Measurement of neutron production in the very forward rapidity at LHC $\sqrt{s}$ = 7 TeV p-p collision

Ultra-high-energy cosmic-rays ``UHECRs'' were observed indirectly, and their primary properties are determined by Monte Carlo simulations with hadronic interaction models. However, uncertainty of the hadronic interaction models due to lack of calibration data at energy near UHECR is associated with the large uncertainty of cosmic-ray observations. Therefore, the hadronic interaction models must be calibrated by using high energy accelerators. The Large Hadron Collider forward (LHCf) experiment was designed to verify the hadron interaction models by using the LHC. Because the LHCf detectors were optimized to measure electro-magnetic showers, the performance of the LHCf detectors for hadron shower measurement has not been studied in detail yet. In order to measure forward neutron spectra, the performance of LHCf detectors for hadron showers was evaluated by using Monte Carlo simulations and 350 GeV test beam protons at CERN-SPS for the first time. The detection efficiency was estimated to be from 70\% to 80\% for neutrons with the energy from 500 GeV to 3.5 TeV. About 40\% of energy resolution with less than 2\% of energy scale non-linearity were achieved. The position resolutions varied from 1.3 mm to 0.3 mm depending on the incident neutron energy. The absolute energy scale was carefully checked with 3.5\% accuracy at 350 GeV using SPS test beams. In order to extract the true energy distribution from the measured energy spectra, the performance of the multi-dimensional unfolding method was studied. We confirmed that the true energy distribution can be reconstructed with 20-60\% accuracy depending on the energy by the unfolding method. Owing to the hadron shower reconstruction methods newly developed in this study, the analysis of forward neutron spectra using LHC $\sqrt{s}$ = 7 TeV {\it p-p} collision data taken in May 2010 was carried out. The neutron energy spectra were measured in three different pseudo-rapidity $\eta$ regions of from 8.81 to 8.99, from 8.99 to 9.22, and from 10.76 to infinity. The experimental results were compared with the MC predictions from known hadronic interaction models of DPMJET 3.04, EPOS 1.99, PYTHIA 8.145, QGSJET II-03 and SYBILL 2.1. No model could reproduce the experimental result perfectly. The experimental results show the most abundant neutron production compared to the known models. The performance of the LHCf detectors for neutron measurement has been confirmed in this study for the first time. It was also demonstrated that it is possible to verify the hadronic interaction models using the neutron energy spectrum obtained by LHCf.