Open-Charm Vector Mesons in Hot and Dense Nuclear Matter

K. Azizi; N. Er

REVIEW 5 major objections 4 minor 44 references

Open-Charm Vector Mesons in Hot and Dense Nuclear Matter

T0 review · 5 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2608.04236 v1 pith:LLP23S5O submitted 2026-08-04 hep-ph hep-exhep-lat

N. Er , K. Azizi This is my paper · ORCID

classification hep-phhep-exhep-lat

keywords QCDsumrulesopen-charmvectormesonsin-mediummesonmassesleptonicdecayconstantsfinitetemperatureanddensityparticle-antiparticlesplittingnuclearmattercondensates

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

A direct falsifier would be a precise measurement of the $D_s^{*}$ or $D^{*}$ mass in cold nuclear matter at a density around $ ho/\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 $ ho/\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.

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Extended reading notes

Core claim

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 $ ho/ ho_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.

Load-bearing premise

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.

Editorial extensions

If this is right

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 $ ho/\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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

What'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.

Now 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 (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.'

Who 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 (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.

Recommendation: send to peer review, but with major revision expected.

Referee Report

5 major / 4 minor

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.

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 (5)

[§II.D, Eq. (23)] 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.
[§II.C, Eqs. (16)–(22)] 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).
[§II.B and Appendix A] 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].
[§III.C, Table I and Fig. 9] 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.
[§III (all figures)] 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.

minor comments (4)

[Abstract and §III] 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.
[§II.C, Eq. (13)] 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.
[§III.C, Fig. 9] 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.
[§II.D, Eq. (23)] 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).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the in-medium predictions are derived from external condensate inputs and an explicitly adopted threshold ansatz, not from the predicted observables.

full rationale

The paper solves finite-temperature and finite-density QCD sum rules for the in-medium masses and decay constants. The medium dependence enters through (i) condensate parametrizations, Eqs. (13)-(22), taken from external QCD inputs (Kumar et al.) with fitting functions imported from the authors' companion work [35], and (ii) the continuum-threshold scaling Eq. (23), explicitly adopted from Dominguez, Loewe and Rojas [36]. Neither ingredient is fitted to the D*_s or D* in-medium observables that are reported, and the vacuum sum rule is checked against the PDG mass. Eq. (23) is a model ansatz that could be wrong, but it is not circular: the threshold is not defined in terms of the output masses or decay constants, and the paper does not claim to derive Eq. (23). Self-citations to [35] supply OPE algebra and fitting functions, but the load-bearing physical content is external and the central claim (in-medium softening and its density/temperature hierarchy) is not equivalent to any of these inputs by construction. The acknowledged omission of four-quark condensates is a stated uncertainty, not a circularity. Thus no step in the claimed derivation reduces to its own output.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central calculation rests on a chain of adopted parametrizations rather than on a self-contained derivation. The light-quark condensate, the gluon condensate, the continuum-threshold scaling, and several density-dependent condensate coefficients are all external inputs, most fitted in the authors' previous work [35] or taken from Refs. [30] and [36]. No new entities are invented, but the numerical outputs inherit whatever accuracy these inputs have.

free parameters (5)

Eq. (13) light-quark condensate fit parameters = A=0.5316, B=0.1370, kappa1=1.2262, D=0.1375, phi=0.3374, alpha=1.2516, F=0.0554, beta=20.0
Eight coefficients define the temperature and density dependence of the light-quark condensate, the dominant nonperturbative input; fitted to numerical results of Ref. [30] in the authors' previous work [35].
Eq. (14) gluon condensate parameters = A3=-4.131e-3 GeV^4, A4=7.696e-3 GeV^4, A5=-8.530e-4 GeV^4
Coefficients of the in-medium gluon condensate parametrization from Ref. [30].
Density couplings in Eqs. (16)-(22) = 3/2, 3 GeV^2, y=0.05, -0.33 GeV^2, 0.18, 0.02, 0.3 GeV^2, m0^2=0.8 GeV^2
Ad hoc coefficients parametrizing quark-number, mixed, and derivative condensates at finite density; m0^2 follows Ref. [34], several others are chosen without derived justification.
Vacuum continuum threshold s0 for D*_s (and D*) = s0=6.3 GeV^2 (central) for D*_s
Chosen in the interval (m+0.3)^2 to (m+0.5)^2 GeV^2 so that the vacuum sum rule reproduces the PDG mass; this calibration fixes the vacuum input before the medium scaling is applied.
Borel window and central Borel parameter = M^2 in [4.0, 8.0] GeV^2, central at 6 GeV^2
Auxiliary parameter window chosen from stability plateaus; results are quoted at the window midpoint without uncertainty propagation.

assumptions (6)

domain assumption Quark-hadron duality: the hadronic spectral representation can be equated to the OPE after Borel transformation (Eqs. 5-8 and 12).
Foundation of the QCD sum rule method; assumed throughout, standard in the field.
domain assumption The in-medium continuum threshold follows the Hilbert-moment scaling relation of Eq. (23), s0(T,rho)/s0 = (langle qbar q rangle(T,rho)/langle qbar q rangle_0)(1-m_c^2/s0)+m_c^2/s0.
Adopted from Ref. [36]; it ties the threshold to the light-quark condensate and strongly shapes the extracted medium dependence.
domain assumption The medium-dependent condensate parametrizations of Ref. [30] as fitted in Ref. [35] are accurate (Eqs. 13-14).
The paper adopts these fits without modification or independent verification; no fit quality or comparison is shown.
ad hoc to paper Equal energy partitioning between fermionic and gluonic sectors, Eq. (15): <Theta_g_00> = <Theta_f_00> = (1/2)<Theta_00>.
A conventional but unproven assumption for the thermal matrix element in the light-quark propagator.
domain assumption The vector self-energy component Sigma'_v in the effective momentum p* is negligible.
Stated in Sec. II A; justified as numerically small, but no estimate is given.
ad hoc to paper The density-dependent strange condensates scale with y=0.05 and the coefficients in Eqs. (16)-(22) are valid at all densities up to 5 rho0.
The strange-quark number condensate is set to zero and the mixed condensates are assigned linear density terms with fixed coefficients; no derivation or lattice input is provided.

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Cite this review

Pith. "Pith review of Open-Charm Vector Mesons in Hot and Dense Nuclear Matter." pith.science (2026). https://pith.science/paper/LLP23S5O

@misc{pith2026260804236,
  author       = {Pith},
  title        = {Pith review of: Open-Charm Vector Mesons in Hot and Dense Nuclear Matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LLP23S5O}},
  note         = {Machine review of arXiv:2608.04236}
}

abstract

We investigate the in-medium properties of the open-charm vector mesons $D_s^{*}$ and $D^{*}$ in hot and dense nuclear matter within the framework of finite-temperature and finite-density QCD sum rules. The analysis incorporates temperature- and density-dependent quark and gluon condensates together with an in-medium continuum threshold constrained by the light-quark condensate. By solving the resulting QCD sum rules, we determine the in-medium masses and leptonic decay constants of the $D_s^{*\pm}$ and $D^{*\pm}$ mesons over a broad region of the $(T,\rho)$ plane. Both vector mesons undergo substantial in-medium softening, with their masses and leptonic decay constants decreasing as the baryon density increases. The masses exhibit a non-monotonic dependence on baryon density, whereas the leptonic decay constants decrease monotonically throughout the investigated density range. Increasing temperature generally weakens the density-induced modifications, although baryon density remains the dominant driver of the in-medium evolution. The largest mass shifts occur at intermediate-to-high densities, reaching approximately $-413~\mathrm{MeV}$ for the $D_s^{*-}$ meson and $-207~\mathrm{MeV}$ for the $D^{*-}$ meson, while the leptonic decay constants are reduced by more than $68\%$ in both channels at the highest densities considered. We further investigate the particle--antiparticle splittings of the masses and leptonic decay constants induced by finite baryon density. Finite baryon density lifts the vacuum degeneracy between the charge-conjugate states, while increasing temperature generally suppresses the resulting asymmetries. Although the strange and non-strange channels exhibit similar qualitative behavior, quantitative differences emerge in both the in-medium modifications and the particle--antiparticle splittings. ....

Figures

Figures reproduced from arXiv: 2608.04236 by the authors.

**Figure 2.** FIG. 2: Vacuum pole mass of the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3: (a) In-medium mass shift of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4: (a) In-medium mass shift of the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Panel (a) shows the absolute shift, ∆fD∗− s = f ∗ D∗− s − fD∗− s , while panel (b) displays the corresponding relative reduction with respect to the vacuum value. For all temperatures considered, the leptonic decay constant decreases monotonically with increasing baryo…

**Figure 6.** Figure 6: FIG. 6: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: FIG. 7: Density dependence of the in-medium [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: FIG. 8: Density dependence of the in-medium leptonic [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: FIG. 9: Density dependence of the antiparticle-particle splitting in the [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 10.** Figure 10: FIG. 10: Density dependence of the splitting between the [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

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1.2 1.4 -160 -140 -120 -100 -80 -60 -40 -20 0 20 T/Tc ΔfDs *- [MeV] (a) ρ/ρ0=0 ρ/ρ0=1 ρ/ρ0=2 ρ/ρ0=3 ρ/ρ0=4 ρ/ρ0=5

0.2 0.4 0.6 0.8 1. 1.2 1.4 -160 -140 -120 -100 -80 -60 -40 -20 0 20 T/Tc ΔfDs *- [MeV] (a) ρ/ρ0=0 ρ/ρ0=1 ρ/ρ0=2 ρ/ρ0=3 ρ/ρ0=4 ρ/ρ0=5
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1.2 1.4 0 5 10 15 20 25 T/Tc (%) Ds *- (b) FIG

0.2 0.4 0.6 0.8 1. 1.2 1.4 0 5 10 15 20 25 T/Tc (%) Ds *- (b) FIG. 4: (a) In-medium mass shift of theD ∗− s meson, ∆mD∗− s , as a function of the reduced temperatureT/T c at fixed normalized baryon densities,ρ/ρ 0 = 0, 1, 2, 3, 4, and 5. (b) Corresponding relative mass reducti...
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1.2 1.4 -500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 50 T/Tc ΔmDs *- [MeV] (a) ρ/ρ0=0 ρ/ρ0=1 ρ/ρ0=2 ρ/ρ0=3 ρ/ρ0=4 ρ/ρ0=5

0.2 0.4 0.6 0.8 1. 1.2 1.4 -500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 50 T/Tc ΔmDs *- [MeV] (a) ρ/ρ0=0 ρ/ρ0=1 ρ/ρ0=2 ρ/ρ0=3 ρ/ρ0=4 ρ/ρ0=5

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