A Final Word on FCNC-Baryogenesis from Two Higgs Doublets

The paper has been somewhat improved with respect to the original submission, but still does not give all the necessary details and overall seems to lack scrutiny. Several of the points raised in my first report are addressed in an unsatisfactory manner. Concretely:

- Refs [3-11] (previously Refs [3-5]) : the list is somewhat more comprehensive now, but really does not justice to the experimental efforts. The text says "measurements of the Higgs Lagrangian" so one should expect first of all the citation of the relevant experimental papers and only second the theorists' fits. This may seem like a minor point, but I see no justification for ignoring the ATLAS+CMS Run 1 combination paper at this point.

- Eq. (1) is duplicated in eq. (9) (previously eq. (8)): I would buy the argument about "fast browsing" in a long review, but not in a ~10 pages article. This is only a stylistic point, but eq. (9) would better be integrated in the text, with reference to eq. (1).

- Constraints on the parameter space mentioned in the two paragraphs after eq. (10): these explanations are completely insufficient. It has to be explained clearly and unambiguously how these constraints are applied (or derived, in case of c_gamma) . Since this was also criticised by Referee 1, I do not go into further detail here.

- Cross sections in Table 2: the visible cross sections of tth, tZ+jets and tWZ are of comparable size, so it is not true that tWZ is subsubdominant. Moreover, the largest single contribution is taken at NLO while smaller contributions are taken at NNLO. This has to be justified (or improved).

- My biggest concern is still the usage of the standard CMS Delphes card for the reinterpretation of the CMS 4 top analysis without any proof that this actually allows to reproduce the results of the CMS analysis with good enough precision. Such a reinterpretation without any validation is simply not acceptable.

- A constraint on rho_tt is now given in the last paragraph of Sec. 4, but only hand-waving arguments are given regarding the consequences of non-zero rho_tt. It is not clear at all how the bounds derived in this study would change both rho_tt and rho_tc were relevant.

All in all, the conclusion from my first report that much more detail and care would be needed to make the paper suitable for publication still holds. The journal's acceptance criteria are not met by this study and I therefore cannot recommend it for publication in SciPost Physics.

The authors have partially addressed my comments and criticism. I copy
below my original report with their replies and my new comments,
marked by `-->'.

# 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.

--> I understand that there is NO motivation for this weird choice of rho_ij,
but just call it "rho_tc-EWBG". The added discussion at the end of
Sec. 4 is interesting, but does not go very far.

# 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.

--> It is positive that the authors have added (now) the checks for
perturbativity, positivity, unitarity and electroweak precision data.
The explanations concerning the Higgs signal strength measurements,
however, remains vague. There are public tools such as Lilith or
Higgssignals that facilitate such a test. This has not been done here,
and how their bounds on c_gamma have been derived remains
unclear. Furthermore, the authors still have not checked whether the
BSM Higgs searches have an impact on their parameters (except the
particular channels analysed).

# Fig. 1 (now Fig. 2):

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.

--> Fig. 2 still suggests that the "preferred range" is already
largely ruled out, which is not discussed (apart from some general
statements on the top of p. 5.)
A minor point: why is mH+ = 300 GeV chosen for Fig. 2, but 350 GeV for
the other figures?

# "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.

--> As for previous items the authors make some "general statements",
but not very substantial ones. It would be interesting to know what
the more detailed results of the checks mentioned here have been.
The role of the CKM matrix has also not been clarified.

# 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.

--> I still fail to see the motivation for their choices. The authors
also have not included their "explanations" into the text.

# Fig. 4 (now Fig. 5):

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.

--> The paper gains with the extended discussion of CRW. Still the
fact that for mH+ = 350 GeV nearly the full parameter space is
excluded, or who the relevance of this exclusion scales with the mass is not clearly discussed.

# 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.

--> The authors now at least included "twiki:" into the reference (now [96]),
which besides that solely consists of the title of that twiki page,
but without any URL. The accessibility of the URL depends on the
details/configuration of the pdf reader.

In summary, the analysis lacks motivation (the authors do not provide any for only considering rho_tc, which looks completely artificial) and partially also the rigorousness I would expect for a published article.