1. Author have taken almost all relevant backgrounds for "b W^+W^+W^-" 3lepton signature, except "t t-bar" one: naively this background would lead only two di-lepton signature, however the third lepton could come from as "fake" one or from b-quark decay: the probability for this lepton is very low - 0.1% - 0.01%, but as we know the tt-bar cross section is huge. So this background can be easily the leading one for the "b W^+W^+W^-" signature. It should bec checked or at least roughly estimated.

Thank you for pointing this out to us. We have now added the contribution from ttbar+jets background in Table 2. The discovery and exclusion limits have become a bit milder. The modified numbers are given in the second last and last paragraph of Sec.3. Correspondingly, Figures 4 and 5 are also modified.

1. I believe that title of the paper is too ambitious -- the paper is well addressing problem of probing of the parameter space only within the framework of 2HDM at the LHC, within the framework of more general/different model the limits in |\rho| and |c_\gamma| would be not necessarily correct or relevant.I think this should be clearly stressed in the conclusions and possibly in the title.

We have modified the title and the last paragraph of Sec.5 to reflect this point. In addition, we have added discussions at other places and a new figure (Fig.1) as suggested by Referees 1 and 2.

• Introduction and section 2:

• As also critisized by the first referee, the model is not motivated well in the paper, nor is the considered parameter space. The reader is left to search the previous literature for details. The relevant references are mentioned throughout the text, but no consistent overview of the previous literature leading up to this work is given. The couplings lambda_ii and rho_ij are introduced completely ad hoc in the introduction; while some explanation comes in section 2, one has to make an effort to piece things together while reading.

We have now modified the introduction regarding our motivation. We have treated the extra Yukawa couplings as independent parameters and turned off all rho_ij couplings except for rho_tc for all practical purposes throughout the paper. We have also added discussions in the last paragraph of Sec 4 on the impact of turning on other rho_ij couplings.

• Refs [3-5] are an extremely selective list of theorists' fits of the Higgs couplings. There exists a vast literature on this subject, most of which is ignored here. Moreover, and perhaps more importantly, dedicated measurements of the Higgs couplings have been published directly by ATLAS and CMS.

We have added a more comprehensive list of Run2 analyses.

• Eq. (1) is duplicated in eq. (8).

We are aware of this, but in the interest of fast browsing we find this duplication useful.

• It is not clear what are the actual constraints on rho_tt, and what are the consequences for this study if both rho_tt and rho_tc are relevant.

We added a discussion regarding this in the last paragraph of Sec.4.

• Section 3

• "For b-tagging as well as c-jet and light-jet rejection, we rely on Delphes" is too vague. The standard ATLAS card can change over time, so details on the assumed reconstruction efficiencies must be given, and not only for (b)jets but also for lepton ID. The same is true for extra jets: details on the matching and merging parameters are necessary.

We now mention the version of Delphes in its first instance i.e. second paragraph of Sec 3. We also mention now that we have used the default ATLAS Delphes card for b-tagging and light-jet rejection in the same paragraph.

• Cross sections in Table 2: while it can be justified to compute sub-leading contributions at lower order, this needs to be justified and explained properly. "for simplicity" is not good enough.

We have accounted for the NLO (or NNLO) correction factors for all leading and subleading backgrounds. Only the subsubdominant backgrounds tWZ and ZZ+jets backgrounds are taken as LO, not because of simplicity, but because their experimental impact is unlikely to be detemined by QCD corrections. In addition, for all dominant backgrounds we have considered up to one additional jet in the final state. The number of additional jets are restricted to one for the different backgrounds due to coputational limitations.

• How many events were actually generated?

For all signal and background events for both the charged and neutral Higgs processes we have generated "at least" 100k events. We have further made sure the number of surviving events after application of selection cuts are statistically significant.

• Run 3 and HL-LHC reach: to what extent are the efficiencies of the standard ATLAS Delphes card appropriate for HL-LHC simulation?

Indeed such standard ATLAS Delphes card would likely be modified for HL-LHC. However as a first attempt we have utilized the current ATLAS based Delphes card of Delphes 3.4.2 for HL-LHC. A sizeable effects could be through the b-tagging rate combined with pile-up subtraction, but we admit that we really have no idea how to estimate this.

• What about pile-up?

We have not considered pile-up in our analysis. Both the processes have leptonic final state and we expect the HL-LHC pile-up effect should not impact our results decisively (beyond the single b-tag).

• Section 4

• Same concerns as above for standard CMS Delphes card and details on the event generation.

Again we adopted similar strategy and used default CMS based detector card of Delphes 3.4.2.

• The CMS 4 top analysis has been reinterpreted with MadAnalysis5 in Phys.Lett.B 784 (2018) 223 [1805.10835]. There, a specific Delphes card was developed to reproduce well the CMS results. This was for 35/fb of integrated luminosity, but an update of the recast code (and appropriately tuned Delphes card) are available also for the 137/fb version, see https://madanalysis.irmp.ucl.ac.be/wiki/PublicAnalysisDatabase While these recast codes consider only the signal regions of the CMS analysis but not the control regions, the fact that a specific tuning was necessary raises severe doubts about the validity of using the standard CMS Delphes card in the present work. How has this been validated? Details on this must be explained and the accuracy of the reinterpretation demonstrated.

We are aware of issues regarding the analysis of Ref.[100] (in current version). We would like to draw your attention to the acknowledgment. We indeed had to seek internal help and private communication for the details of the selection criteria mentioned in Eq.(19). Eq.(19) is not clearly mentioned not only in Ref.[100] but also its predecessor with up to 2016 data (Eur. Phys. J. C 78, 140 (2018)). As a first attempt we have not validated different control and signal regions of Ref.[100] and simply utilized default CMS based detector card of Delphes 3.4.2 in our analysis. This is primarily due to this reason we advocated a dedicated same sign-top search in the current manuscript and in Refs.[33,102].

• The same-sign top search is a crucial for this work. Why is it relegated to the appendix? Again, relevant details are not explained.

While it indeed can probe the parameter space for |rho_tc|, however, the process has very mild dependence to c_gamma. However we have now elevated the appendix to the main text and with details of cut based analysis as suggested.

• Given the very strong conclusions about ruling out the model under investigation, the impact of the uncertainties mentioned in the last paragraph before the conclusions should be quantified.

We had already briefly discussed on systematics however leave out a detailed analysis for future.

In conclusion, while the study is interesting in principle, much more detail (and care) is needed to make the paper suitable for publication. I actually have more comments on the paper, but given the shortcomings listed above I refrain from going into finer details in this iteration.

• General remark: for the sake of reproducibility, the MadGraph model (UFO) file, all the Monte Carlo settings for the event generation (i.e. the MG5, Pythia, Delphes cards) and the analysis codes should be made public on an appropriate versioned and citable open-access repository, for example Zenodo. Ideally, this would be supplemented moreover with the numerical results (event counts) of the simulations.

Thank you. We indeed maintain a twiki page for the neutral Higgs processes such as cg > tA/tH > t t cbar for experimental usage. There indeed is a UFO file which is validated with an existing 2HDM model in FeynRules model database. The link is given below. We chose not to advertise it in the current paper since the charged Higgs processes are not incorporated into the UFO yet.

https://twiki.org/cgi-bin/view/Sandbox/FlavorChangingNeutralHiggs

model definition:

The potential is defined in eq. (4) and the couplings to fermions in eq. (6). It remains unclear what are the input parameters of the model. The various choices of the rho matrices have to be deduced from information scattered over the article. The choide of the elements of the rho matrices appears fully ad-hoc to satisfy experimental constraints. Is there any underlying model that would produce such a extremely weird pattern that the authors employ?

Our primary focus is to probe the parameter space required for rho_tc-EWBG. For practical purposes, we have turned off all rho_ij couplings except for rho_tc. We have added a discussion in the last paragraph of Sec.4 on the impact of turning on other rho_ij couplings. The dynamical parameters in the 2HDM potential would be subjected to constraints from perturbativity, positivity, unitarity, and oblique parameters. We have now added discussion regarding this in the first paragraph of page 4.

checks on the model parameters:

There is hardly any information on the checks performed. The authors mention in passing perturbativity, positivity, unitarity, and electroweak precision data. It remains completely unclear what the effects of these are on the model as such and on the particular parameter choices the authors make. Completely absent seem to be checks for the properties of the SM-like Higgs boson at 125 GeV, as well as checks for the BSM Higgs searches for the additional Higgs bosons (except the particular channels the authors are analysing later).

We have added discussions and parameter scans (see Fig.1) for the allowed parameter space by perturbativity, positivity, unitarity, and electroweak precision data (checked via 2HDMC). As we turn off all rho_ij couplings, and given that rho_tc does not enter the Higgs signal strengths at tree level, the impact is minimal. However the mixing angle c_gamma would receive some constraints via hZZ, hWW etc. vertices. We had already checked that the chosen c_gamma range [0.1,0.3] is allowed by Higgs STXS measurements. We now added discussion in second paragraph of page 4.

Fig. 1:

What is the point in showing it for MH+- = 300 GeV and 500 GeV? The only difference seems to come from Bs-Bsbar mixing. What are the other relevant parameters here? How do they influence the excluded regions? Furthermore, it appears that the searches for t -> ch can rule out the scenario under investigation in the (near?) future. The authors do not comment on this.

The plots for mH+ = 300 and 500 GeV are chosen for illustration. Along with the B_s mixing, the reach of cg > b H+ > b h W+ process is also different for the respective masses. In the previous version we inadvertently put the wrong 2sigma contour for the HL-LHC exclusion from cg > b H+ > b h W+ process in the left panel of Fig.4 (previous version). Please see the modified left panel Fig.5 in the latest version for comparision. We have added the projected HL-LHC reach for the t > ch decay, including comments in the first paragraph of page 5.

"usual" BSM Higgs production and decay modes:

The authors are investigating solely the channels they are interested in. However, there should be some "usual" channels, such as gb -> tH+-, H+- -> tb, which may be suppressed (because of the weird and unmotivated choice of rho^U,D), but via CKM mixing they should still play a significant role. The authors do not comment on this.

Indeed, due to our choice of parameters such processes are not relevant and we have checked the constraints from searches such as gb -> tH+-, H+- -> tb are well within the experimental reach with our choice of parameters. We added discussions regarding this in the last paragraph of Sec 4.

Calculation of signal and background:

Some channels are calculated at NLO, others at LO, which in particular seems to include the signal channels. Why? I do not see any motivation for this from the physics point of view.

For the charged Higgs production cg > b H+ > b h W+ we have normalised our LO background cross sections upto NLO (at least) for all backgrounds, except for the SM tWZ background which is subsubdominant. Same is true for neutral Higgs production cg > tA/tH > t t cbar. In addition, we have considered at least one additional jets in the final state for all dominant backgrounds and signals. However, a full estimation of QCD corrections for the signal processes is beyond the scope of the current paper. Therefore we believe our discovery and exclusion contours are conservative.

Fig. 4:

It seems that what the authors label "CRW" alone is already excluding a lot of the allowed parameter space, so this should be looked at first, since it is an existing limit. Also this channel, which is not in the main focus of the authors, seems to be able to rule out their scenario with future LHC runs. Again this is not discussed.

The cg > tA/tH > t t cbar process can indeed probe a large part of the parameter space for |rho_tc|. However, we re-iteriate that the c_gamma dependence is very mild in cg > tA/tH > t t cbar, as can be seen from Fig.5. It is solely for this reason we put discussion on cg > b H+ > b h W+ process prior to neutral Higgs production cg > tA/tH > t t cbar. We have elevated the discussion in the appendix and merged it into the main text. As mentioned in the previous version (see also reply for Referee 2) the CRW region of Ref.[100] is not optimized for the cg > tA/tH > t t cbar process. Therefore we advocate a simple dedicated search for cg > tA/tH > t t cbar process as discussed in Sec.4.

I do not include several smaller issues that I have, e.g. concerning citations, since the above issues are far more relevant. But looking at Ref. [84] I wonder whether the authors really read their article before submitting it.

We use its estimate of the NLO SM ttbarh cross section to determine the QCD correction factor for SM ttbarh background. We are not entirely sure what the problem is and why this has to be phrased in a rather unprofessional and not even funny manner.