Long-lived neutral-kaon flux measurement for the KOTO experiment

The KOTO ($K^0$ at Tokai) experiment aims to observe the CP-violating rare decay $K_L \rightarrow \pi^0 \nu \bar{\nu}$ by using a long-lived neutral-kaon beam produced by the 30 GeV proton beam at the Japan Proton Accelerator Research Complex. The $K_L$ flux is an essential parameter for the measurement of the branching fraction. Three $K_L$ neutral decay modes, $K_L \rightarrow 3\pi^0$, $K_L \rightarrow 2\pi^0$, and $K_L \rightarrow 2\gamma$ were used to measure the $K_L$ flux in the beam line in the 2013 KOTO engineering run. A Monte Carlo simulation was used to estimate the detector acceptance for these decays. Agreement was found between the simulation model and the experimental data, and the remaining systematic uncertainty was estimated at the 1.4\% level. The $K_L$ flux was measured as $(4.183 \pm 0.017_{\mathrm{stat.}} \pm 0.059_{\mathrm{sys.}}) \times 10^7$ $K_L$ per $2\times 10^{14}$ protons on a 66-mm-long Au target.