# Design and Diagnostics of High-Precision Accelerator Neutrino Beams
## 12 Conclusions: A Step beyond the State-of-the-Art  
In the previous chapters, we reviewed the main components of an accelerator neutrino beam, the techniques for diagnostics and the barriers that hinder a per-cent level precision. Such precision is needed for the next generation of long-baseline experiments (DUNE, HK and other proposed facilities) and short-baseline experiments (for cross-section measurements and neutrino physics beyond the Standard Model). The reader may wonder what are the leading systematics that jeopardize high-precision diagnostics and the most effective counter-measurements. We can illustrate it considering the world best measurement of the flux performed in the 1-10 GeV range by MINER\(\
u\)A in 2016 [62]. This analysis used one of the largest datasets of ancillary measurements both off-site and on-site:  
* the MIPP data on thick Carbon target [167]
* the NA49 and NA61/SHINE data on thin Carbon target [168; 169; 170]
* the muon chambers located after the beam dump
* the neutrino-electron elastic scattering at the MINER\(\
u\)A detector
* the low-\(\
u\) neutrino-nucleus scattering at the MINER\(\
u\)A detector  
combined with beam diagnostics: the alignment tolerance on the beamline elements [29; 171; 172], the horn current (\(180\pm 2\) kA) and the detector geometrical parameters. The POT were estimated by two toroids located upstream of the target with a 0.5% precision [29]. The beam losses were monitored by sealed-gas ionization chambers and four total loss monitors (These devices are coaxial cables filled with a Ar-CO\({}_{2}\) mixture. They produce a signal proportional to the ionization caused by protons lost before the target). Like ENUBET, the NuMI designers installed three layers of muon chambers after the beam dump to estimate the energy and flux of the \(\mu^{+}\) from \(\pi^{+}\) decay. However, since the decay volume is located on axis with the horn, the environment is much harsher and does not provide muon monitoring at the single-particle level. Ionization chambers were also installed just before the dump to make a rough estimate of the total undecayed hadrons and, especially, the beam spot size. In this case, the rate is extremely high: up to \(10^{9}\) charged particles/cm\({}^{2}\)/spill (\(10^{14}\) Hz/cm\({}^{2}\)) during beam operation, consisting mainly of 120 GeV/c primary protons that have not interacted in the beamline. These monitors are crossed by \(2\times 10^{9}\) neutrons/cm\({}^{2}\)/spill originated by the albedo in the beam dump. The particle fluence at the center of the monitor is also very large: 1.3 Grad/year. These rates support the need to decouple the proton and hadron dump in high-precision beams like the monitored neutrino beams. The entire NuMI beamline is simulated with GEANT4 and the external data from MIPP and NA61/SHINE are introduced as weights in the theoretical distributions of the hadron yields. Tertiary production in the beamline or secondary meson absorption is simulated with GEANT4 correcting the cross section by external data coming mainly from T2K [61]. Measurements in the MINER\(\
u\)A neutrino detector are used both as a check of flux predictions and as an additional constraint to the flux. The results achieved at NuMI show that classical diagnostics (GEANT4/FLUKA simulation with beam monitors, including the muon chambers) can achieve a precision of 10-25% depending on the energy range. The hadron production data reduce such uncertainty to 5.4% and completely dominate the current systematic uncertainty of NuMI and most of the other neutrino beams. Muon chambers at such a high rate play a minor role to constrain the flux but monitor relative flux variations during the data taking. The uncertainties on the beamline geometry and the horn current are generally negligible with respect to hadron production except in the falling-edge region of the flux. All these considerations support the improvements of hadron production experiments for high-intensity long-baseline experiments.