Precise Measurement of $\delta$ at LBL Experiments Using Only The Neutrino Sector

Abstract

Currently, the CP-violating phase $\delta$ is the least precisely known among the neutrino mixing parameters. In the coming years, accelerator neutrino experiments such as DUNE and Hyper-K will measure $\delta$, significantly increasing the precision. Such a measurement is usually performed by comparing the oscillation probabilities in the neutrino and antineutrino sectors, thereby directly observing the CP violation. This approach, however, has some downsides: in particular, it is more challenging to obtain good statistics in the antineutrino sector, leading to increased statistical errors. In principle, however, it is possible to determine $\delta$ by looking only at the neutrino sector, studying the energy dependence of the oscillation probability. We investigate this possibility in detail; we find that, if this approach is used, the main issue would be the degeneracies with other mixing parameters, which affect the sensitivity to $\delta$. Those parameters, however, have already been measured with great precision, which will increase even more in the next few years; if those constraints are taken into account by introducing Gaussian penalty terms in the $\chi^2$, it is possible to achieve better results focusing only on the neutrino sector, rather than using the standard approach. Those degeneracies could also be broken by exploring a wider range of $L/E$: this can be achieved, for instance, by increasing the neutrino energy. In this way, the total beam intensity could also increase due to the relativistic boost (however, the conversion efficiency could decrease, affecting the total luminosity). We find that if the relativistic boost increases the number of events in the high-energy configuration, the best performance would be achieved in such a set-up; otherwise, the optimal approach would be to focus only on the neutrino mode without changing the beam energy.