Projected sensitivity of CTAO to axion-like particles from blazars with a machine learning approach

Problem Statement
Axion-like particles (ALPs) are hypothetical pseudo-scalar particles predicted by various extensions of the Standard Model. A primary method for their detection involves the mixing of photons and ALPs in external magnetic fields, which can lead to distinct spectral signatures in gamma-ray sources. Blazars, specifically, serve as ideal laboratories for this search due to their cosmological distances, strong magnetic fields in their relativistic jets, and the resulting absorption of very high-energy (VHE) gamma rays by the extragalactic background light (EBL). The presence of ALPs could induce energy-dependent spectral "wiggles" or a hardening of the spectrum at high energies by allowing photons to convert into ALPs, traverse cosmological distances without EBL absorption, and reconvert into photons in the Milky Way's magnetic field.

The Cherenkov Telescope Array Observatory (CTAO) is expected to offer significant improvements in energy resolution and point-source sensitivity over current ground-based telescopes. However, extracting ALP signals from blazar spectra is challenging due to the complex, non-linear nature of the spectral distortions and potential systematic uncertainties. While standard statistical approaches based on the likelihood-ratio test (LRT) are commonly used, this paper investigates whether machine learning (ML) classifiers can offer a robust alternative for constraining the ALP parameter space ($m_a$ and $g_{a\gamma}$).

Methodology
The study focuses on two well-known TeV blazars, Mrk 501 and PKS 2155−304, simulating observations for both their baseline and flaring states using the CTAO "Alpha" configuration.

1. Data Simulation:

   • Mock data was generated using the Gammapy package, simulating 50 hours of observation for baseline states and 5 hours for flaring states.
   • Spectral models were derived from the 4FGL-DR4 catalog (log-parabola for baseline) and historical flare data (log-parabola for Mrk 501, exponential cutoff power law for PKS 2155−304).
   • ALP-photon oscillations were modeled using the gammaALPs Python package, incorporating magnetic field environments in the blazar jets (helical and tangled components), the Milky Way's galactic magnetic field, and EBL absorption.
   • The ALP parameter space was scanned over $m_a \in [0.1, 1000]$ neV and $g_{a\gamma} \in [0.03, 7] \times 10^{-11}$ GeV$^{-1}$.

2. Statistical Approaches:

   • Likelihood-Ratio Test (LRT): A standard benchmark method was employed. A test statistic (TS) was defined based on the difference in log-likelihoods between the ALP hypothesis and the best-fit model. Since Wilks' theorem does not strictly apply to ALP searches, the TS distribution was empirically determined by simulating 100 datasets with ALP effects and fitting them with a Gamma probability distribution function (PDF).
   • Machine Learning (ML) Classifiers: A novel approach was introduced using the XGBoost algorithm.
     • A grid of classifiers was trained over the ALP parameter space.
     • Each classifier was trained to distinguish between 20,000 simulated datasets containing ALP effects and 20,000 datasets with only EBL absorption (no ALPs).
     • The input features were the normalized excess photon counts in energy bins, designed to focus on spectral shape rather than absolute flux.
     • For each $(m_a, g_{a\gamma})$ pair, the classifier output a score representing the likelihood of a dataset being "ALP-like." A complementary statistic $\Pi$ was defined to evaluate exclusion significance.
     • The distribution of $\Pi$ for ALP-like datasets was fitted with a Beta PDF to calculate confidence levels and exclusion significance (z-scores).

Key Contributions

• Projected Sensitivity: The paper provides projected 2$\sigma$ exclusion regions for CTAO observations of Mrk 501 and PKS 2155−304, demonstrating the observatory's potential to improve upon current limits.
• ML Application in ALP Searches: The work introduces and validates a machine learning-based method for constraining ALP parameters. It demonstrates that XGBoost classifiers can effectively learn the non-linear spectral features induced by ALP-photon mixing without relying on explicit parametric models of the spectral distortions.
• Comparison of Methods: The study directly compares the ML approach with the standard LRT, showing that the ML method yields consistent results with the traditional technique.

Results

• Exclusion Regions: Both the LRT and ML methods predict that CTAO will be able to exclude significant portions of the ALP parameter space, particularly in regions where the critical energy for strong mixing falls within the CTAO energy range.
• Method Consistency: The exclusion contours derived from the ML classifier (using the $\Pi$ statistic) align closely with those obtained from the LRT.
• Performance Limits: The ML classifiers achieve high accuracy (>90%) in regions where ALP-induced spectral distortions are distinct. However, performance degrades in regions of large $m_a$ and small $g_{a\gamma}$, where spectral distortions are weak and difficult to distinguish from the ALP-less case. In these regions, the classifiers correctly fail to exclude the hypothesis, mirroring the behavior of the LRT.
• Systematic Uncertainties: The authors note that the ML approach may help reduce the impact of systematic model-dependent uncertainties, as the classifiers learn the spectral shape directly from the data rather than relying on specific functional forms for the intrinsic source spectrum.

Significance and Claims
The paper claims that CTAO, with its enhanced energy resolution and sensitivity, will consistently improve current limits on the ALP parameter space. The primary significance of this work lies in the demonstration that machine learning classifiers are a viable and effective alternative to standard likelihood-ratio tests for ALP searches. The authors suggest that this new method could be valuable for future searches by potentially mitigating systematic uncertainties associated with spectral modeling. The study does not claim to discover ALPs but rather to establish the projected capability of CTAO to constrain their existence. The results are presented as an estimate of CTAO's constraining power based on simulated data, serving as a benchmark for future observational campaigns.