SciPost Submission Page
Probing the Parameter Space of Axion-Like Particles Using Simulation-Based Inference
by Pooja Bhattacharjee, Christopher Eckner, Gabrijela Zaharijas, Gert Kluge, Giacomo D'Amico
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Pooja Bhattacharjee |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2509.20578v1 (pdf) |
| Date submitted: | Sept. 26, 2025, 9:06 p.m. |
| Submitted by: | Pooja Bhattacharjee |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | The 2nd European AI for Fundamental Physics Conference (EuCAIFCon2025) |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Experimental, Computational, Phenomenological, Observational |
Abstract
Axion-like particles (ALPs), hypothetical pseudoscalar particles that couple to photons, are among the most actively investigated candidates for new physics beyond the Standard Model. Their interaction with gamma rays in the presence of astrophysical magnetic fields can leave characteristic, energy-dependent modulations in observed spectra. Capturing such subtle features requires precise statistical inference, but standard likelihood-based methods often fall short when faced with complex models, large number of nuisance parameters and limited analytical tractability. In this work, we investigate the application of simulation-based inference (SBI), specifically Truncated Marginal Neural Ratio Estimation (TMNRE), to constrain ALP parameters using simulated observations from the upcoming Cherenkov Telescope Array Observatory (CTAO). We model the gamma-ray emission from the active galactic nucleus NGC 1275, accounting for photon-ALP mixing, extragalactic background light (EBL) absorption, and the full CTAO instrument response. Leveraging the Swyft framework, we infer posteriors for the ALP mass and coupling strength and demonstrate its potential to extract meaningful constraints on ALPs from future real gamma-ray data with CTAO.
Current status:
Reports on this Submission
Strengths
1) Constraining axion properties with gamma-ray spectra using simulation-based inference (SBI) is a promising idea 2) Their method produces (nearly) unbiased posteriors 3) The paper is well written
Weaknesses
1) The fact that the posteriors are already quite broad - despite the fact that the authors currently keep most of the 15 physical parameters fixed - raises doubts on the ability of the method to obtain strong bounds on axion properties in a more realistic setting where all physically relevant parameters need to be inferred or marginalized over 2) The plot labels could be improved
Report
Requested changes
1) In the operator $\mathcal{L}_{\alpha \gamma}$, $\alpha$ and $\gamma$ should be subscripts 2) "For tractability, uncertainties in most of the 15 nuisance parameters are kept fixed" -> The clarity of this sentence could be improved, as it's not entirely clear at this point if the values of the nuisance parameters themselves or only their standard deviations are kept fixed (while their values would be allowed to float) 3) The font size in the legend, as well as of the tick labels, of Fig. 1 is very small - please consider increasing it (there's still empty space in the figure) 4) The labels of the posterior results in Fig. 2 are somewhat misleading: the x-axis of the $m_a$ plot reads $m_a$, but what seems to be shown is actually $\log_{10} m_a$, and similarly for the coupling strength. Please make the axis labels consistent with the data / values indicated by the tick labels. 5) "...which leverages neural networks trained on simulated data to approximate likelihood ratios." -> "Likelihood ratios" is very generic; it would be good to mention that swyft specifically targets the posterior-to-prior or equivalently the likelihood-to-evidence ratio 6) "While most nuisance parameters are held fixed to reduce computational complexity, variations in the magnetic field are implicitly included, as each simulation uses a randomly generated realization, capturing the stochastic nature of the environment. " -> the authors seem to infer 2 parameters (mass and coupling strength) and to marginalize over another parameter (magnetic field). Can the authors please state this clearly already at an earlier point where they wrote "For tractability, uncertainties in most of the 15 nuisance parameters are kept fixed." 7) Please mention the input dimensionality (i.e. number of energy bins) of the spectra shown to the neural network. 8) The authors write: "However, the contours remain relatively broad, reflecting the limited training sample density and potential degeneracies between parameters." It would be good to mention the size of your training dataset and perhaps also to comment on what makes you believe that increasing the training dataset size would lead to much tighter constraints. 9) The future effort enumeration lists "Incorporation of astrophysical systematics, including magnetic field..." -> but earlier you wrote: " variations in the magnetic field are implicitly included, as each simulation uses a randomly generated realization"; please clarify to what extent this is already included and what is still missing 10) The authors seem to be worried about the calibration, but in my opinion, their coverage plot looks decent. What worries me more is that the constraints in Fig. 2 look quite broad (as the authors note themselves) - despite the fact that most of the 15 nuisance parameters mentioned by the authors are kept fixed. On the other hand, this work only considers a single AGN. Could the authors briefly discuss the potential of their method for deriving ALP constraints jointly from multiple sources?
Recommendation
Ask for minor revision
Report
Dear authors, editors,
thanks a lot for these nicely prepared proceedings. I found them well written and clear, so I recommend them to be published with the following minor clarifications: * could you write how many of the nuisance parameters are not kept fixed? Currently you write “most” are kept fixed, but knowing how many aren’t is an important figure * could you clarify what is meant in section 3 with “variations in the magnetic field are implicitly included, as each simulation uses a randomly generated realization, capturing the stochastic nature of the environment”? Are these variations nuisance parameters or you are referring to the fact that the model is an stochastic one, and therefore your studies are really SBI and not a simple regression of the likelihood? Cheers, your referee
Recommendation
Ask for minor revision
Referee Report
We thank the referees for their remarks and suggestions. We address all the
points raised by the referees one by one below. We hope that, with all the queries addressed, the draft is now acceptable for publication in SciPost Physics Proceedings.
Reviewer 1:
1)Dear authors, editors,
thanks a lot for these nicely prepared proceedings. I found them well written and clear, so I recommend them to be published with the following minor clarifications: * could you write how many of the nuisance parameters are not kept fixed? Currently you write “most” are kept fixed, but knowing how many aren’t is an important figure * could you clarify what is meant in section 3 with “variations in the magnetic field are implicitly included, as each simulation uses a randomly generated realization, capturing the stochastic nature of the environment”? Are these variations nuisance parameters or you are referring to the fact that the model is an stochastic one, and therefore your studies are really SBI and not a simple regression of the likelihood? Cheers, your referee
Response: We thank the referee for these queries. All 15 nuisance parameters are fixed to their fiducial values; only ALP mass (ma) and coupling constant (gaγ) are inferred. Magnetic-field parameters are also fixed, and the reported “variations” refer to stochastic realizations generated by the forward model. This intrinsic stochasticity motivates the use of SBI rather than a simple likelihood regression.
With Kind Regards,
Pooja Bhattacharjee
Author: Pooja Bhattacharjee on 2026-01-14 [id 6225]
(in reply to Report 2 on 2025-12-15)Referee Report
We thank the referees for their remarks and suggestions. We address all the
points raised by the referees one by one below. We hope that, with all the queries addressed, the draft is now acceptable for publication in SciPost Physics Proceedings.
Reviewer 1:
1)In the operator Lαγ, α and γ should be subscripts.
Response: We have corrected the notation in the revised draft.
2)"For tractability, uncertainties in most of the 15 nuisance parameters are kept fixed" -> The clarity of this sentence could be improved, as it's not entirely clear at this point if the values of the nuisance parameters themselves or only their standard deviations are kept fixed (while their values would be allowed to float)
Response: We have clarified that the values of all 15 nuisance parameters are fixed to their fiducial values for computational tractability. Only the ALP mass (ma) and coupling constant (gaγ) are inferred. The sentence has been revised accordingly.
3)The font size in the legend, as well as of the tick labels, of Fig. 1 is very small - please consider increasing it (there's still empty space in the figure)
Response: The font size of the legend and tick labels in Fig. 1 has been increased.
4)The labels of the posterior results in Fig. 2 are somewhat misleading: the x-axis of the ma plot reads ma, but what seems to be shown is actually log10ma, and similarly for the coupling strength. Please make the axis labels consistent with the data / values indicated by the tick labels.
Response: The axis labels have been corrected to reflect log10ma and log10gaγ.
5)"...which leverages neural networks trained on simulated data to approximate likelihood ratios." -> "Likelihood ratios" is very generic; it would be good to mention that swyft specifically targets the posterior-to-prior or equivalently the likelihood-to-evidence ratio
Response: As the referee suggested, the phrasing has been revised to state that Swyft targets the likelihood-to-evidence ratio.
6)"While most nuisance parameters are held fixed to reduce computational complexity, variations in the magnetic field are implicitly included, as each simulation uses a randomly generated realization, capturing the stochastic nature of the environment. " -> the authors seem to infer 2 parameters (mass and coupling strength) and to marginalize over another parameter (magnetic field). Can the authors please state this clearly already at an earlier point where they wrote "For tractability, uncertainties in most of the 15 nuisance parameters are kept fixed."
Response: We clarified earlier in the manuscript that magnetic-field parameters are fixed, while stochastic field realizations are sampled via random configurations. The wording has been revised to clearly distinguish this from parameter inference.
7)Please mention the input dimensionality (i.e. number of energy bins) of the spectra shown to the neural network.
Response: We now explicitly state that each spectrum is represented by 100 energy bins.
8)The authors write: "However, the contours remain relatively broad, reflecting the limited training sample density and potential degeneracies between parameters." It would be good to mention the size of your training dataset and perhaps also to comment on what makes you believe that increasing the training dataset size would lead to much tighter constraints.
Response: We have added that the training dataset consists of 10^5 simulated spectra. The discussion has been expanded to note that limited training density and residual parameter degeneracies lead to broad contours, and that denser sampling is expected to tighten constraints.
9)The future effort enumeration lists "Incorporation of astrophysical systematics, including magnetic field..." -> but earlier you wrote: " variations in the magnetic field are implicitly included, as each simulation uses a randomly generated realization"; please clarify to what extent this is already included and what is still missing
Response: We clarified that stochastic magnetic-field realizations at fixed model parameters are already included. Future work refers to incorporating systematic uncertainties through alternative magnetic-field and plasma models. We also revised the statement accordingly.
10)The authors seem to be worried about the calibration, but in my opinion, their coverage plot looks decent. What worries me more is that the constraints in Fig. 2 look quite broad (as the authors note themselves) - despite the fact that most of the 15 nuisance parameters mentioned by the authors are kept fixed. On the other hand, this work only considers a single AGN. Could the authors briefly discuss the potential of their method for deriving ALP constraints jointly from multiple sources?
Response: We added a brief discussion noting that this study focuses on a single AGN, and that joint inference across multiple sources, which is naturally supported within the SBI framework, is expected to significantly improve constraints.
With Kind Regards,
Pooja Bhattacharjee