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arxiv: 2604.25449 · v1 · submitted 2026-04-28 · ✦ hep-ph · nucl-th

A study of J/psi mass shift and bound states: Impact of D D and DD^* meson loops

Manpreet Kaur , Arvind Kumar This is my paper

Pith reviewed 2026-05-07 15:56 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords J/ψ mesonnuclear mattermass shiftbound statesmeson loopschiral SU(3) modelQCD sum rulesnuclear physics
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0 comments X

The pith

J/ψ mesons undergo a negative mass shift in nuclear matter due to DD and DD* loops, allowing possible bound states with nuclei.

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

The paper investigates the modification of the J/ψ meson mass in asymmetric nuclear matter at zero and finite temperatures. It employs an effective Lagrangian approach that includes contributions from DD and DD* meson loops. The medium dependence of D meson masses comes from the hadronic chiral SU(3) model combined with QCD sum rules. Findings show a negative mass shift with increasing baryonic density, pointing to attraction by nuclear mean fields and the potential for meson-nucleus bound states. Calculations of binding energies and absorption widths for ground and excited states in oxygen-16, calcium-40, zirconium-90 and lead-208 nuclei are provided to support interpretation of future experimental data.

Core claim

Using an effective Lagrangian that accounts for DD and DD* meson loop contributions, the J/ψ mass shows a negative shift as baryonic density rises in nuclear matter at both zero and finite temperatures. The D meson masses entering the loops are obtained from the hadronic chiral SU(3) model via scalar condensates fed into QCD sum rules. This mass reduction implies attraction to nuclear mean fields and therefore the possibility of J/ψ bound states inside nuclei, with explicit binding energies and absorption decay widths computed for the ground and excited states of O^{16}, Ca^{40}, Zr^{90} and Pb^{208}.

What carries the argument

Effective Lagrangian approach that incorporates self-energy corrections from DD and DD* meson loops, with D meson masses supplied by the hadronic chiral SU(3) model and QCD sum rules.

If this is right

  • The negative mass shift permits the formation of J/ψ bound states with nuclei including O^{16}, Ca^{40}, Zr^{90} and Pb^{208}.
  • Binding energies and absorption decay widths are obtained for both ground and excited states in these nuclei at zero and finite temperatures.
  • The results apply to asymmetric nuclear matter and are intended to aid interpretation of data on low-momentum charmed mesons produced inside nuclei.
  • The mass modification grows with baryonic density, strengthening the case for attraction to nuclear mean fields.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the mass shift persists at finite momentum, it could alter J/ψ production and suppression patterns observed in heavy-ion collisions.
  • The same loop mechanism might generate analogous shifts for other hidden-charm states such as ψ(2S).
  • Comparison with J/ψ photoproduction or electroproduction data off nuclei would provide a direct test of the calculated binding energies.
  • The temperature dependence suggests the bound-state signals could weaken but remain visible at moderate temperatures reached in current facilities.

Load-bearing premise

The medium dependence of D meson masses is determined using the hadronic chiral SU(3) model, where scalar condensates are calculated and subsequently utilized in the QCD sum rules approach.

What would settle it

Direct measurement of the J/ψ invariant-mass peak position inside nuclear targets or observation of narrow bound-state signals in low-momentum production experiments at Jefferson Lab or FAIR would confirm or refute the predicted negative mass shift and binding energies.

Figures

Figures reproduced from arXiv: 2604.25449 by Arvind Kumar, Manpreet Kaur.

Figure 1
Figure 1. Figure 1: The up ⟨uu¯⟩ρB and down ⟨d ¯d⟩ρB condensates are analyzed as function of the baryon density ratio ρB/ρ0 in isospin asymmetric nuclear matter, considering isospin asymmetric parameter Ia = 0 and 0.3 and temperatures T = 0 and 100 MeV. Dαs π G a µνG aµνE ρB = 8 9 " (1 − d) χ 4 +  χ χ0 2  m2 π fπσ + √ 2m2 KfK − √ 1 2 m2 π fπ  ζ  # , (5) where d = 2 11 serves as a parameter associated with the QCD beta fu… view at source ↗
Figure 2
Figure 2. Figure 2: The individual and total terms of gluon condensates ( view at source ↗
Figure 3
Figure 3. Figure 3: In medium masses of D+, D0 , D∗+, and D∗0 mesons as function of the baryon density ratio ρB/ρ0 within isospin asymmetric nuclear matter, Ia = 0 and 0.3, and temperatures, T = 0 and 100 MeV. as depicted in Figs. 3(a), (b), (c), and (d), respectively. The in-medium values of m∗ D at different fixed values of ρB, Ia, and T are tabulated in Table II. In view at source ↗
Figure 4
Figure 4. Figure 4: Density dependence of the DD and DD∗ loop contribution to the J/ψ mass shift (∆mψ) in asymmetric nuclear matter at I = 0.3 and T = 100 MeV for different values of the cutoff ΛD. ;B=;0 0 1 2 3 " m A ( M e V ) -10 -8 -6 -4 -2 0 DD Loop (a) ;B=;0 0 1 2 3 " m A ( M e V ) -10 -8 -6 -4 -2 0 DD$ Loop (b) T = 0 MeV T = 100 MeV view at source ↗
Figure 5
Figure 5. Figure 5: Density dependence of the DD and DD∗ loop contributions to the J/ψ mass shift (∆mψ) in asymmetric nuclear matter at I = 0.3 and ΛD = 2 GeV for different values of temperatures. MeV, using a cutoff mass parameter ranging from 1 to 3 GeV. We observe that as the density of the medium increases, the magnitude of ∆mJ/ψ becomes more negative for a given ΛD. When moving to higher ΛD values, a more substantial dow… view at source ↗
Figure 6
Figure 6. Figure 6: The D∗D∗ loop contribution to the J/ψ mass shift as function of the baryon density ratio ρB/ρ0 is examined in symmetric nuclear matter at T = 0 MeV, with various cutoff values ΛD. 4(b), which is consistent with the findings reported in Ref. [48]. This negative mass shift of J/ψ indicates the strong coupling of vector D∗ mesons with the scalar and vector fields of the medium compared to the pseudoscalar D m… view at source ↗
Figure 7
Figure 7. Figure 7: The result of J/ψ mass shift as a function of r in nuclei O16, Ca40, Zr90, and Pb208 at different value of cut off parameter ΛD, from the DD loop contribution, illustrated in subfigures (a) and (c), and the DD∗ loop contribution, presented in subfigures (b) and (d). U(r) = m∗ ψ (r) − mψ = ∆mψ(ρi,0) ρB(r) ρi,0 , (28) 20 view at source ↗
Figure 8
Figure 8. Figure 8: The J/ψ mass shift as a function of r in nuclei O16, Ca40, Zr90, and Pb208 arises from the total contribution of DD and DD∗ loops, depicted in subfigures (a) for ΛD = 2 GeV, and (b) for ΛD = 3 GeV. Now, we present the results of the J/ψ mass shift as a function of radial distance r from the center of the nuclei O16, Ca40, Zr90, and Pb208, evaluated at various values of the cutoff parameter ΛD. These result… view at source ↗
read the original abstract

We investigate the modification of the $J/\psi$ meson mass in asymmetric nuclear matter at zero and finite temperatures employing an effective Lagrangian approach that considers the contributions of $DD$ and $DD^*$ meson loops. The medium dependence of $D$ meson masses is determined using the hadronic chiral SU(3) model, where scalar condensates are calculated and subsequently utilized in the QCD sum rules approach. Our findings indicate that an increase in baryonic density results in a negative mass shift of the $J/\psi$ meson. This suggests that the $J/\psi$ meson is attracted to nuclear mean fields indicating the possibility of the formation of meson-nucleus bound states. Moreover, we have also determined the binding energy and absorption decay width of the $J/\psi$ meson for both the ground and excited states of $\text{O}^{16}$, $\text{Ca}^{40}$, $\text{Zr}^{90}$, and $\text{Pb}^{208}$ nuclei. These results are expected to contribute to the understanding of experimental data from upcoming studies at Jefferson lab and the facility for antiproton and ion research, where low-momentum charmed mesons can be produced and examined within nuclei.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper claims that an effective Lagrangian approach incorporating DD and DD* meson loops yields a negative mass shift for the J/ψ in asymmetric nuclear matter at zero and finite temperatures. D and D* masses are obtained by computing scalar condensates in a hadronic chiral SU(3) model and feeding them into QCD sum rules; the resulting density-dependent shift is used to compute binding energies and absorption widths for J/ψ ground and excited states in O^{16}, Ca^{40}, Zr^{90}, and Pb^{208} nuclei, suggesting possible meson-nucleus bound states.

Significance. If the central result holds, the work would supply concrete predictions for J/ψ attraction in nuclei that could be confronted with data from Jefferson Lab and FAIR. The combination of loop self-energy with in-medium D masses is a standard pipeline, but the absence of uncertainty quantification and cross-checks against lattice QCD or alternative heavy-light frameworks reduces the immediate impact.

major comments (3)
  1. [D-meson mass determination (method section)] The medium dependence of the D-meson masses (obtained from chiral SU(3) condensates inserted into QCD sum rules) is load-bearing for the sign of the J/ψ shift. The manuscript provides no sensitivity analysis to variations in the SU(3) parameters, no comparison with lattice QCD results for charmed mesons in medium, and no alternative heavy-quark effective-theory calculation to confirm that the D-mass decrease with density is robust.
  2. [Loop self-energy and numerical results] The real part of the DD and DD* loop self-energy determines the reported negative J/ψ mass shift. The paper does not quote error bars, does not vary the free loop coupling constants, and does not show how the shift changes when the D-mass input is altered within its model uncertainty; this directly affects the binding-energy and width numbers quoted for the listed nuclei.
  3. [Bound-state calculations for nuclei] The binding energies and absorption widths for finite nuclei are obtained by mapping the infinite-matter mass shift onto a nuclear potential. The manuscript does not specify the functional form of the potential, the averaging procedure over the nuclear density profile, or the treatment of the imaginary part of the self-energy at finite temperature.
minor comments (2)
  1. [Abstract and formalism] The asymmetry parameter of the nuclear matter is mentioned but its numerical value is not stated in the abstract or results; this should be given explicitly.
  2. [Figures and tables] Figure captions and axis labels should include the temperature and density ranges used so that the plotted mass shifts can be directly compared with the tabulated binding energies.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We address each of the major comments in detail below, indicating the changes we will implement in the revised version.

read point-by-point responses

  1. Referee: [D-meson mass determination (method section)] The medium dependence of the D-meson masses (obtained from chiral SU(3) condensates inserted into QCD sum rules) is load-bearing for the sign of the J/ψ shift. The manuscript provides no sensitivity analysis to variations in the SU(3) parameters, no comparison with lattice QCD results for charmed mesons in medium, and no alternative heavy-quark effective-theory calculation to confirm that the D-mass decrease with density is robust.

    Authors: We agree that additional checks would strengthen the conclusions. The parameters in the chiral SU(3) model are taken from established literature and have been used consistently in our previous studies on light and strange hadrons. To address the lack of sensitivity analysis, we will include in the revised manuscript a new subsection or appendix showing the variation of D-meson masses with changes in key parameters (e.g., the sigma-nucleon coupling and the value of the gluon condensate) within their phenomenological uncertainties. This will demonstrate that the negative J/ψ mass shift remains robust. For lattice QCD comparisons, we note that while there are limited lattice results for D mesons in nuclear matter, we will add a discussion referencing available lattice data on related in-medium effects and other model calculations in the literature. An alternative calculation within heavy-quark effective theory is not included in the present work as it would require a separate framework, but we will mention this as a possible direction for future research. revision: yes

  2. Referee: [Loop self-energy and numerical results] The real part of the DD and DD* loop self-energy determines the reported negative J/ψ mass shift. The paper does not quote error bars, does not vary the free loop coupling constants, and does not show how the shift changes when the D-mass input is altered within its model uncertainty; this directly affects the binding-energy and width numbers quoted for the listed nuclei.

    Authors: We acknowledge the importance of uncertainty quantification. The coupling constants for the DD and DD* loops are fixed by matching to the vacuum properties and decay processes of the J/ψ and related states. In the revised version, we will add error estimates to the mass shift results by considering reasonable variations in these couplings (e.g., ±10% around the central values) and present the corresponding ranges for the binding energies and widths. Furthermore, we will show explicitly how the J/ψ mass shift varies when the input D and D* masses are changed within the uncertainties obtained from the QCD sum rule analysis. This will be incorporated into the numerical results section. revision: yes

  3. Referee: [Bound-state calculations for nuclei] The binding energies and absorption widths for finite nuclei are obtained by mapping the infinite-matter mass shift onto a nuclear potential. The manuscript does not specify the functional form of the potential, the averaging procedure over the nuclear density profile, or the treatment of the imaginary part of the self-energy at finite temperature.

    Authors: We appreciate this comment as it highlights areas where the presentation can be clarified. The nuclear potential for each nucleus is obtained by using the density-dependent J/ψ mass shift calculated in infinite matter as the potential, with the density profile modeled by a Woods-Saxon distribution parameterized for O^{16}, Ca^{40}, Zr^{90}, and Pb^{208}. The binding energies are found by solving the Schrödinger equation with this potential, and the averaging is performed by integrating the local mass shift over the nuclear density distribution. For the imaginary part at finite temperature, it is incorporated via the temperature dependence in the loop integrals for the self-energy. We will revise the manuscript to explicitly state these details, including the specific form of the Woods-Saxon potential and the numerical procedure used for the finite nuclei calculations. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain.

full rationale

The paper's central result (negative J/ψ mass shift from real part of self-energy in DD and DD* loops) is obtained by feeding medium-modified D and D* masses—computed independently via the hadronic chiral SU(3) model plus QCD sum rules—into an effective Lagrangian loop integral. No equation in the provided text reduces the output mass shift to a redefinition or fit of the input D masses themselves; the loop calculation is a distinct step. No self-citation is invoked as a uniqueness theorem or load-bearing premise, and the chiral-model parameters are not fitted inside this work to the J/ψ observable. The derivation therefore remains self-contained against external benchmarks such as lattice QCD or alternative heavy-meson approaches.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on two established but parameterized effective models whose inputs are fitted to other data rather than derived from first principles.

free parameters (1)
  • DD and DD* loop coupling constants
    Introduced in the effective Lagrangian to compute the J/ψ self-energy from the meson loops.
axioms (2)
  • domain assumption Hadronic chiral SU(3) model accurately captures D-meson mass dependence on nuclear density via scalar condensates
    Invoked to obtain medium-modified D and D* masses before loop calculation.
  • domain assumption QCD sum rules can reliably extract the required scalar condensates for D mesons in medium
    Used after the chiral model to determine D-meson properties.

pith-pipeline@v0.9.0 · 5517 in / 1408 out tokens · 55264 ms · 2026-05-07T15:56:53.419374+00:00 · methodology

discussion (0)

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