Measurements of the charge ratio and polarization of cosmic-ray muons with the Super-Kamiokande detector

We present the results of the charge ratio ($R$) and polarization ($P_0^{\mu }$) measurements using the decay electron events collected from 2008 September to 2022 June by the Super-Kamiokande detector. Because of its underground location and long operation, we performed high precision measurements by accumulating cosmic-ray muons. We measured the muon charge ratio to be $R=1.32\pm 0.02$ $(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$ at $E_{\mu }\cos {\theta }_{\mathrm{Z}\mathrm{e}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{h}}=0.7_{-0.2}^{+0.3}$ $\mathrm{T}\mathrm{e}\mathrm{V}$, where $E_{\mu }$ is the muon energy and ${\theta }_{\mathrm{Z}\mathrm{e}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{h}}$ is the zenith angle of incoming cosmic-ray muons. This result is consistent with the Honda flux model while this suggests a tension with the $\pi K$ model of $1.9\sigma$. We also measured the muon polarization at the production location to be $P_0^{\mu }=0.52\pm 0.02$ $(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$ at the muon momentum of $0.9_{-0.1}^{+0.6}$ $\mathrm{T}\mathrm{e}\mathrm{V}\mathrm{/}c$ at the surface of the mountain; this also suggests a tension with the Honda flux model of $1.5\sigma$. This is the most precise measurement ever to experimentally determine the cosmic-ray muon polarization near $1\mathrm{T}\mathrm{e}\mathrm{V}\mathrm{/}c$. These measurement results are useful to improve the atmospheric neutrino simulations.