A Template-based $\gamma$-ray Reconstruction Method for Air Shower Arrays

We introduce a new Monte Carlo template-based reconstruction method for air shower arrays, with a focus on shower core and energy reconstruction of $\gamma$-ray induced air showers. The algorithm fits an observed lateral amplitude distribution of an extensive air shower against an expected probability distribution using a likelihood approach. A full Monte Carlo air shower simulation in combination with the detector simulation is used to generate the expected probability distributions. The goodness of fit can be used to discriminate between $\gamma$-ray and hadron induced air showers. As an example, we apply this method to the High Altitude Water Cherenkov $\gamma$-ray Observatory and its recently installed high-energy upgrade. The performance of this method and the applicability to air shower arrays with mixed detector types makes it a promising reconstruction approach for current and future instruments.