Reconstruction of Shower-like Events in NEON Using Likelihood and Graph Neural Network Methods
The Neutrino Observatory in the Nanhai (NEON) is a proposed deep-sea neutrino telescope deployed in the South China Sea. Accurate reconstruction of shower-like events is crucial for neutrino energy measurements and multi-messenger astronomy, yet it poses significant challenges due to seawater optical attenuation, irregular detector geometry, and substantial $^{40}\mathrm{K}$ ambient background. In this work, we present the first comprehensive reconstruction framework for shower-like events in NEON, encompassing both a physics-driven maximum likelihood estimation (MLE) method and a data-driven Graph Neural Network (GNN). The traditional MLE framework integrates spatial-isochronic hit selection, vertex reconstruction via time-residual M-estimator minimization, and decoupled directional and energy estimation based on pre-computed photon distribution tables. Physical calibrations, including PMT angular acceptance, hit-level time slewing corrections, and an effective line-source shower extension, are incorporated into the likelihood formulation. In parallel, a two-stage GNN is developed to capture intra-DOM PMT correlations and distance-weighted inter-DOM topological patterns. Simulation studies show that the MLE method achieves an overall median angular resolution of $4.19^\circ$ and an energy resolution of 25\%-37\% over 1 TeV to 1 PeV with negligible systematic bias. The GNN further improves reconstruction fidelity in the low-to-intermediate energy regime, achieving a median angular resolution of $1.8^\circ$ at 30 TeV and an energy resolution of $\sim$ 20\% between 40 and 300 TeV. Based on these reconstruction performances, the effective area and point-source discovery potential of NEON are evaluated. This framework establishes an essential reconstruction benchmark for NEON and provides practical methodologies for future next-generation deep-sea neutrino telescopes.