# Design and Diagnostics of High-Precision Accelerator Neutrino Beams
## 1 Introduction
These data are essential for DUNE and HK because long-baseline experiments study the oscillation of \(\
u_{\mu}\) into \(\
u_{e}\) and its CP-conjugate \(\bar{\
u}_{\mu}\to\bar{\
u}_{e}\). They thus need an exquisite precision in \(\sigma_{\
u_{e}}(E)\) and \(\sigma_{\bar{\
u}_{e}}(E)\). * Cross sections for the study of the _disappearance channel_ (A disappearance channel is a \(\
u_{f}\to\
u_{f}\) oscillation, where the number of observed \(\
u_{f}\) is smaller that the \(\
u_{f}\) at the source because some of them have changed flavor. An appearance channel is a \(\
u_{f}\to\
u_{f^{\prime}}\) oscillation where a new flavor \(f^{\prime}\) appears into the detector.) \(\
u_{\mu}\to\
u_{\mu}\) and \(\bar{\
u}_{\mu}\to\bar{\
u}_{\mu}\) in long-baseline experiments. This measurement is essential to determine the mixing parameters and must be combined with the above-mentioned \(\
u_{e}\)_appearance channels_ (\(\
u_{\mu}\to\
u_{e}\)and \(\overline{\
u}_{\mu}\to\overline{\
u}_{e}\)) to disentangle effects due to CP violation from effects due to the neutrino mass hierarchy and (if any) deviations from the Standard Model [11]. In this case, a 1% level measurement of \(\sigma_{\bar{\
u}_{\mu}}(E)\) and \(\sigma_{\bar{\
u}_{\mu}}(E)\) is mandatory. * The knowledge of the absolute flux is less critical for long-baseline oscillation experiments than for short-baseline cross section experiments because DUNE and HK use ancillary detectors (\"Near Detector\", ND) located near the source to estimate the incoming rate of neutrinos. At the same time, the absolute fluxes \(\phi_{\
u_{\mu}}\) and \(\phi_{\overline{\
u}_{\mu}}\) must be known with \(<\)5% precision because the Near Detector samples a flux that is not exactly the same as the flux reaching the \"Far Detector\" (FD), which is located far from the source and designed to observe the oscillations. The imperfections in the flux cancellation arising by the ND-versus-FD comparison cannot be neglected any more in modern facilities. Similar considerations hold for the size of the wrong-flavor contamination (e.g., \(\
u_{e}\) at the source) that can pollute the \(\
u_{\mu}\to\
u_{e}\) measurement at the FD. In this work, we will show that high-precision cross section measurements need short-baseline experiments with a dedicated design for the beamline and tailor-made diagnostics. For instance, in the _monitored neutrino beams_[12], the flux is derived most straightforwardly by measuring the charged leptons produced in the decay volume of the beam. These leptons are directly proportional to the number of neutrinos created at the source. On the other hand, the design of the Near Detector in long-baseline beams must be tailored to measure the flux and wrong-flavor contamination at a few per-cent level. Spectral information on \(\phi_{f}(E)\) is very useful to mitigate the systematics arising from an imperfect ND-versus-FD cancellation. This task is substantially eased if the corresponding beamlines are complemented by diagnostic tools inherited from monitored neutrino beams and if the cross sections are known with a precision of \(\sim\)1%.