Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

File is attached.

Comments for author File: Comments.pdf

Author Response

We thank the referee for recommending the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

Review Report: Sfot dynamics associated with QCD-critical point and color superconductivity--pseudogap, anomalous delepton production and electric conductivity:

This is a well-written and comprehensive theoretical study investigating the soft mode dynamics associated with two important phase transitions in QCD: the QCD critical point (QCD-CP) and the two-flavor color superconductivity (2SC) phase transition. The authors employ the Nambu-Jona-Lasinio (NJL) model and linear response theory to systematically analyze collective excitations, pseudogap formation, and their effects on electromagnetic observables in relativistic heavy-ion collisions.

The paper presents a coherent and unified framework connecting fundamental aspects of QCD phase transitions to experimentally accessible observables. The authors successfully bridge concepts from condensed matter physics (para-conductivity, Aslamazov-Larkin diagrams) with heavy-ion phenomenology. The manuscript is suitable for publication before some clarifications and moderate revisions.

Q1: The calculations rely heavily on the NJL model with a three-momentum cutoff Λ = 631 MeV. How robust are the quantitative predictions (especially the critical exponents and magnitudes of enhancement) to variations in the model parameters? The authors vary GD/GS but keep GS and Λ fixed from vacuum properties. Could changes in the regularization scheme (e.g., proper-time regularization) significantly alter the results near the critical points?

Q2: The QCD-CP in the NJL model appears at T_CP ≈ 46.7 MeV, which is quite low compared to lattice QCD expectations (where the CP might not exist at all for physical quark masses). Does the low critical temperature affect the applicability of these results to realistic heavy-ion collisions? The authors should discuss how their conclusions might change if the CP were located at higher temperatures. 

Q3:The entire analysis is based on mean-field theory and the RPA. However,  in the introduction section it is mentioned by the authors that gauge field fluctuations may alter the 2SC transition from second to first order. The authors acknowledge this but proceed with the second-order assumption. Could you quantify or discuss how a weakly first-order transition would modify the soft mode behavior and the resulting observables? Would the divergences be cut off, and if so, at what scale? 

Q4: The expansion in Eq. (3.36) has a term c_S ω/|k|, which makes the soft mode non-analytic at the origin. The critical exponent for the conductivity along the crossover line is ∼ ϵ_CP^{-1} (Eq. 5.70). How reliable is this exponent given the non-analyticity and the fact that the expansion breaks down in the time-like region? Have you compared with other theoretical approaches (e.g., functional renormalization group) for the critical exponents?

Q5: The pseudogap shown in Fig. 5 is a striking result. However, the calculation uses a non-self-consistent T-matrix approximation (Fig. 3). Could self-consistency (e.g., including the self-energy in the propagators that form the T-matrix) significantly modify the pseudogap structure? In condensed matter, self-consistency often affects the pseudogap properties quantitatively. 

 

Minor issues and suggestion

1. The paper cites a large body of relevant literature. However, some recent works on the functional renormalization group approach to the QCD-CP (beyond Ref. [18,19]) and transport properties near critical points could be added for completeness.
2. Please check whether eq. 3.38 is correct?
3. Ithink in Eq. (4.42), the integral appears to be missing d^3k/(2π)^3 in the notation. Correct me if I am wrong

 

 

 

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf