Cosmic-Ray Mass Composition around the Knee via Principal Component Analysis

In this paper, we apply Principal Component Analysis (PCA) to experimental data recorded by the KASCADE experiment to reconstruct the mass composition of cosmic rays around the \textit{knee} region. A set of four extensive air shower parameters sensitive to the primary particle mass ($LCm$, $N_{\mu}$, $N_{e}$, and lateral shower $age$) was considered, whose coordinates were transformed into a new orthogonal basis that maximally captures the data variance. Based on the experimental distributions of the first two principal components (PCA0 vs.\ PCA1) and full Monte Carlo simulations of the KASCADE array considering five types of primary particles (p, He, C, Si, and Fe) and three hadronic interaction models (EPOS-LHC, QGSjet-II-04, and SIBYLL~2.3d), we obtained the evolution of the abundance of each primary species as a function of energy, as well as the evolution of the mean logarithmic mass with energy. We found that the reconstruction of the mass composition resulting from this comprehensive analysis significantly reduces dependence on the hadronic interaction model used in the simulation process, even though the initial input parameters are model-dependent. Moreover, the results support the idea that around the \textit{knee} region, the abundance of the light component (protons) decreases, while the heavy component shows a slight increase. The evolution of $\langle \ln (A) \rangle$ as a function of energy derived from this analysis shows excellent agreement with recent results from the LHAASO--KM2A experiment and aligns very well with the predictions of the data-driven GSF model.