Search for anomalous quartic gauge couplings in the process $\mu^+\mu^-\to \bar{\nu}\nu\gamma\gamma$ with a nested local outlier factor

Dear Editor,

We are grateful to the referee for the careful review of our manuscript and for the constructive and valuable comments on ``Search for anomalous quartic gauge couplings in the process $\mu^+\mu^-\to \bar{\nu}\nu\gamma\gamma$ with a nested local outlier factor''(scipost_202507_00021v1). We appreciate the opportunity to revise our manuscript, and sincerely appreciate the helpful suggestions that reviewer has provided, which have significantly enhanced the quality of our manuscript. The following is the one-to-one response.

1. About the unsupervised'' terminology: I still think the wording in the Abstract/Introduction should be softened a bit. LOF itself is an unsupervised algorithm, but the overall pipeline used here (threshold optimisation, coefficient extraction, etc.) is clearly not fully unsupervised. It would help if the authors explicitly said something likeunsupervised anomaly score, with supervised optimisation for EFT sensitivity'' at least once, just to avoid giving the impression that the entire analysis is model-agnostic.

Thank you very much for the suggestion. We have emphasis the statement of the ``supervised optimisation'' in abstract and in the second paragraph of introduction.

1. Connection to autoencoder-based approaches: Since the paper already mentions using dimensionality reduction or latent-space methods, it would be good to briefly note (e.g. in the Introduction or Outlook) that NLOF could naturally be combined with the AE-based aQGC studies already in the literature (such as Ref. [21]). A short remark on how NLOF might behave in a learned latent space would make the paper more complete.

Thank you for the suggestion. Since the main computational cost of the LOF/NLOF algorithm lies in calculating distances, it can be anticipated that applying dimensionality reduction and implementing LOF/NLOF in the latent space will significantly reduce computational complexity and improve the algorithm's operational efficiency. We have added the statement in the third paragraph in section 4.1.

1. Detector realism and systematics: I would encourage adding a more explicit paragraph on detector effects and systematics. In particular:\
2. State clearly that the results are purely statistical and do not include detector systematics or beam-induced backgrounds.
3. Add a short qualitative comment (with references) on photon-ID efficiency, resolutions, and how these could affect the chosen observables. This can be done textually - no need for new MC - but the current ``we neglect these backgrounds'' is too brief.

Thank you very much for the suggestion.

Since the muon collider is a future collider, at this stage the effect of the detector can only be estimated using simulation. In this work, we choose the default muon collider card in Delphes. That means, the results are purely statistical and do not include detector systematics or beam-induced backgrounds. Denoting $E_{\gamma}$ and $\eta _{\gamma}$ as the energy and pseudo-rapidity of a photon, the photon efficiency is $94\%$ when $E_{\gamma}\geq 2\;{\rm GeV}$ and $|\eta_{\gamma}|<0.7$, and $90\%$ when $E_{\gamma}\geq 2\;{\rm GeV}$ and $2.5\geq |\eta_{\gamma}|\geq 0.7$, and otherwise zero. The photon is considered as isolated when $\sum p_T/p_T^{\gamma} < 0.2$ where the sum runs over other particles in the vicinity of the photon with $\Delta R<0.1$ and with $p_T>0.5\;{\rm GeV}$, where $p_T$ is the transverse momentum, and $\Delta R=\sqrt{\Delta \eta^2+\Delta \phi^2}$ where $\Delta \eta$ and $\Delta \phi$ are differences of pseudo-rapidities and azimuth angles of two particles. The photon energy resolution is parameterized as $\sigma(E)/E = \sqrt{(1\%)^2 + (st^2/\sqrt{E}) }$, with $st$ denoting the stochastic term varying across three pseudo-rapidity regions: $15.6\%$ for $|\eta| \leq 0.78$, $17.5\%$ for $0.78 < |\eta| \leq 0.83$, and $15.1\%$ for $0.83 < |\eta| \leq 2.5$. We expect that, as machine learning algorithms, LOF/NLOF are insensitive to these parameters.

We have added the statement as the second paragraph in section 4.1.

1. Minor editorial corrections:
2. a tradition counterpart'' $\to$a traditional counterpart''
3. compare of NLOF'' $\to$comparison of NLOF''
4. exhibit a spin comparable'' $\to$exhibit a span comparable'' (I assume ``span'' is meant)

Thank you very much for the careful reading of our manuscript. We have revised those minor mistakes in the revision.

Our primary revisions are marked in red. We hope that our responses and the revised manuscript address the concerns.

With Best Regards.

Yours sincerely.

Ke-Xin Chen, Yu-Chen Guo and Ji-Chong Yang Department of Physics, Liaoning Normal University, Dalian 116029, China

1. We have softened the statement on ``unsupervised'' in both abstract and introduction.

2. We have added the note to encourage a latent space LOF/NLOF in the third paragraph in section 4.1 .

3. We have added the statement on detector simulation as the second paragraph in section 4.1.

4. Minor revisions are made for the linguistic errors.