^4$ tau (anti-) neutrinos can be collected per year thus this proposal can serve as a brighter tau neutrino factory. Moreover, 5 standard deviations of sensitivity can be easily reached for CP phase as $|\pi/2|$, with only 1--2 years of data taking, by combining tau and muon (anti-) neutrino appearances.
Comment: Updated version with additional applications and references added; Happy Mu Nu Year!