# Design and Diagnostics of High-Precision Accelerator Neutrino Beams
## 5 Hadron Yields  
Nowadays, hadron production experiments are critical for high precision accelerator neutrino beams. The differential distributions predicted by Monte Carlo codes used to compute the hadron production yields from fragmentation models are usually not able to reproduce the kinematic distribution of secondaries, even if the models are tuned with external data. Mastering the hadron production mechanisms at a level sufficient to predict the accepted flux before the focusing and decay volume in high-precision neutrino experiments is still outside the reach of these models. There are two types of hadron production experiments that are of relevance in our field:  
* General purpose experiments aimed at measuring differential cross sections for pion and kaon production using thin targets of various materials. The materials are chosen among the most common candidates for neutrino targets (see Section 4)
* Replica target experiments, where the yields and differential cross-sections are measured for an exact copy of the target used in the corresponding neutrino experiment. In practice, both the knowledge of the cross-sections and the yields (typically performed with replica targets) is crucial for the correct normalization of the number of hadrons and, hence, neutrinos. The experiments performed in the 80s and 90s were mostly mass spectrometers with a narrow acceptance and excellent particle identification [15]. This choice was driven by the fact that the experiments were not designed as hadron production facilities but were based on existing experiments studying standard or exotic QCD processes. A renowned example is NA56/SPY [101] at CERN that took data in 2002-2003 modifying NA52: a high precision mass spectrometer for the searches of strangelets in ion-ion interactions. Despite these limitations, SPY produced essential results (see Figure 5) for the design of the CERN-to Gran Sasso (CNGS) neutrino beam and the interpretation of the NOMAD data [27], both based on primary protons at 450 GeV (the CERN SPS). The most precise data were taken on Beryllium in a secondary momentum range from 7 to 135 GeV/c and \(p_{T}\) values up to 600 MeV, where a precision of 5-10% was achieved. The \(K^{+}/\pi^{+}\) ratio was measured in this momentum range with a typical precision of 3%. Even if the precision achieved was quite high, the limited \(p_{T}\) acceptance and the choice of thin beryllium targets increased the systematic budget when applied to real neutrino experiments due to the extrapolation to thick targets of different materials. SPY was, hence,  
Figure 4: Kaon yields as a function of the graphite target length. The primary beam simulated is a 400 GeV/c proton beam. The figure of merit for this study is the number of kaons of given energy with 10% momentum bite that enters an ideal beamline with \(\pm\)20 mrad angular acceptance (AA) in both planes, placed 30 cm after the target (Lq). The error bars are not plotted to ease the reading; statistical errors are negligible (1%), while the Monte-Carlo systematics amounts to \(\sim\)20%. useful in the design phase of CNGS to estimate the expected neutrino rates but did not constrain the actual neutrino flux below 25%. Modern hadron production experiments designed after the discovery of neutrino oscillations are dedicated facilities with a large \(p_{T}\) acceptance, running both with thin and replica targets. HARP [102] was the first dedicated hadron production experiment designed for a future Neutrino Factory and operated at the CERN PS (primary proton momentum: 25 GeV/c) with a large acceptance spectrometer. The secondary momentum range was 0.5-8 GeV/c and the maximum angle reached 250 mrad. A special configuration (\"large angle\") studied secondaries below 1 GeV/c up to polar angles of 2150 mrad.