Vector-like quarks: status and new directions at the LHC

Dear Editors,

We thank the Referees for valuable comments on the manuscript. We have replaced the manuscript on the arXiv addressing the comments raised by the Referees. We provide our detailed response to the specific comments below:

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Regarding points 1 and 2:

They are indeed typos and have been corrected.

Regarding point 3:

The negative numbers in Figs. 2 and 5 are actually meant to be taken as such, because what we are plotting is the contribution of the signal plus the interference between the signal and the background. Clearly, after adding the contribution of the background the overall cross-section is positive. We find that this way of presenting the results of the simulation is clearer, since it indicates where the presence of the signal leads to a decrease of the overall cross section.

We explain this fact in section 2, when discussing the definition of $\delta_{SB}$, as well as in the fourth bullet point in section 3. See also footnote 7.

In the figures, we used the symmetric mixed log-linear scale (symlog) in the y axis, which scales logarithmically in the positive and negative quadrants for absolute y values larger than a given threshold, and linearly between those values, crossing 0. We briefly describe this behaviour in the revised caption of Fig. 2.


Regarding point 4:

We added a comment on the width of the scalar at the end of section 3. Notice that, for the models at hand, the widths of the scalars are generically narrow.

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Regarding point 1:

We reported the background cross-sections because in the plots we only display cross-section ratios. For this reason, the numbers for the background cross-sections serve as a baseline to understand the actual values of signals' cross-sections.

The cuts are loose because we want to show the theoretical cross-sections before any selection or kinematical cuts, and show also how the ratios behave for varying mass and total widths of the VLQ.

The divergence is regulated only by the pT cut, and not by the dR cut due to the non-zero bottom mass, so the dR cuts won't affect our results. This is reasonable to expect since we are not looking at two jets or two bottoms coming from gluon splitting in the final state. The jet is always spectator, the bottom (when there is one) is always coming from the other parton. Consequently, they do not have a small dR between them as they go in opposite directions. The other bottom from gluon splitting participates to the hard scattering and the bottom which appears in the final state is nearly central because it comes from the T decay.

We wrote all the cuts to allow readers to fully reproduce our results if needed. On the other hand, dRjj has been written by mistake, indeed there are no processes with two jets in any final state. We have removed it from the text.

In the main text we wrote why we reported the background cross-sections following the argument above, in the sentence leading to footnote 4, where we also mentioned the importance of the pT cut to avoid divergences.


Regarding point 2:

The gg -> S0 -> Tt process has two suppressions: 1) as the Referee correctly noted, it's loop induced but 2) it goes through off-shell S0, since we assume S0 to be lighter than T, as we mentioned in Eq.(11) and the sentence below it. In our analysis we indeed always scan over the branching ratio of T > S0 t and not viceversa. For this reason this process is more and more subdominant as the mass gap between T and S0 increases. In the composite Higgs models, S0 arises as pNGBs, and therefore it is reasonable to expect that they are lighter than the VLQs. However, in the context of generic models, such as 2HDM, it would be interesting to consider the limit where S0 is heavier than T, but this is outside the scope of our analysis. Furthermore, this process has a different final state than all the other single T production that we consider, which always have a forward jet.

Nevertheless, we numerically evaluated the one-loop process to prove our arguments and indeed we found that for BR(T->tS)=0.5 and width/mass=0.01 and 0.1 (the two benchmarks in Fig. 5) the cross-section for pp -> S0 -> Tt is of order 0.1 ab and 1 ab respectively, much smaller than any of the other processes. We also checked the case of BR(T -> tS)=1, where processes mediated by SM particles are not even possible, and the cross-sections are still of order 0.1 ab and 1 ab respectively, which are tiny.

We wrote a footnote in page 9 justifying why we neglect this process according to these arguments.

Thus, within the above criteria, the cross-sections in Fig. 5 (black curves) still show the maximum at BR(T->S0t)=1/2.

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We hope that with the clarifications provided to the issues raised by the Referees and the changes incorporated in the text, the manuscript can now be considered for publication.

Sincerely,
Avik Banerjee
(on behalf of all Authors)

Point by point list of changes in the revised manuscript:

1. Typo corrected in Fig. 1.

2. Typo corrected on page 5, the paragraph starting with "The effects of": m_t \lesssim 2 TeV is modified to m_T \lesssim 2 TeV.

3. Clarification added regarding the use of symlog scale in the caption of Fig. 2.

4. Comment added at the end of section 3 (last paragraph of page 11) on the width of the scalar.

5. Clarification added regarding the background cross-sections in the sentence leading to footnote 4.

6. Typo corrected and more clarifications added in footnote 4.

7. Footnote 6 added in page 9.

8. References updated.