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Description
In this work, the proton-air inelastic cross section at a primary cosmic ray energy of $1~\mathrm{PeV}$ is measured with LHAASO experiment. The analysis is based on hybrid observational data from KM2A and WFCTA. The depth of air shower maximum $X_{\max}$ is reconstructed using the WFCTA geometrical observable ${Dist}$. The distribution of $X_{\max}$ is strongly correlated with the exponential distribution of the first interaction depth $X_0$. The proton-air inelastic cross section is obtained through Monte Carlo calibration, using the k-factor method to relate the attenuation length of the exponential part of the reconstructed $X_{\max}$ distribution to the attenuation length of $X_0$. From the LHAASO experiment, the proton-air inelastic cross section at $1~\mathrm{PeV}$ is obtained as $\sigma_{p\text{-air}} = 391.84 \pm 11.8~(\mathrm{stat.})^{+13.53}_{-28.09}~(\mathrm{syst.})~\mathrm{mb}$, in an energy region not yet covered by other ground-based cosmic ray experiments.