TeV-scale neutrino cross-section measurement using upward through-going muons in Super-Kamiokande

Neutrinos provide a unique probe of both particle physics and the high-energy universe, traversing astronomical distances with minimal interaction. Their charged-current scattering cross section encodes fundamental information about weak interactions and nucleon structure across a vast energy range, yet measurements at TeV energies remain sparse. Here we report the first determination of the flux-averaged muon neutrino and anti-neutrino charged-current total cross section using high-energy atmospheric neutrinos observed in Super-Kamiokande. Using 3989 upward through-going muon events collected over 4269 days, together with a Bayesian fit to atmospheric flux and detector simulations, we measure the flux-averaged charged-current cross section in the 500-5000 GeV range to be $\sigma/E_\nu=(0.51\pm 0.11)\times 10^{-38}$ cm$^2$GeV$^{-1}$, with the highest precision to date in the TeV regime. Our results are consistent with accelerator-based measurements at lower energies and collider-based measurements at higher energies, bridging a critical gap between accelerator experiments and neutrino telescopes. This work demonstrates the capability of large underground detectors to perform precision cross-section measurements with atmospheric neutrinos, opening a new window for probing Standard Model physics and potential new physics searches at multi-TeV energies.