{"id":"8146a54f-842c-40db-bf89-705060abbbba","arxiv_id":"2608.04236","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Using finite-temperature and finite-density QCD sum rules, the authors predict strong density-dependent mass reductions up to about 413 MeV for D*_s^- and decay-constant suppressions of about 70% for open-charm vector mesons.","lead":"This paper computes how the masses and decay constants of the charmed vector mesons D* and D*_s change inside hot and dense nuclear matter, using QCD sum rules. The main results are large density-driven softening of these mesons and new predictions for particle-antiparticle differences that future heavy-ion experiments at FAIR, NICA, and J-PARC could test.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline mass shifts (-413 MeV, -207 MeV) are largely imposed by the unvalidated continuum-threshold prescription of Eq. (23); a threshold-ansatz sensitivity check is required before the quantitative softening claims can be accepted as robust.","rationale":"The reader's weakest assumption — Eq. (23), the Hilbert-moment threshold scaling — is the same assumption I identify, so no verdict adjustment is needed. What makes it load-bearing is quantitative: at T=0 the condensate ratio of Eq. (13) drops to ~0.33 by ρ/ρ₀ = 3.3, and Eq. (23) converts that drop directly into a collapse of the continuum edge from 6.3 to ≈3.2 GeV², so the extracted pole mass, which tracks the Borel-weighted spectral integral bounded by s0, is largely forced to the reported negative shifts. The paper neither quantifies the sensitivity to the s0 scaling nor compares with alternative prescriptions used elsewhere in the in-medium sum-rule literature, leaving the headline numbers resting on an unvalidated modeling choice. Under the review rules I additionally flag three in-manuscript signals of missing support: the explicit delegation of the OPE algebra to companion preprint [35] ('identical... not repeated here') covering the D* channel and most Lorentz structures; the unspecified ⟨s̄s⟩(T,ρ) parametrization required for the strangeness channel; and the authors' own closing remark that the omitted four-quark condensates are 'the dominant source of theoretical uncertainty.' Each reinforces a CONDITIONAL verdict without overturning the qualitative picture. Credit where due: the vacuum calibration against the PDG D*_s mass within the stated Borel window (Fig. 2) is a genuine internal consistency check; the QCD sum-rule framework is standard; and the density-dominated softening with temperature moderating the effect is consonant with the condensate evolution of Fig. 1, so the qualitative direction of the central claim is plausible. The proposed threshold-variation test at the point of maximum shift decides whether the quantitative claim is prescription-dominated or robust; a large spread would move the numerical claims toward REJECT, whereas the current evidence supports UNCHANGED (CONDITIONAL).","tokens_in":18191,"tokens_out":18131,"duration_ms":158993,"concrete_test":"At (T=0, ρ/ρ₀ = 3.3), where the largest D*_s shift occurs, recompute the in-medium mass and decay constant from the coupled sum rules (Eq. (12)) three times, changing only the threshold ansatz: (a) Eq. (23) as published; (b) s0 fixed at its vacuum value; (c) s0/s0₀ = (⟨q̄q⟩/⟨q̄q⟩₀)^{1/3} without the m_c² floor. If Δm_{D*_s} spreads by more than ~150 MeV across (a)–(c), Eq. (23) is load-bearing and the abstract's numbers should be reported as prescription-dependent; if the spread is under ~50 MeV, the softening claim is robust. A second necessary check: verify Eq. (23) against the actual derivation in Ref. [36] and re-derive the unpublished D* OPE to rule out a companion-preprint error.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim — mass collapses of ~413 MeV (D*_s) and ~207 MeV (D*), decay constants down >68% — depends above all on the assumed in-medium continuum threshold, Eq. (23). With the condensate fit of Eq. (13) at T=0, r = ⟨q̄q⟩/⟨q̄q⟩₀ falls to ~0.33 at ρ/ρ₀ = 3.3 (the shift maximum) and ~0.26 at ρ/ρ₀ = 5; Eq. (23) then drags s0 from 6.3 GeV² down to ≈3.2 and ≈2.8 GeV². Because the Borel-weighted spectral integral shrinks along with its upper limit, the hundreds-of-MeV negative shifts track this single prescription, which is adopted, with its m_c² floor, from a finite-temperature Hilbert-moment analysis [36] and is never tested against equally plausible alternatives (fixed s0; s0 ∝ r^{1/3}; s0 tied to the in-medium D* mass). The non-monotonic mass turnaround at ρ/ρ₀ ≈ 3–3.5 cannot come from the condensate inputs themselves, which are monotone on [0,5]; it is fixed by the linear-density terms (Eqs. (16)–(22)) and the self-energy Σv operating beyond their low-density regime of validity. Two support gaps compound this: the OPE for the D* channel and for four of the five Lorentz structures in Eq. (12) is not shown, being delegated to companion preprint [35] ('identical... not repeated here'), and the strange-quark condensate ⟨s̄s⟩(T,ρ) needed for the D*_s channel is never specified in the manuscript. The conclusion itself concedes that the omitted four-quark condensates are 'the dominant source of theoretical uncertainty.' If Eq. (23) overstates the threshold drop, the quantitative headline weakens substantially; the qualitative softening direction is more robust.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents a QCD-sum-rule analysis of the open-charm vector mesons D_s^* and D^* in nuclear matter at finite temperature and baryon density. The authors set up five coupled in-medium sum rules (Eq. (12)), use temperature- and density-dependent quark and gluon condensates fitted to Ref. [30] via their previous work [35], and adopt a light-quark-condensate-scaled continuum threshold (Eq. (23)). They report large negative mass shifts (up to about -413 MeV for D_s^{*-} at T=0, ρ/ρ0=3.3 and -207 MeV for D^{*-}), monotonic reductions of the leptonic decay constants exceeding 68%, a non-monotonic density dependence of the masses, and particle-antiparticle splittings. The vacuum sector is calibrated against the PDG D_s^* mass, and a Borel window of 4-8 GeV^2 is justified.","tokens_in":18745,"tokens_out":9104,"duration_ms":80369,"significance":"If the results hold, they would provide useful benchmarks for open-charm observables at FAIR, NICA, and J-PARC and would extend QCD-sum-rule studies of heavy-light vector mesons from the B sector to the charm sector while including both temperature and density. Strengths of the paper include the simultaneous treatment of temperature and density, the comparison of strange and non-strange channels, and a vacuum calibration step. However, the quantitative claims rest on a single continuum-threshold ansatz that is not tested against alternatives, on inputs that are either delegated to an unpublished companion paper or not explicitly specified, and on in-medium results that carry no uncertainty estimates. These gaps must be closed before the quoted numbers can be regarded as robust predictions.","major_comments":[{"comment":"Equation (23) is the main control parameter for the central results. With the condensate fit of Eq. (13), the ratio ⟨q̄q⟩/⟨q̄q⟩_0 falls to about 0.33 at ρ/ρ0=3.3 and 0.26 at ρ/ρ0=5, so Eq. (23) pushes s0 from 6.3 GeV² down to about 3.2 and 2.8 GeV², respectively. Because s0 is the upper limit of the Borel-transformed spectral integral, the mass shifts of hundreds of MeV and the decay-constant suppressions above 68% track this prescription almost directly. The Hilbert-moment scaling is adopted from Ref. [36], but that reference concerns finite temperature, and no argument is given for its validity at finite baryon density. A sensitivity study comparing Eq. (23) with alternatives such as a fixed s0, s0 ∝ (⟨q̄q⟩/⟨q̄q⟩_0)^{1/3}, or s0 tied to the in-medium pole mass is required before the quantitative softening claims can be accepted.","section":"§II.D, Eq. (23)"},{"comment":"The density range extended to ρ/ρ0=5 is not justified. Equations (16)–(22) are linear in ρ (apart from the gluon condensate), and the vector self-energy Σ_v is treated as a quasi-particle shift; such linear-density mean-field parametrizations are normally valid only at moderate densities. The non-monotonic mass turnaround near ρ/ρ0≈3–3.5 cannot come from the condensates themselves, which are monotonic on [0,5], and must therefore be generated by these linear terms and Σ_v operating beyond their low-density regime of validity. The authors should state a validity criterion, identify where the linear-density parametrizations break down, and reconcile the high-density predictions with the hadronic description underlying Eq. (10).","section":"§II.C, Eqs. (16)–(22)"},{"comment":"Only the p_μ p_ν QCD-side expression is written out (Appendix A). The QCD expressions for the g_{μν}, p_μ u_ν, p_ν u_μ, and u_μ u_ν structures entering Eq. (12) are delegated to the companion preprint [35] with the statement that they are 'identical' to the B-meson case. Since [35] is an unreviewed preprint and concerns B vector mesons rather than charmed mesons, the reader cannot verify the charm-quark mass dependence, the signs of the density terms, or the strange-quark contributions. In addition, the strange-quark condensate ⟨s̄s⟩(T,ρ) needed for the D_s^* channel is never explicitly defined; Eqs. (18) and (21) use it, but only a vague 'scaling factor y=0.05' is mentioned. Please provide the missing expressions or a precise dictionary to [35].","section":"§II.B and Appendix A"},{"comment":"Table I reports a maximum decay-constant splitting |δf|_max for D_s^{*±} of 7.6 MeV at T=155 MeV and ρ/ρ0=0, and a corresponding 1.8 MeV for D^{*±}. At zero baryon density and zero chemical potential, charge-conjugation symmetry forbids a splitting between D^{*+} and D^{*-} even at finite temperature. This either indicates that the axes or labels are misstated, or that the particle and antiparticle sum rules are internally inconsistent. Since the particle-antiparticle splittings are an advertised result, this issue must be resolved before the splitting predictions can be trusted.","section":"§III.C, Table I and Fig. 9"},{"comment":"No uncertainty estimates are provided for any in-medium result. The vacuum calibration (Fig. 2) shows an s0 sensitivity of roughly ±100 MeV even within the Borel window, and the conclusion admits that the four-quark condensates are 'the dominant source of theoretical uncertainty.' Yet all figures and Table I show single curves with no error bands. To support the quoted benchmark numbers, please propagate at least the uncertainty in s0, the condensate fit parameters of Eq. (13), and m_0^2, and estimate the omitted four-quark condensate contribution.","section":"§III (all figures)"}],"minor_comments":[{"comment":"The abstract states that masses and decay constants decrease as baryon density increases, but the mass is non-monotonic in density (Figs. 3 and 7); the abstract should explicitly mention the turnaround.","section":"Abstract and §III"},{"comment":"The fit parameters in Eq. (13) are given without uncertainties; if they come from a fit in Ref. [35], the covariance or at least the individual uncertainties should be stated.","section":"§II.C, Eq. (13)"},{"comment":"The text near Fig. 9(b) refers to the largest splitting being 'obtained in vacuum,' but the Table lists it at ρ/ρ0=0 and T=155 MeV, which is not a vacuum state; this terminology should be clarified.","section":"§III.C, Fig. 9"},{"comment":"The heavy-quark mass entering Eq. (23) as the floor m_c^2/s0 should be defined in a definite scheme (pole mass, MS-bar mass, or the mass used in the OPE) and kept consistent with the propagator in Eq. (11).","section":"§II.D, Eq. (23)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is potentially publishable after major revision. The decisive issue is that the headline mass shifts and decay-constant suppressions are largely imposed by the unvalidated continuum-threshold ansatz of Eq. (23). I would require the threshold-sensitivity study, the transparency about the OPE expressions and the strange condensate, and a discussion of the validity of the density range before recommending acceptance. The apparent nonzero particle-antiparticle splitting at ρ/ρ0=0 should also be checked carefully, as it may indicate an error in the particle/antiparticle construction rather than a mere labeling issue."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know: this is a straightforward extension of the authors' previous B*_s/B* work to the open-charm vector sector, and the quantitative headline — mass drops of ~413 MeV and ~207 MeV, decay constants down ~70% — is largely governed by one prescription, the in-medium continuum threshold of Eq. (23). If that prescription is wrong, the numbers move a lot. The paper itself doesn't test that sensitivity, and the reader's stress-test concern lands on reading it.\n\nWhat's genuinely new and worth credit: it gives the first unified QCD sum-rule prediction for D*_s and D* masses, decay constants, and C-parity splittings across a broad (T,rho) plane. The strange vs. non-strange comparison is a legitimate scientific question, and the vacuum calibration (Fig. 2, Borel window, central s0 reproducing the PDG mass) is done cleanly. The qualitative picture — density-driven softening, temperature as a secondary moderator, finite baryon density lifting particle–antiparticle degeneracy — is plausible and consistent with the condensate inputs.\n\nNow the soft spots, in proportion. The load-bearing issue is Eq. (23): the Hilbert-moment scaling of s0(T,rho) is adopted from Ref. [36] and never checked against other reasonable ansätze (fixed s0, s0 tied to the in-medium D* mass, s0 ∝ r^{1/3}). Because the condensate fit in Eq. (13) drives r down to ~0.26–0.33 at high density, s0 collapses and drags the extracted masses with it. The non-monotonic turnaround near rho/rho0 ~ 3–3.5 also cannot come from the monotone condensates; it's set by the linear-density terms in Eqs. (16)–(22), which are ad hoc and being used far beyond their natural low-density regime. That alone makes the specific numbers provisional. Smaller but real gaps: no error bars on any in-medium result; the OPE for four of the five Lorentz structures is delegated to companion preprint [35] rather than shown; the strange-quark condensate <ss>(T,rho), needed for the D*_s channel, is never specified; and the density range is pushed to 5 rho0 with no validity discussion. To the paper's credit, the conclusion admits the four-quark condensates are the dominant theoretical uncertainty — that's honest, but it cuts against calling these predictions 'benchmarks.'\n\nWho is this for? Practitioners in heavy-flavor phenomenology at FAIR-CBM, NICA, or J-PARC who need in-medium open-charm inputs, and QCD sum-rule specialists who can assess the threshold prescription. The paper deserves a serious referee, but the review should ask for a threshold-ansatz sensitivity analysis, error propagation from the condensate fit, an explicit <ss>(T,rho), and either a truncation or a justification of the high-density region. With those, the qualitative claims would stand; without them, the headline numbers are not yet usable.\n\nRecommendation: send to peer review, but with major revision expected.","headline":"Competent extension of the authors' own in-medium sum-rule framework to D*_s and D*, but the headline mass shifts are mostly imposed by an unvalidated continuum-threshold ansatz, so the numbers should be treated as conditionally model-dependent.","tokens_in":19208,"tokens_out":1913,"would_cite":true,"duration_ms":19050,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper predicts that in hot, dense nuclear matter the open-charm vector mesons $D_s^{*}$ and $D^{*}$ become substantially softer — their masses and leptonic decay constants drop as baryon density rises, with the largest mass shift…","keywords":["QCD sum rules","open-charm vector mesons","in-medium meson masses","leptonic decay constants","finite temperature and density","particle-antiparticle splitting","nuclear matter","condensates"],"falsifier":"A direct falsifier would be a precise measurement of the $D_s^{*}$ or $D^{*}$ mass in cold nuclear matter at a density around $\rho/\\rho_0 \\simeq 3$, where the paper predicts a mass shift near $-413$ MeV (or $-207$ MeV): if the measured shift is much smaller in magnitude, or if the mass continues to decrease monotonically beyond $\rho/\\rho_0 \\simeq 3$ without the predicted partial recovery, the threshold scaling or the condensate parametrization would be ruled out. A lattice QCD calculation of the in-medium $D_s^{*}$ mass at finite baryon density, if feasible, would provide a complementary, model-independent check.","tokens_in":17995,"feed_emoji":"⚛️","tokens_out":3200,"duration_ms":29381,"temperature":0.7,"pith_summary":"The paper uses finite-temperature and finite-density QCD sum rules to compute the in-medium masses and leptonic decay constants of the open-charm vector mesons $D_s^{*}$ and $D^{*}$. It finds that both mesons undergo significant medium-induced softening: as baryon density increases, the masses first drop steeply, reach a minimum near three times nuclear saturation density, and then partially recover, while the leptonic decay constants decrease monotonically throughout the density range. Temperature acts as a secondary effect, generally moderating the density-driven suppression. A finite baryon density also breaks particle–antiparticle degeneracy, producing distinct mass and decay-constant splittings between the $D^{*-}$ and $D^{*+}$ (and $D_s^{*-}$ and $D_s^{*+}$) states. These results provide quantitative predictions for open-charm observables in dense matter, relevant for future heavy-ion experiments at FAIR, NICA, and J-PARC.","feed_headline":"Open-charm mesons soften by up to 413 MeV in dense matter","feed_subtitle":"QCD sum rules predict strong mass and decay-constant softening, with density the main driver and temperature a secondary brake.","key_machinery":"The central object is the in-medium two-point correlation function of the vector current, evaluated both in a hadronic representation with a quasi-particle pole and in the operator product expansion (OPE) with medium-dependent condensates. The sum rules are obtained by matching the coefficients of independent Lorentz structures, yielding coupled equations for the in-medium mass, leptonic decay constant, and vector self-energy. The key input that controls the density and temperature dependence is Eq. (23), the Hilbert-moment scaling of the effective continuum threshold, $s_0(T,\\rho)/s_0 = (\\langle \\bar{q}q\\rangle(T,\\rho)/\\langle \\bar{q}q\\rangle_0)(1 - m_c^2/s_0) + m_c^2/s_0$, which ties the threshold to the light-quark condensate. The numerical analysis uses temperature- and density-dependent parametrizations of the quark and gluon condensates, a Borel window of $4.0 \\le M^2 \\le 8.0$ GeV$^2$, and a vacuum threshold $s_0$ chosen to reproduce the PDG mass of $D_s^{*\\pm}$. The mechanism that produces the non-monotonic mass behavior is the competition between the falling condensates and the density-dependent threshold, which together control the extracted hadronic parameters.","core_discovery":"Within a single QCD sum-rule framework that combines temperature- and density-dependent quark and gluon condensates with an in-medium continuum threshold, the mass of $D_s^{*-}$ is reduced by up to about $413$ MeV and that of $D^{*-}$ by up to about $207$ MeV at zero temperature and densities around $\rho/\rho_0 \\simeq 3$–$3.3$. The leptonic decay constants of both channels are suppressed by more than $68\\%$ at the highest densities considered, and this suppression is monotonic in density. The mass shifts are non-monotonic in density, showing a partial recovery at high densities, while increasing temperature weakens the density-induced modifications. Finite baryon density lifts the degeneracy between charge-conjugate states, producing mass splittings up to about $75$ MeV in the strange channel and about $38$ MeV in the non-strange channel, with the antiparticle ($D_s^{*-}$, $D^{*-}$) more strongly bound than the particle. The strange and non-strange channels behave qualitatively alike, but the strange channel shows quantitatively larger mass modifications.","pith_inferences":["The authors' use of a single, universal scaling of the continuum threshold by the light-quark condensate implies that the entire medium dependence of the masses and decay constants is essentially inherited from the condensate parametrization; if future data show a different density profile, the discrepancy would immediately point to the threshold prescription rather than to the OPE itself.","One testable extension of this framework is to apply the same threshold scaling to other open-charm channels, such as the pseudoscalar $D_s$ and $D$ mesons, and to compare the predicted mass shifts with existing (already published) QCD sum-rule results; consistency there would increase confidence in the vector-channel predictions.","The predicted non-monotonic mass behavior is a direct consequence of the specific analytic form of the condensate fits, so the turnaround at high densities is not a robust model-independent feature; a measurement that finds a continued monotonic decrease would not falsify QCD sum rules but would indicate that the condensate parametrization or threshold scaling needs revision.","The calculated $\\sim 70\\%$ reduction of the leptonic decay constants at high density is unusually large, and since the decay constant enters the $D^* \\to \\ell \\nu$ width quadratically, this would imply a dramatic in-medium suppression of the leptonic decay rate that could be searched for in $D^*$ production in dense nuclear environments."],"forward_implications":["If these predictions hold, open-charm vector mesons in dense nuclear matter will be considerably lighter than their vacuum masses, which would affect the interpretation of dilepton and $D^*$ spectra in heavy-ion collisions at high baryon density.","The predicted large reduction of the leptonic decay constants implies a correspondingly weaker coupling of $D_s^*$ and $D^*$ to the vector current in medium, which would modify the production rates of these mesons and their decay into lepton pairs.","The particle–antiparticle mass splitting, which reaches tens of MeV, provides a observable signature of charge-conjugation symmetry breaking in baryonic matter that could be searched for in comparisons of $D^{*-}$ and $D^{*+}$ production.","The non-monotonic density dependence of the masses, with a minimum near $\rho/\\rho_0 \\simeq 3$, suggests that the in-medium softening is strongest at intermediate densities, so experiments probing densities around three times saturation may see the largest effect.","The strange channel ($D_s^{*}$) is predicted to be more strongly modified than the non-strange channel, so a comparative measurement of the two channels would directly test flavor-dependent medium effects."],"supporting_citations":[{"why":"Supplies the Hilbert-moment scaling relation, Eq. (23), that ties the in-medium continuum threshold to the light-quark condensate; this is the key medium-dependence prescription used in the sum rules.","marker":"[36]"},{"why":"Provides the numerical results for the temperature- and density-dependent light-quark and gluon condensates that enter the OPE side of the sum rules.","marker":"[30]"},{"why":"The authors' previous analysis of heavy-light vector $B$ mesons, from which the analytic parametrizations of the condensates and the sum-rule setup are adopted.","marker":"[35]"},{"why":"The PDG compilation supplies the experimental vacuum masses and quark masses used to fix the vacuum threshold and to validate the sum-rule output.","marker":"[29]"},{"why":"Establishes the QCD sum-rule formalism for $D$ and $B$ mesons in nuclear matter, including the treatment of particle–antiparticle splittings that this paper extends to vector mesons.","marker":"[20]"},{"why":"Originates the in-medium QCD sum-rule approach for baryons, providing the foundational method for handling the medium four-velocity and the odd Lorentz structures that lead to particle–antiparticle differences.","marker":"[21]"},{"why":"The classic reference for QCD sum rules for vector mesons in the nuclear medium, establishing the framework that this paper applies to open-charm states.","marker":"[4]"}],"fun_headline_variants":["Charm meson mass drops up to 413 MeV at high density","D_s* down by 413 MeV in dense nuclear matter","Charm meson decay constants cut by 68% in dense matter","Density, not temperature, drives charm meson softening","Particle-antiparticle gap in charm mesons: up to 75 MeV"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central load-bearing premise is the assumed scaling of the in-medium continuum threshold, Eq. (23), which ties the threshold directly to the light-quark condensate; if that scaling is inaccurate, the predicted mass shifts and decay-constant reductions would change substantially.","fun_headline_variants_meta":{"raw":{"variants":["Charm meson mass drops up to 413 MeV at high density","D_s* down by 413 MeV in dense nuclear matter","Charm meson decay constants cut by 68% in dense matter","Density, not temperature, drives charm meson softening","Particle-antiparticle gap in charm mesons: up to 75 MeV"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001372,"raw_usage":{"total_tokens":5646,"prompt_tokens":1116,"completion_tokens":4530,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":732,"completion_tokens_details":{"reasoning_tokens":4437}},"tokens_in":732,"tokens_out":4530,"duration_ms":26965,"temperature":1.0,"reasoning_tokens":4437,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:41:05.314686+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct falsifier would be a precise measurement of the $D_s^{*}$ or $D^{*}$ mass in cold nuclear matter at a density around $\rho/\\rho_0 \\simeq 3$, where the paper predicts a mass shift near $-413$ MeV (or $-207$ MeV): if the measured shift is much smaller in magnitude, or if the mass continues to decrease monotonically beyond $\rho/\\rho_0 \\simeq 3$ without the predicted partial recovery, the threshold scaling or the condensate parametrization would be ruled out. A lattice QCD calculation of the in-medium $D_s^{*}$ mass at finite baryon density, if feasible, would provide a complementary, model-independent check.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Hilbert-moment scaling relation, Eq. (23), that ties the in-medium continuum threshold to the light-quark condensate; this is the key medium-dependence prescription used in the sum rules."},{"cited_title":"Kumar, ”Heavy Scalar, Vector, and Axial-Vector Mesons in Hot and Dense Nuclear Medium,” Adv","cited_arxiv_id":null,"evidence_quote":"Provides the numerical results for the temperature- and density-dependent light-quark and gluon condensates that enter the OPE side of the sum rules."},{"cited_title":"More about the B and D mesons in nuclear matter,","cited_arxiv_id":null,"evidence_quote":"The authors' previous analysis of heavy-light vector $B$ mesons, from which the analytic parametrizations of the condensates and the sum-rule setup are adopted."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The PDG compilation supplies the experimental vacuum masses and quark masses used to fix the vacuum threshold and to validate the sum-rule output."},{"cited_title":"QCD sum rules for D and B mesons in nuclear matter,","cited_arxiv_id":null,"evidence_quote":"Establishes the QCD sum-rule formalism for $D$ and $B$ mesons in nuclear matter, including the treatment of particle–antiparticle splittings that this paper extends to vector mesons."},{"cited_title":"From hadrons to quarks in neutron stars: a review,","cited_arxiv_id":null,"evidence_quote":"Originates the in-medium QCD sum-rule approach for baryons, providing the foundational method for handling the medium four-velocity and the odd Lorentz structures that lead to particle–antiparticle differences."},{"cited_title":"Hatsuda and S","cited_arxiv_id":null,"evidence_quote":"The classic reference for QCD sum rules for vector mesons in the nuclear medium, establishing the framework that this paper applies to open-charm states."}],"review_version":1}