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

TL;DR

This work addresses the challenge of interpreting gamma-ray DM limits without access to raw data by introducing a generalized IRF-based framework that forecasts and recasts upper limits on the annihilation cross section $⟨σv⟩$ or decay lifetime $τ$. It derives a likelihood-based UL expression and a practical recasting ratio that transfers limits across DM models and channels, including an IRF-missing approximation using $V_i$ coefficients. The methodology is validated with toy MC tests and applied to real data from MAGIC, Fermi-LAT, and CTAO, including applications to Higgsino-like and cosmiXs DM spectra. The approach enables rapid reinterpretation of existing limits, highlighting the importance of sharing instrument response information to maximize scientific return and guide future indirect-detection analyses.

Abstract

We present a novel method for both forecasting and recasting upper limits (ULs) on dark matter (DM) annihilation cross sections, $\left< σv \right>^{UL}$, or decay lifetime $τ^{LL}$ . 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 $b\bar{b}$, $W^+W^-$, $τ^+τ^-$, and $μ^+μ^-$, 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.

Figures (10)

• Figure 1: DM $\gamma$-ray spectra for pure WIMP annihilation into specific channels, obtained with gammapygammapy:2023gammapy:zenodo-1.2 and based on the PPPC parametrization (solid lines) by Cirelli:2010xx for three values of masses and from arina2024cosmixs (dashed line) for the $W^+W^-$ channel only. Also shown is an Higgsino-like spectrum with annihilation into $W^+W^-,ZZ,\gamma\gamma/\gamma Z$ with branching ratios $BR_i=0.611,0.382,0.008$ respectively.
• Figure 2: Effective area (left) and energy resolution (right) for Fermi-LAT aeff_FermiLAT, CTAO CTAOwebsite, MAGIC MAGIC:performance, and LHAASO LHAASO:2019qtb.
• Figure 3: Each panel summarizes $10^{5}$ Monte Carlo realizations generated under the null (no-signal) hypothesis with the CTAO IRFs. Left column: recast performed with the exact IRF using \ref{['eq:ratio']}. Right column: recast performed with the IRF–free approximation of \ref{['Eq:recast_approx']}. Top row: ULs for the $\tau^{+}\tau^{-}$ channel reconstructed from $b\bar{b}$ ULs. Bottom row: ULs for the $W^{+}W^{-}$ channel reconstructed from $\mu^{+}\mu^{-}$ ULs. Color code: light-grey bands show the $1\sigma$ containment of the benchmark (input) channels; dark-grey bands show the $1\sigma$ containment of the true ULs for the target channel; zebra pattern (alternating blue and transparent stripes) show the corresponding recast ULs. Black curves give the mean ULs over all simulations, while blue curves give the mean of the recast ULs. The lower sub-panel in each plot displays the fractional difference in percentage between true and recast ULs.
• Figure 4: Forecasted 95% CL upper limits on the DM annihilation cross section toward Draco I, assuming a $J$-factor of $10^{18.7} \, \text{GeV}^2/\text{cm}^5$ within $0.5^\circ$, 100 hours of observation time and the CTAO IRF ctao_irfs. Left: Comparison between forecasted ULs (blue lines) and published CTAO results (black lines and bands) for the $b\bar{b}$ and $\tau^+\tau^-$ channels. Our forecast ULs (blue solid and dashed lines) are overlaid on the original CTAO plot, figure 8 of Ref. CTAO-dphs. Right: Same comparison for the $W^+W^-$ and $\mu^+\mu^-$ channels.
• Figure 5: In both panels the image represents the originally published ULs from the MAGIC collaboration MAGIC:2021mog. The black line denotes the UL (solid for the observed one, dashed for the median), the green/yellow shaded regions denote the $68\%$/$95\%$ band of the null hypothesis, as derived from Monte Carlo sampling. Overlaid is our recast UL (thick solid blue line) obtained using \ref{['Eq:recast_approx']} to recast limits for $W^{+}W^{-}$ annihilation from the $b \bar{b}$ channel. Left: ULs obtained using coefficients $V_i$ inferred using the $\tau^{+}\tau^{-}$ channel as a second benchmark. Right: ULs obtained using coefficients $V_i$ inferred using the $\mu^{+}\mu^{-}$ channel. The bottom subplot in each case shows the relative difference (in %) between the published median expected limit and our recast ULs.