Tetraquark-Jet Systems at the High-Luminosity LHC
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript reviews theoretical predictions of Fragmentation Functions of tetraquarks composed of heavy quarks, for which robust predictions can be derived within perturbation theory and nonrelativistic QCD, owing to the large masses of the constituents. These predictions are important for the interpretation of tetraquark candidates, and QCD dynamics more broadly, and will be possible to test in future colliders such as the Hi-Lumi LHC and EIC. The review is well-written, covers a substantial amount of material, with an extensive bibliography, and also presents some new and improved predictions in relation to existing literature. In particular, it provides a systematic discussion of the theoretical uncertainties of the predictions.
I recommend the manuscript for publication in its present form. Nevertheless, I have spotted a few minor issues that the author might want to correct in the final document:
1) In Fig. 5, I don't see any indigo arrows.
2) The acronym VFNS, appearing for the first time on page 5, has not been defined (in contrast to FFNS, which has been defined). I suggest that the author define and add VFNS to the list of acronyms starting on page 29.
3) Right below Eq. (17), there's a typo in the definition of the digamma function ("prime" rather than "\prime").
Author Response
We sincerely thank the Referee for the very positive assessment of our manuscript, for the appreciation of the technical and phenomenological relevance of the work, and for recommending its publication in the present form.
We also thank the Referee for spotting a few minor issues. We have carefully addressed each of them in the revised version of the manuscript, as detailed below.
1) Referee's comment:
“In Fig. 5, I don't see any indigo arrows.”
Response:
We thank the Referee for noticing this. The arrows were mistakenly described as indigo in an earlier draft. Their actual color is orange, and the caption has now been corrected accordingly.
2) Referee's comment:
“The acronym VFNS, appearing for the first time on page 5, has not been defined. I suggest that the author define and add VFNS to the list of acronyms starting on page 29.”
Response:
Done. The VFNS acronym is now properly defined at its first appearance and included in the list of acronyms in the Appendix.
3) Referee's comment:
“Right below Eq. (17), there's a typo in the definition of the digamma function (‘prime’ rather than ‘\prime’).”
Response:
We thank the Referee for spotting this typo. It has now been corrected in the revised manuscript.
Reviewer 2 Report
Comments and Suggestions for AuthorsVery good paper. Congratulations.
Note that Hi-Lumi is generally not used any more. Looking at the CERN site, the preference is for either High-Luminosity LHC or HL-LHC.
L37-38: "massless vector bosons mediating color interactions" needs to be set off from the rest of the sentence, perhaps with dashes, commas, or parentheses.
L54-58: this is mostly repeated in lines 74-79. The differences should be made clearer or the two revolutions should be mentioned closer together in the text and a distinction drawn between the two named revolutions.
L138: bottomoniumlike -> bottomonium-like
L211: insert "the" before "HyF"
L251-253: Sentence is unclear. What exactly is ~1/m_Q referring to in this sentence?
L370: molecularlike -> molecular-like
In some places you use "bottom states" and others you use "bottomed states." The former is preferable, as is consistency.
Author Response
Response to Referee 1
We warmly thank the Referee for the very positive overall assessment of our work, for the constructive suggestions, and for the careful reading of the manuscript.
All remarks have been taken into account, and the manuscript has been revised accordingly. Below we provide a detailed, point-by-point reply.
1) Comment:
“Note that Hi-Lumi is generally not used any more. Preference is for either High-Luminosity LHC or HL-LHC.”
Response:
We thank the Referee for this clarification. All occurrences of Hi-Lumi have been replaced with High-Luminosity LHC or HL-LHC, depending on the context.
2) L37–38:
“‘massless vector bosons mediating color interactions’ needs to be set off from the rest of the sentence.”
Response:
Corrected. The phrase is now isolated with a em dash (—) to improve readability.
3) L54–58:
“This is mostly repeated in lines 74–79. The differences should be made clearer or the two revolutions mentioned closer together.”
Response:
We thank the Referee for this useful remark. We have rewritten the relevant passages to avoid repetition and to clarify the distinction between the two historical milestones. The revised text now presents the Quarkonium Revolution,'' the Second Quarkonium Revolution,'' and the subsequent ``Exotic-matter Revolution'' in a single, coherent block, ensuring conceptual continuity and eliminating overlap.
4) L138:
“bottomoniumlike -> bottomonium-like”
Response:
Corrected.
5) L211:
“insert ‘the’ before ‘HyF’”
Response:
Done.
6) L251–253:
“Sentence is unclear. What exactly is ~1/m_Q referring to?”
Response:
Thank you for spotting this. The sentence has been rewritten for clarity, now explicitly stating that $m_Q$ is the the heavy-quark mass.
7) L370:
“molecularlike -> molecular-like”
Response:
Corrected.
8) Consistency between “bottom states” and “bottomed states”
“The former is preferable.”
Response:
All occurrences have been harmonized to bottomed states throughout the manuscript.
Reviewer 3 Report
Comments and Suggestions for AuthorsReport of the Referee
Manuscript Ref.: Universe-4025372
Title: "Tetraquark-jet systems at the Hi-Lumi LHC"
=====================================================
The author presented a comprehensive review on the production of tetraquark-jet systems in high-energy hadronic collisions at the LHC and their relevance to multiquark dynamics in QCD. The manuscript discusses the production of tetraquark systems in proton-proton collisions, using a hybrid factorization approach that combines BFKL resummation with the collinear dynamics of QCD. The cross section for tetraquark production is derived in two steps, using high-energy factorization and matching with the colinear factorization description. In particular, the TQ4Q1.1 set of collinear FFs for fully heavy tetraquarks have been explored. High-energy logarithm resummation is incorporated, resulting in a unified description valid across different energy regimes. Numerical results are presented for different spin channels of tetraquarks, with comparisons between hybrid factorization predictions and fixed-order results. The analysis shows that tetraquark production is stable and sensitive to high-energy dynamics, especially at HL-LHC energies.
In my opinion the calculations and discussions presented in the paper are of great interest in the research area of exotic QCD states production in hadron-hadron collisions at the LHC. The paper is very well presented and the references are adequate. The topic is hot and of interest for the researchers studying heavy meson/barion production. The subject of the manuscript is relevant and the quality of the paper corresponds to the level of the journal “Universe”. The manuscript is well-written, presenting ideas and methods clearly and analyzing the results thoroughly.
I do not have suggestions for substantial changes. The manuscript can be published in its current form.
Author Response
We sincerely thank the Referee for her/his careful reading of our manuscript and for the very positive and encouraging evaluation. We are grateful for the appreciation of the relevance of our study to the research area of exotic QCD states and for highlighting the clarity of the presentation, the adequacy of the references, and the broad interest of the topic for the heavy-meson and heavy-baryon communities.
We are also pleased that the Referee finds the manuscript well-written and appropriate for Universe, and we warmly acknowledge the recommendation for publication without modifications. The Referee’s remarks reinforce our commitment to providing high-quality and comprehensive studies for the phenomenology of fully heavy multi-quark systems.
