Recasting and Forecasting Dark Matter Limits Without Raw Data: A Generalized Algorithm for Gamma-Ray Telescopes

We present a novel method for both forecasting and recasting upper limits (ULs) on dark matter (DM) annihilation cross sections, $\left< \sigma v \right>^{UL}$, or decay lifetime $\tau^{LL}$ . The forecasting method relies solely on the instrument response functions (IRFs) to predict ULs for a given observational setup, without the need for full analysis pipelines. The recasting procedure uses published ULs to reinterpret constraints for alternative DM models or channels. We demonstrate its utility across a range of canonical annihilation channels, including $b\bar{b}$, $W^+W^-$, $\tau^+\tau^-$, and $\mu^+\mu^-$, and apply it to several major gamma-ray experiments, including MAGIC, \textit{Fermi}-LAT, and CTAO. Notably, we develop a recasting approach that remains effective even when the IRF is unavailable by extracting generalized IRF-dependent coefficients from benchmark channels. We apply this method to reinterpret ULs derived from standard spectra (e.g., PPPC4DMID) in terms of more recent DM scenarios, including a Higgsino-like model with mixed final states and spectra generated with the CosmiXs model. Extensive Monte Carlo simulations and direct comparison with published results confirm the robustness and accuracy of our method, with discrepancies remaining within statistical uncertainties. The algorithm is generally applicable to any scenario where the expected signal model is parametric, offering a powerful tool for reinterpreting existing gamma-ray limits and efficiently exploring the DM parameter space in current and future indirect detection experiments.