ALPs and HNLs at LHC and Muon Colliders: Uncovering New Couplings and Signals

- well written
- clear presentation
- extensive theory section

- lack of background estimates
- lack of efficiency estimate

The manuscript considers a model consisting of ALPs with GeV masses and one or two heavy neutral leptons (HNLs) with multi-100-GeV masses. As described at the beginning of the paper, HNLs are well motivated by various types of Seesaw mechanisms, but typically have very weak coupling to SM particles and are therefore rarely produced. This issue is overcome by postulating an additional coupling to ALPs, allowing large production rates at colliders.

The authors then first discuss the phenomenology of a single HNL, focussing on the pp > a* > NN > 2l2W channel, which is referred to as JALZ topology. The authors then proceed to the two HNL case, focussing on the pp > a* > N1 N2 > N1 N1 a > 2l2W a channel. For both cases, they estimate the rate for this process and (assuming perfect signal efficiency and negligible backgrounds) obtain projections on the model parameters, and conclude that "strong sensitivity can be achieved for various benchmark models".

The manuscript is well organized, the presentation is clear and the work seems technically correct.

My main concern regards the underlying assumptions of perfect signal efficiency and negligible backgrounds when estimating the projected sensitivities. In particular, there may be sizable combinatorial background or backgrounds where light jets were mis-tagged as hadronic W. Without a quantitative estimate, at least at the order of magnitude level, it is not clear whether the made assumptions are valid, and whether the main conclusion holds. Therefore, I cannot recommend publication at the moment. A realistic estimate of background rates and efficiencies need to be added before the paper can be considered for publication.

1) You say that "these effects cannot be observed experimentally". Neutrinoless double beta decay experiments are in principle able to experimentally observe effects of large Majorana masses.

2) The last 3 paragraphs of page 2 have 150 references. That seems a bit excessive. Please reconsider if all references are truly needed.

3) "the process has a fully reconstructible final state with no SM background": If I see correctly, you have a 2l+jets final state. This could be faked at the LHC, for example by tt+jets. Although the various on-shell conditions will clearly help to reduce such backgrounds, claiming 'no SM background' is likely misleading.

4) Does Fig 6 include any selection cuts (pt, eta, deltaR) and efficiencies? If yes, the assumption should be described in the text. If not, this should be clearly stated in the caption.

5) Page 17 qualitative explains why we would expect backgrounds to be low and how such a search could be performed. However, it does not attempt to estimate these backgrounds. It is therefore not clear if the assumption of negligible combinatorial backgrounds is correct.  In particular, note that there is a sizable rate of quarks/gluons being misidentified as hadronic W-bosons. Looking at ATL-PHYS-PUB-2023-020, for a signal efficiency of 50% the misidentification rate is still about 1%. Given the large rate of jets at the LHC, this could cause a substantial background.  I strongly suggest obtaining some quantitative background estimate to validate this assumption using established tool chains, for example using Madgraph / Pythia / Delphes.

5) In Fig 8 you show the expected sensitivity. Do I understand correctly that this is obtained directly from Fig 6 by requiring at least 3 events or so, so using the explicit assumption of vanishing backgrounds and 100% signal efficiency. If yes, that should be clearly stated in the caption/text.  Since you didn't actually show that these backgrounds are indeed negligible, it is not clear if those results are actually correct.

6) Fig 12 shows sensitivity results. Do I understand correctly that these again assume negligible backgrounds and 100% signal efficiency? As before, estimating the sensitivity requires a background estimate and should include efficiencies.

7) The result figures consider a very light ALP, around GeV masses. Why was this chosen, in comparison to, for example, weak scale mass ALPs?  Please clarify.

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Model-building creativity
Comprehensiveness
Supplementary details, extensive bibliography

Treatment of ALP EFT
Discussion of experimental backgrounds and complementary ALP searches

The manuscript "ALPs & HNLs at LHC and Muon Colliders: Uncovering New Couplings and Signals" considers an extension of the Standard Model featuring two types of new particles: heavy neutral leptons that mix with the neutrinos of the SM, and axion-like particles described by an effective field theory. If the two particles couple to each other, HNLs can be produced via off-shell ALPs at the HL-LHC and future muon colliders. The subsequent decays of the HNLs then give rise to distinctive signatures that can be used to search for the ALPs.

The article is quite lengthy with many detailed explanations and an extensive bibliography. Given that the goal is to fill in some additional details to a previous study of this model, this is not unwelcome. Nevertheless, there is a risk that the reader loses focus. It might help to state the goal and the main findings of the study more clearly in the introduction and to introduce the main processes and signatures at an earlier point in the paper, so that the reader can distinguish relevant from supplementary information.

The analysis itself is detailed and thoughtful and the results are interesting. I could imagine that these kinds of models and signatures will be an attractive target for future searches at the LHC and beyond. The paper therefore can potentially be published in SciPost. However, the following points need to be addressed first:

1) The authors seem to take a lot of the motivation for their study from the fact that assuming comparable Wilson coefficients for different fermions in the EFT approach, ALPs will couple dominantly to the heaviest fermions. However, for this argument to be convincing, the authors should demonstrate that indeed similar Wilson coefficients are generated for the different fermions in plausible UV completions. For SM fermions this can be motivated through the assumption of minimal flavour violation. But how do the HNLs feature in this argument?

2) I am not convinced by the way how the authors treat the loop-induced couplings to SM gauge bosons for the case of ALPs coupled to SM fermions. These couplings arise through one-loop diagrams, which have a complicated dependence not only on the centre-of-mass energy, but also on additional mass scales, such as the mass of the fermion in the loop or the momentum transfer to additional gauge bosons radiated from the virtual fermions. It is not possible (probably not even for an order-of-magnitude estimate) to estimate these effects using RGE-induced effective couplings to gauge bosons, which have no dependence on the kinematics. The authors need to clarify the approximate nature of their treatment and quantify the resulting uncertainty.

3) I find the claim that the signature is without background at $3\,\mathrm{ab}^{-1}$ very bold. This seems plausible for the case of same-sign leptons, but for the opposite-sign leptons, there will be a smooth SM background, on top of which a peak has to be identified. I would encourage the authors to demonstrate more explicitly, that the SM background is small in the kinematic regions of interest.

4) The authors discuss that decays of on-shell ALPs are not strongly constrained for ALP masses between 0.1 GeV and 10 GeV. This is broadly correct right now, but will it remain true until 2040? In other words, is there really no chance to directly detect on-shell ALPs in this mass range on similar timescales? Presumably both the HL-LHC and a muon collider should have some sensitivity, as will other experiments. Is it really easier to search for the ALP in the decay of HNLs compared to direct production from SM particles?

5) Is it actually possible (using for example angular correlations) to distinguish the case of HNL production via ALPs from other scenarios? Or can the ALP only be identified in the scenario with two HNLs?

6) The numbers in table 2 require a choice of $c_N$, which is however not stated prominently in the text.

7) What does JALZ stand for? If it's just a different way of writing $j4\ell2$, I would much prefer the latter for clarity.

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