Quantum collider probes of the fermionic Higgs portal

This paper studies NLO corrections to off-shell Higgs production in the ZZ channel, and to double Higgs production from a dimension-5 fermionic Higgs portal operator. It also compares the sensitivity of tree-level VBF pair production of the new fermions, through an off-shell Higgs. The studies are performed in the context of the future HL-LHC, HE-LHC and FCC colliders.

The authors are requested to provide clarifications and additional results on the following points, before the manuscript can be considered for publication:

1. The primary results are shown with a cut-off scale of f=3v. However, as the authors emphasize, the high-energy tails of the relevant kinematic distributions provide the dominant sensitivity to the new operators. Furthermore, for the HE-LHC and FCC, the authors consider invariant mass values of 1000 GeV and 1500 GeV, which are much larger than 3v. Hence, the EFT analysis is not valid in these kinematic regimes. Proper event-by-event kinematic conditions must be imposed to ensure the validity of an EFT analysis at an hadron collider.

2. In order to ensure renormalizability, the authors needed to introduce two other dim-6 SMEFT operators. But from the discussions, it seems often these operators drive the sensitivity. How is then the analysis a direct probe of the dim-5 Higgs portal operator? The results can remain the same even if the Wilson co-efficient of the dim-5 operator is zero at high scale, and those of the other two operators are non-zero.

3. Often very aggressive values of systematic uncertainties are considered. Please use values that are supported by the analyses of the experimental collaborations, and show results for at least two choices each, one conservative and another somewhat optimistic.

4. Because of the above concerns regarding the validity of the EFT analysis, the authors are requested to redo the analysis in a simple s-channel UV-completion of the dim-5 operator in Eq.(1). The simplest possibility would be to consider an SM singlet scalar mediator coupled to both the |H|^2 operator and the new fermion bi-linear. Please compute the relevant NLO corrections to the considered processes in this model, and then compare it with the EFT results by using a mapping of the EFT and simplified model parameters. In this way, we can know when the EFT analysis is actually valid and when it begins to fail. That would be an useful addition to the literature, since at the NLO level such comparisons are not often found.

While interesting t-/u-channel UV completions are also possible, they require a fermion mediator with the same electroweak charge as the SM Higgs field, thereby requiring more work in the renormalisation of the theory. These latter UV-completions will also generate additional dim-6 operators.

5. Finally, the authors are requested to compare the size of the NLO corrections from the new physics operator, with the higher order QCD and QCD-EW corrections from the SM for the studied processes. Are there any features in the kinematic distributions which distinguish these two contributions?

The paper "Quantum collider probes of the fermionic Higgs portal" by Haisch and collaborators provides a summary of the sensitivity of different collider processes to a fermionic Higgs portal. The work is complete, scientifically sound, and detailed. It provides a good contribution to the ongoing BSM efforts pursued at the LHC as well as an outlook towards future colliders. I recommend publication in SciPost.

The present manuscript investigates how upcoming hadron collider experiments can constrain the fermionic Higgs portal, specifically when new fermions are not directly observed in exotic Higgs decays. The study assesses the reach of the HL-LHC, HE-LHC, and FCC for off-shell Higgs and double-Higgs production. Their findings show that quantum-enhanced indirect probes offer the best sensitivity. While the paper is worthy of publication, certain aspects would benefit further refinement for publication.

1) Please comment on the validity of the EFT analysis of Eq. 1. In particular, I observed that Eq. 26 introduces terms scaling as $c_\psi^6$ at the cross-sectional level for double Higgs production. It appears that these terms dominate the new physics contributions rather than the lower-dimensional ones.

2) In this context, what is the rationale behind including only the two dim-6 operators in Eq. 4? Considering that the final calculation accounts for significantly higher-order terms in the EFT expansion, what motivates the specific choice to limit the inclusion to these two operators?

3) Considering the chosen cutoff for the theory (f=3v), there seems to be a lack of justification for the upper range of the $m_{4l}$ analysis, specifically including events up to $m_{4l}=1$ TeV for the HE-LHC and $m_{4l}=1.5$ TeV for the FCC.

4) On page 11: "The inclusion of higher-order QCD corrections furthermore reduces the scale uncertainties of DS by a factor of about 3 from around 7.5% to 2.5%." Please provide more details on how these scale uncertainties are derived.

5) Regarding Fig. 5, it would be beneficial to assess the size of the threshold contributions at $2m_\psi$. Hence, I recommend extending the plot and/or using different masses for illustration to enhance clarity in this aspect.

6) What is the rationale for setting the renormalization and factorization scales to $2m_h$ for the double Higgs simulation, as opposed to the more common practice in the literature of dynamically varying them with theoretically motivated scales?

7) What justifies the systematic uncertainty of 4% for the ZZ analysis? The referenced work (Ref. [27]) presents results in two scenarios, 8% and 4%, recognizing them as challenging targets (refer to page 9 of the same reference). Similar to Ref. [27], it would be beneficial to display the uncertainties in two scenarios: a more aggressive 4% and a more conservative 8%.

8) For the VBF channel, a 1% systematic uncertainty is specified, a choice that appears too aggressive. It is advisable to align the systematic uncertainty with the experimental analyses.

9) The manuscript lacks a conclusion section. I recommend including such a section for a more structured presentation.