Comparative study and optimization of SDHCAL hadronic energy reconstruction methods

We present a detailed study of hadronic shower energy reconstruction methods for the Semi-Digital Hadronic Calorimeter (SDHCAL) within the ILD detector concept, using the Particle Flow Algorithm (PFA) APRIL. Using samples of single $K^0_L$ and dijet ($u,d,s$) events, we compare linear, quadratic, split, and polynomial regression-based reconstruction formulas, focusing on their impact on linearity and resolution. The study also addresses angular corrections required in the barrel region due to non-perpendicular particle incidence. Results show that while all methods achieve good overall performance, the split method and the polynomial regression provide the best compromise across different energy regimes, offering improved resolution at low energies without compromising linearity at higher energies. For dijets, sensitivity to PFA confusion dominates the resolution at high energies. These findings highlight the potential of future improvements, notably the integration of precise timing information from the T-SDHCAL into APRIL, to further reduce confusion and enhance hadronic energy reconstruction for next-generation lepton colliders.