Hadronic Molecules with Four Charm or Beauty Quarks

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

General: 

It is unclear why the paper has been kept so brief, as this brevity sometimes results in unclear explanations of the findings. Many details regarding the calculations and numerical evaluations are omitted or not sufficiently explained, with the authors quickly jumping to conclusions about the existence or non-existence of molecular states.

As a result, the conclusions and remarks in various subsections can be obscure, lacking the necessary context and details for a deeper understanding. Without sufficient guidance, readers may struggle to grasp the details and fully comprehend the methodology that leads to the given conclusions.

My general recommendation is to expand on the conclusions presented in subsections 2.1, 2.2, and 2.3, as well as in section 3. Providing more detailed discussions and justifications for the findings would enhance the clarity and impact of the paper.

 

Abstract:

L1: formalism +TO+ study

L3: can only be → are

L4-11: rephrase as follows reducing the length of the sentences: We solve the coupled-channel Bethe-Salpeter equation to derive two poles in the bb\bar{c}\bar{b} system and two poles in the cc\bar{c}\bar{b} system. There are also four charge-conjugated poles in the\bar{b}\bar{b}cb and \bar{c}\bar{c}cb systems. In the bb\bar{c}\bar{b} system, one pole corresponds to a sub-threshold bound state when the cutoff momentum is set to L > 850 MeV. The other pole in this system corresponds to a sub-threshold bound state when L > 1100 MeV. In the cc\bar{c}\bar{b} system, the two poles correspond to sub-threshold bound states only when L > 1550 MeV and L > 2650 MeV. This makes them difficult to identify as deeply-bound hadronic molecules. We propose investigating the two poles of the bb\bar{c}\bar{b} system in the mu^+mu^-B_c^-​ channel at the LHC.

 

Main text:

L16: Put some references, maybe some review articles like (Prog. Part. Nucl. Phys., 107:237–320, 2019, Rept. Prog. Phys., 86(2):026201, 2023) after molecular states.

L27: resolution → understanding of their nature

L31: remove -all-

L36: the relative lighter meson J/psi → a J/psi

L41-43: rephrase as: Our results indicate the possible existence of two bound states in the bb\bar{c}\bar{b} system, along with two charge-conjugated states in the \bar{b}\bar{b}cb system. However, their manifestation depends on the cutoff momentum, where they may appear as threshold effects.

L43-44: rephrase as : Both structures share the same spin-parity quantum number, J^P = 1^+, and can potentially be observed in the mu^+mu^-B_c^- channel at the LHC.

L55-58: it might be useful to highlight here why some of the assumptions needed to use this formalism are questionable. 

L64: remove -any more-. Or specify in which occasion it was used.

L76: what are the possible implications of setting this coefficient to zero?

L79: remove -that-

L97: would it be good that to highlight already here that the experimentally observed states are then good candidates to be tetraquark states? Or what you observe is just a possible feature of your model (see above the question about the formalisms being questinable)?

L95: does it mean that also the b\bar{b}b\bar{b} are not molecular states in your calculations? Might be better to specify it.

L100: instead of former, specify cc\bar{c}\bar{b}

L106: to be → is

L 106: Rephrase as: hence hadronic molecules in the PP sector are not expected to exist.

L108: coefficients are

Eq 14: instead of a comma put +and+
Eq 18: instead of a comma put +and+

Eq 20: instead of a comma put +and+

L121: coefficients are

Eq 21: instead of a comma put +and+

Eq 2: instead of the first comma put +and+ and instead of the second comma put a full stop.

L123: Start a new sentence, The relevant

L124: it would be beneficial to extend more on the discussion on why the existence of hadronic molecule is not supported

L146: remove -the- before virtual states

L148: remove -actually-

L148 and at L 150: remove -only-

L150-151: it would be better here to clarify and expand what the existence of hadronic molecules is not supported

L154: also here it would be nice to expand on why you can make those conclusions based on some L values. The full paragraph from L 145 to L158 should be explained in more detail.

L160: remove -systematically-

L165: put a full stop after closing the bracket

 

 

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The reviewed paper by Wen-Ying Liu and Hua-Xing Chen presents study of heavy-flavour meson-meson interaction, considering the exchange of ccbar, bbbar, and cbbar pseudoscalar and vector mesons. After a brief introduction about the status of the field, the authors describe the calculations performed in the local hidden gauge formalism, in order to search for poles in the molecular systems formed by 2 heavy-flavour mesons. No poles are found in the fully charm system (c-c-cbar-cbar), while two poles are found in the b-b-cbar-bbar system and two in the c-c-cbar-bbar system (plus four in the charge conjugates of these). The poles in the c-c-cbar-bbar system however only for very high value of the momentum cutoff, therefore these results do not support the existence of deeply bound molecules in this system.

I would like to congratulate with the authors for the very interesting calculations presented in this paper that are surely important for the field. The method presented in this paper is solid and it is well described. In general I recommend this manuscript to be published in the Universe journal, however I have a few minor comments that should be addressed before the publication:

- line 94: here you mention that the b-b-bbar-bbar system can be similarly investigated. Does this mean that also in that case the interaction is vanishing and therefore no molecules are expected also in the fully bottom system? If so, please add a comment in line 97.

- Figure 2: enlarge the size of the text in the figures (axis labels, legends, etc) which are very small and difficult to see

- line 180: here you comment about heavy-meson and light-meson exchange, could you please also comment about the heavy-light systems? Is this formalism applicable in that case?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In the paper is done a systematically study the fully heavy meson-meson interactions looking for possible bound states. The authors found two heavy hadronic molecules suggesting channels to confirm the existence of such states.On the other hand they do not find any other molecules. The results obtained are consistent with the exchange heavy meson Bc* as was pointed out before in a previous study. The paper is very interesting, doing a carefully study well presented and can shed ligth to the formation of heavy mesoon-meson molecules.

   I recommend the publication

Author Response

Thank you very much for your valuable review of our manuscript and for acknowledging our work.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I was very happy to see that the received comments had been properly implemented and helped improve the paper and the delivery of the physics message. I found that the added text and explanations improved the readability and the discussion of the physics message. 

i have no further comments on the manuscript. 
Congratulations to the authors.