Measurement of the production cross section of 31 GeV/c protons on carbon via beam attenuation in a 90-cm-long target

Neutrino beams at accelerator-based neutrino experiments originate from meson decays in flight. These mesons are produced in hadron-nucleus interactions in extended targets. Detailed understanding of the neutrino source is key to neutrino cross-section and oscillation measurements. However, Monte Carlo prediction of the neutrino flux has a limited precision mainly due to large hadron production uncertainties. To improve the flux prediction and lower its systematic uncertainty, modeling of hadronic interactions in simulations is tuned with hadron production data. These data include particle yields and interaction cross sections, which are used to re-weight particle production and interaction rates in Monte Carlo. Purposeful hadron production measurements are performed at the NA61/SHINE fixed target experiment at the CERN Super Proton Synchrotron. Currently, these measurements are tailored to the requirements of the T2K experiment in Japan and the Fermilab long-baseline neutrino beamlines. Employed are beams of different type and energy on targets of various thickness and material. Some NA61/SHINE results have already been implemented in the T2K neutrino flux prediction and have considerably reduced its total systematic uncertainty. The T2K beam is produced in the decays of hadrons, which emerged from the interactions of a 31 GeV/c proton beam inside a 90-cm-long graphite target. These interactions are recreated at the NA61/SHINE experiment when a 31 GeV/c incident proton beam collides with a replica of the T2K target. Analysis of such data collected in the year 2010 is the focus of this work. The task is to extract the production cross section in $p+C$ interactions at 31 GeV/c beam momentum. The maximal magnetic field configuration of the NA61/SHINE spectrometer is used. The dataset contains about 1.2 M recorded events. The adopted strategy is to measure the beam attenuation in the thick target and relate it to the production cross section. Such an approach minimizes the physics model dependence of the final result. The estimated production cross section is $$\sigma_{\mbox{prod}} = 227.6 \pm 0.8 \mbox{(stat)} ^{+1.9}_{-3.2} \mbox{(sys)} - 0.8 \mbox{(model)}~[\mbox{mb}].$$ It is in agreement with previous NA61/SHINE results obtained in measurements with a thin graphite target. Compared to them, the current estimate provides improved precision with a total fractional uncertainty of less than 2$\%$. The accordance between the reported production cross section and thin-target values suggests the reason for the observed tension between neutrino flux predictions tuned with thin- and replica-target data is still to be determined. Moreover, the presented result is to be used to constrain the output of the T2K beam simulation by re-weighting the interaction rate of beam protons inside the target. This is expected to further reduce the uncertainty of the T2K neutrino flux.