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REVIEW 3 major objections 5 minor 109 references

An Undergraduate Approach to the Quantum Hadrodynamics and the Physics of Neutron Stars Part II: Neutron Stars' Exotic Content

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Hyperons in neutron-star cores can coexist with 2.2-solar-mass stars in a QHD model once SU(3) vector couplings are tuned and a sigma-field cutoff is added.

desk verdict An honest, clearly-written pedagogical synthesis of exotic degrees of freedom in QHD neutron-star models, but the headline 2.2 solar-mass results rest on an ad hoc cutoff that the author himself calls artificial. read the letter →

arxiv 2608.00439 v1 pith:VDT666E6 submitted 2026-08-01 nucl-th astro-ph.HE

Luiz L. Lopes This is my paper · ORCID
classification nucl-thastro-ph.HE
keywords quantumhadrodynamicsneutronstarshyperonpuzzlehyperonsdeltaresonancesantikaoncondensateSU(3)flavorsymmetryequationofstate
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

This paper, the second half of a pedagogical exposition of quantum hadrodynamics for neutron stars, tries to establish that the so-called hyperon puzzle can be circumvented inside one relativistic mean-field model, the eL3ωρ parametrization. The author argues that once hyperon-vector-meson couplings are fixed by SU(3) flavor symmetry with a single free parameter αV, and a hand-added cutoff potential keeps the nucleon effective mass from vanishing, hyperon-rich matter yields stars of $M_{\max}=2.22\,M_\odot$, and adding Δ resonances raises this to $2.23\,M_\odot$. Such stars satisfy the mass-radius constraints from PSR J0740+6620, so the presence of hyperons in neutron-star cores would no longer conflict with the observed two-solar-mass pulsars. A sympathetic reader should care because the result identifies which symmetry assumption, rather than a fine-tuned interaction, is doing the work in resolving the puzzle.

What carries the argument

The load-bearing machinery is the mean-field QHD Lagrangian with σ, ω, ρ, and φ mesons, together with SU(3) Clebsch-Gordan coefficients that convert the single parameter αV into the full set of hyperon-vector couplings. The φ meson, introduced through a vector-meson mixing scheme, adds repulsion that suppresses hyperon populations. A logarithmic cutoff potential $U_{\rm cut}(\sigma)=\alpha\ln[1+\exp(\beta(f-f_c))]$ with $f_c=0.85$ prevents the nucleon effective mass from vanishing, and the mechanism that ultimately stiffens the equation of state is ω dominance: the repulsive vector field grows with baryon density and controls the high-density pressure. The paper's quantitative results follow from integrating the Oppenheimer-Volkoff equations with these ingredients.

What would settle it

Rerun the Oppenheimer-Volkoff integration for hyperonic and NYD matter at αV = 0.25 with the cutoff threshold moved to $f_c=0.65$ or removed entirely; if the maximum mass falls below the PSR J0740+6620 mass of $2.08\,M_\odot$, or no true maximum is reached before the nucleon effective mass vanishes, the paper's resolution of the hyperon puzzle is an artifact of the cutoff choice. A second check is to measure the Λ and Δ potential depths at saturation: if $U_\Lambda$ is more repulsive than $-28$ MeV or $U_\Delta$ lies above $-70$ MeV, the predicted onsets and masses shift.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the hyperon puzzle is resolved by the combination of three ingredients: the eL3ωρ equation of state, the φ meson, and a deviation from exact SU(6) symmetry controlled by αV. At αV = 0.25 the hyperon-ω couplings grow enough that ω dominance stiffens the equation of state at high density, giving $M_{\max}=2.22\,M_\odot$ for matter with the baryon octet and $2.23\,M_\odot$ when Δ resonances are included, while all αV ≠ 1 cases remain compatible with PSR J0740+6620. The same mechanism suppresses exotic baryon fractions at high density, and adding an antikaon condensate lowers the ceiling to about $2.10\,M_\odot$ across compositions. The paper also reports that without the cutoff potential the numerical solutions terminate when the nucleon effective mass reaches zero, so the 2.2-solar-mass results depend on that added term.

Load-bearing premise

The load-bearing premise is that the hand-added cutoff potential $U_{\rm cut}(\sigma)$ with $f_c=0.85$, chosen so the nucleon effective mass stays positive, represents a legitimate modification of the equation of state; if this term is unphysical or its onset mistuned, the reported maximum masses of $2.22$-$2.23\,M_\odot$ change or become undefined.

Editorial extensions

If this is right

  • Hyperonic neutron stars can reach $2.22\,M_\odot$, so the existence of PSR J0740+6620 does not by itself rule out hyperons in the core.
  • Adding Δ resonances slightly raises the maximum mass to $2.23\,M_\odot$ at αV = 0.25 and shrinks the canonical-star radius, while the 1.4$M_\odot$ radius remains at 12.82 km when only hyperons are present.
  • Antikaon condensation caps maximum masses near $2.10\,M_\odot$ for all baryonic compositions considered, weakening the stiffening obtained by lowering αV.
  • Except for the pure SU(6) choice αV = 1, all hyperonic and Δ-admixed equations of state in the paper satisfy the PSR J0740+6620 mass-radius constraint and the canonical-star radius constraint.
  • The σ cutoff converts what would otherwise be a numerical breakdown (vanishing nucleon mass) into a finite maximum mass, which is what allows the 2.2-solar-mass stars to exist.

Reading between the lines

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

  • If the cutoff is treated as a stand-in for a genuine high-density mechanism such as many-body or quarkyonic effects, the paper's 2.2-solar-mass numbers should be read as an upper envelope; a natural regulator would likely move them.
  • The same SU(3) machinery predicts that Δ resonances lower the radius of a 1.4$M_\odot$ star while barely changing the maximum mass, so a precise radius measurement of a canonical neutron star could discriminate compositions that the mass alone cannot.
  • The antikaon ceiling near $2.10\,M_\odot$, combined with a future confirmed neutron star above $2.2\,M_\odot$ whose core contains hyperons but not kaons, would disfavor strong antikaon condensation.
  • Because the vector couplings are fixed by symmetry rather than by hypernuclear data, the framework implies that high-density observations, not terrestrial hypernucleus experiments, are what ultimately decide the hyperon puzzle.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper is the second part of a pedagogical series on quantum hadrodynamics in mean-field approximation applied to neutron stars. It extends the eL3ωρ model of Part I to include muons, the full baryon octet, Δ resonances, and antikaon condensation in beta-equilibrated charge-neutral matter. The author fixes vector-meson couplings using the quark-isospin counting rule, Sakurai's proposal, and SU(3) flavor symmetry with a free αV parameter, introduces an ad hoc σ-field cutoff potential Ucut(σ) to prevent the nucleon effective mass from vanishing, and solves the Oppenheimer-Volkoff equations to obtain masses and radii. The headline result is that with αV = 0.25 and the cutoff potential, hyperonic stars reach Mmax = 2.22 M⊙ (Table III), 2.23 M⊙ with Deltas (Table V), and that antikaon condensation lowers this to about 2.10 M⊙ (Table VII), still compatible with PSR J0740+6620. The paper concludes that the hyperon puzzle is 'completely circumvented' within this model.

Significance. If the claimed maximum masses were robust, the paper would be a useful pedagogical confirmation that RMF models with strange and Δ degrees of freedom can satisfy the two-solar-mass constraint, and it gives a transparent and well-referenced derivation of the SU(3)/G-parity coupling schemes. The manuscript is honest about several limitations: it explicitly labels the cutoff potential as artificial and with no experimental or theoretical reason, it flags the kaon mean-field treatment as 'an approximation within an approximation,' and it acknowledges the large uncertainty in U_Kbar. The parameter tables and step-by-step OV calculations are a strength for a tutorial. However, the central quantitative claim is not robust, because the >2.2 M⊙ masses are generated by the unconstrained cutoff potential and by scanning αV to the value that satisfies the mass constraint. The paper is therefore better read as an illustrative model exercise than as a resolution of the hyperon puzzle.

major comments (3)
  1. [Sec. IV.B, Eq. (26), Tables III/V] The headline maximum masses (2.22 and 2.23 M⊙) are produced by the ad hoc cutoff potential Ucut(σ)=α ln[1+exp(β(f−fc))], with fc=0.85. The author states that Ucut is an artificial stiffening with no experimental or theoretical reason; it is active at the central densities of the maximum-mass stars, since Table III (αV=0.25) and Table V (αV=0.25) give nc=0.97 fm−3, while Fig. 3 shows Ucut becoming relevant around 0.64 fm−3. Without Ucut, the nucleon effective mass vanishes and the OV integration stops before a true maximum is reached (Sec. IV.A, Fig. 2(d)). The high-mass conclusion in Sec. VI.C therefore rests on the untested functional form and on the hand-picked fc; a different fc or regulator can shift Mmax substantially or remove the maximum altogether. The manuscript should either justify the regulator from physics, provide a sensitivity study over fc and β, and/or clearly present the >2.2 M⊙ values as an illustrative artifact of the model choice.
  2. [Sec. VI.B, Table III] αV is treated as a free parameter scanned between 1.0 and 0.25, and the maximum mass increases monotonically as αV decreases because every hyperon-ω coupling grows (Table II). The value αV=0.25 is not selected by any independent observable; it is the value that happens to push Mmax to 2.22 M⊙. Consequently, the claim that the hyperon puzzle is 'completely circumvented' is generated by the parameter choice rather than by the model. The paper should place αV in the context of hypernuclear constraints (potential depths, scattering data, or a Bayesian posterior) and should not present the αV=0.25 row as the resolution of the puzzle without showing this value is allowed by other data.
  3. [Sec. VII.B] The Δ resonances are treated with the spin-1/2 formalism by setting the degeneracy factor γ=4 and asserting that the spin-3/2 energy eigenvalue is 'exactly the same' as for spin-1/2. Rarita-Schwinger fields have additional off-shell degrees of freedom and known complications in the mean-field description of dense matter; these are neither discussed nor referenced. Because the NYD masses in Table V are part of the paper's central exotic-content results, this step needs a justification or an explicit caveat that the Δ contribution is only schematic.
minor comments (5)
  1. [Sec. III.C] The phrase 'from 2.31 M⊙ to 12.30 M⊙' should read 'to 2.30 M⊙'.
  2. [Eq. (14)] The Fermi momentum labels for protons and neutrons appear interchanged; as written, the proton chemical potential uses k_Fn and the neutron one uses k_Fp.
  3. [Eq. (17)] The right-hand side should be squared for the electron term; the condition μ_μ=μ_e gives k_Fμ^2 = m_e^2 + k_Fe^2 − m_μ^2.
  4. [Sec. V.A, Eq. (35)] The chain of equalities for the ρ couplings is garbled; gΣΣρ/gNNρ = 2 and gΞΞρ/gNNρ = 1 should be written as separate relations, and the denominator of the Λ relation should be gNNρ rather than gNNω.
  5. [Figs. 7 and 13] Several figures and text contain typos, e.g., 'Paticle population' in Fig. 7 and 'progressivaly' in Sec. VIII.E; a careful proofread is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper openly scans model parameters and discloses the ad hoc cutoff; the reported masses are model outcomes, not fitted or definitionally forced.

full rationale

The paper is a model-parameter study rather than a derivation whose output is equivalent to its input. The eL3ωρ parametrization is fixed by nuclear saturation properties (Table I), and the hyperon, Δ, and antikaon couplings are fixed by potential depths plus SU(3)/G-parity rules. The parameter αV is explicitly treated as a free parameter and scanned (Sec. VI A, Table II), and the resulting maximum masses are reported as possible outcomes for each chosen αV, not as quantities fitted to reproduce 2.22 M⊙. The cutoff potential Ucut(σ) (Eq. 26) is admittedly ad hoc: the paper states that it was introduced 'to artificially stiffen the EOS' and that there is 'no experimental or theoretical reason beyond this desirable stiffening.' The author also discloses that fc = 0.85 is chosen so that the known L3ωρ region up to about 4n0 is unaffected. This is a genuine correctness limitation — without Ucut the OV integration terminates before a true maximum, and the central densities of the reported maximum-mass stars exceed the cutoff onset — but it is not circular: Ucut is not defined in terms of Mmax, no parameter was fitted to the headline mass, and the regulator dependence is acknowledged rather than concealed. The self-citations to Refs. [12,47,75] supply the base model and coupling schemes, but those are independently published constructions and are not invoked as forced uniqueness results; the central TOV calculation integrates the stated EOS. The overall conclusion is therefore model-dependent but not circular.

Assumptions & free parameters 5 free parameters · 8 assumptions · 1 invented entities

The calculations rest on a chain of model choices: QHD-MFA, exact SU(3) flavor symmetry with αV free, ideal vector mixing, an ad hoc σ cutoff, experimentally uncertain hyperon, Delta, and kaon potential depths, and a mean-field treatment of kaons that the paper itself calls an approximation within an approximation. The central masses depend on all of these; varying U_Kbar alone can change Mmax by roughly 0.2 to 0.5 M⊙ according to cited literature. These ingredients are not derived from first principles.

free parameters (5)
  • αV (vector-meson F/(F+D) ratio) = 0.25, 0.50, 0.75, 1.00 (SU(6))
    Free parameter in the SU(3) coupling scheme; not determined by theory or by potential depths. Scanned to find EOSs that satisfy PSR J0740+6620; the SU(6) value is rejected for failing the 2 M⊙ constraint.
  • σ cutoff onset fc = 0.85
    Chosen so Ucut(σ) becomes active above about 4 n0, the region where L3ωρ was previously tested. Controls when the nucleon mass stops dropping and directly affects Mmax.
  • Delta potential depth UΔ = -90 MeV
    Chosen from the literature range -100 to -70 MeV; fixes the scalar couplings for Delta resonances. The author invites the reader to explore different values.
  • antikaon potential depth U_Kbar = -140 MeV
    Chosen from the wide estimated range -180 to -60 MeV; strongly affects whether and how much kaon condensate forms and the resulting Mmax.
  • g10/g8 ratio for the baryon decuplet = 1
    Not fixed by SU(3) because octet and decuplet are independent multiplets; assumed equal to 1 following Sakurai's proposal in the SU(6) limit.
assumptions (8)
  • domain assumption QHD mean-field approximation: baryons move in classical meson fields, with meson field equations obtained from Euler-Lagrange and expectation values.
    The entire formalism, Eqs. (1)-(10), is built on the MFA. Exchange terms, Dirac sea, and tensor couplings are neglected (Sec. II and IX).
  • domain assumption SU(3) flavor symmetry is exact for baryon-vector-meson couplings; only SU(6) is allowed to be broken via αV.
    Sec. VI A states 'I assume that SU(3) flavor symmetry is exact'. This fixes the relative coupling constants; SU(3) breaking would change hyperon, Delta, and kaon populations and Mmax.
  • ad hoc to paper The σ cutoff potential Ucut(σ) with chosen α, β, fc is a valid addition to the Lagrangian.
    Eq. (26) is introduced in Sec. IV B; the author calls its stiffening 'artificial' and admits there is no experimental or theoretical reason beyond keeping the nucleon effective mass finite.
  • domain assumption Spin-3/2 Delta resonances can be described with the spin-1/2 energy eigenvalue Eq. (43) and degeneracy γ=4.
    Sec. VII B asserts the energy eigenvalues are exactly the same as spin-1/2 without derivation; this bypasses Rarita-Schwinger complications.
  • domain assumption Mean-field treatment of (anti)kaon condensation is valid despite the coupled-channel nature of kaon-nucleon interactions.
    Sec. VIII B acknowledges this is 'an approximation within an approximation'; the paper nevertheless presents kaon EOS results.
  • domain assumption G-parity determines signs of antikaon couplings: g_KbarKbarω = -g_KKω and g_KbarKbarφ = -g_KKφ.
    Sec. VIII C adopts Ref. [75]; this choice excludes the alternative Ref. [83] parametrization and sets gππω = 0.
  • domain assumption Ideal vector meson mixing θV = 35.264° and z = 1/√6 fix the singlet-octet mixing and gNNφ = 0.
    Sec. VI A fixes these from quark content and the Gell-Mann-Okubo formula; used in all coupling tables.
  • domain assumption Beta equilibrium with zero net charge, T = 0, and vanishing neutrino contributions.
    Chemical equilibrium equations (13), (19), (36), (57), and (75) assume cold, neutrino-free, beta-stable matter.
invented entities (1)
  • σ-field cutoff potential Ucut(σ)
    purpose: Adds a term α ln[1 + exp(β(f - fc))] to prevent the nucleon effective mass from vanishing and to allow stable OV solutions at high density.
    Introduced ad hoc in Eq. (26); no independent experimental evidence; the author labels the resulting stiffening artificial.

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Pith. "Pith review of An Undergraduate Approach to the Quantum Hadrodynamics and the Physics of Neutron Stars Part II: Neutron Stars' Exotic Content." pith.science (2026). https://pith.science/paper/VDT666E6

@misc{pith2026260800439,
  author       = {Pith},
  title        = {Pith review of: An Undergraduate Approach to the Quantum Hadrodynamics and the Physics of Neutron Stars Part II: Neutron Stars' Exotic Content},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VDT666E6}},
  note         = {Machine review of arXiv:2608.00439}
}
read the original abstract

In this second part, I discuss how to introduce and the role played by non-atomic degrees of freedom in neutron stars' core using the formalism developed in Part I.

Figures

Figures reproduced from arXiv: 2608.00439 by the authors.

Figure 1
Figure 1. FIG. 1: ( [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: ( [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Effective nucleon mass for [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The fraction of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: |Particle population ( [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: |Particle population ( [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Paticle population for different values of [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Effects of different values of [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Particle population for different values of [PITH_FULL_IMAGE:figures/full_fig_p024_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Influence of [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: Particle population for NK matter. ( [PITH_FULL_IMAGE:figures/full_fig_p032_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Particle population for different values of [PITH_FULL_IMAGE:figures/full_fig_p033_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: EOSs (left) and the adiabatic index (right) for the N [PITH_FULL_IMAGE:figures/full_fig_p034_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14: OV solutions and astrophysical constraints relate [PITH_FULL_IMAGE:figures/full_fig_p035_14.png]

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Works this paper leans on

109 extracted references · 43 canonical work pages

  1. [1]

    Baldo, G

    M. Baldo, G. F. Burgio, and H.-J. Schulze, Phys. Rev. C 58, 3688 (1998), URL https://link.aps.org/doi/10.1103/PhysRevC.58.3688

    work page doi:10.1103/physrevc.58.3688 1998

  2. [2]

    Dapo, B.-J

    H. Dapo, B.-J. Schaefer, and J. Wambach, Phys. Rev. C 81, 035803 (2010), URL https://link.aps.org/doi/10.1103/PhysRevC.81.035803

    work page doi:10.1103/physrevc.81.035803 2010

  3. [3]

    L. L. Lopes and D. P. Menezes, Nucl. Phys. A 1009, 122171 (2021), ISSN 0375-9474, URL https://www.sciencedirect.com/science/article/pii/S0375947421000361

    2021

  4. [4]

    K. D. Marquez, D. P. Menezes, H. Pais, and C. m. c. Providên cia, Phys. Rev. C 106, 055801 (2022), URL https://link.aps.org/doi/10.1103/PhysRevC.106.055801

    work page doi:10.1103/physrevc.106.055801 2022

  5. [5]

    N. K. Glendenning and J. Schaffner-Bielich, Phys. Rev. C 60, 025803 (1999), URL https://link.aps.org/doi/10.1103/PhysRevC.60.025803

    work page doi:10.1103/physrevc.60.025803 1999

  6. [6]

    L. L. Lopes, Universe 11 (2025), ISSN 2218-1997, URL https://www.mdpi.com/2218-1997/11/8/276

    2025

  7. [7]

    B. D. Serot, Rep. Progr. Phys. 55, 1855 (1992), URL https://doi.org/10.1088/0034-4885/55/11/001

    doi:10.1088/0034-4885/55/11/001 1992

  8. [8]

    N. K. Glendenning, Compact stars: (2 ed. Edition, Springer New York, 2000)

    2000

Show all 109 references
  1. [9]

    D. P. Menezes, Universe 7 (2021), ISSN 2218-1997, URL https://www.mdpi.com/2218-1997/7/8/267

    2021

  2. [10]

    Miyatsu, M.-K

    T. Miyatsu, M.-K. Cheoun, and K. Saito, Phys. Rev. C 88, 015802 (2013), URL https://link.aps.org/doi/10.1103/PhysRevC.88.015802

    2013 doi

  3. [11]

    Fattoyev et al., Phys

    F. Fattoyev et al., Phys. Rev. C 82, 055803 (2010)

    2010

  4. [12]

    L. L. Lopes, K. D. Marquez, and D. P. Menezes, Phys. Rev. D 107, 036011 (2023), URL https://link.aps.org/doi/10.1103/PhysRevD.107.036011

    2023 doi

  5. [13]

    L. L. Lopes, Commun. Theor. Phys. 74, 015302 (2022), URL https://dx.doi.org/10.1088/1572-9494/ac2297

    2022 doi

  6. [14]

    Dutra, O

    M. Dutra, O. Lourenço, S. S. A vancini, et al., Phys. Rev. C 90, 055203 (2014), URL https://link.aps.org/doi/10.1103/PhysRevC.90.055203

    2014 doi

  7. [15]

    Oertel, M

    M. Oertel, M. Hempel, T. Klähn, and S. Typel, Rev. Mod. Ph ys. 89, 015007 (2017), URL https://link.aps.org/doi/10.1103/RevModPhys.89.015007

    2017 doi

  8. [16]

    Essick, I

    R. Essick, I. Tews, P. Landry, and A. Schwenk, Phys. Rev. Lett. 127, 192701 (2021), URL https://link.aps.org/doi/10.1103/PhysRevLett.127.192701

    2021 doi

  9. [17]

    J. R. Oppenheimer and G. M. Volkoff, Phys. Rev. 55, 374 (1939), URL https://link.aps.org/doi/10.1103/PhysRev.55.374

    1939 doi

  10. [18]

    Miller et al., Astrophys

    M. Miller et al., Astrophys. J. Lett. 918, L28 (2021), URL https://doi.org/10.3847/2041-8213/ac089b

    2021 doi

  11. [19]

    Riley et al., Astrophys

    T. Riley et al., Astrophys. J. Lett. 918, L27 (2021), URL https://dx.doi.org/10.3847/2041-8213/ac0a81

    2021 doi

  12. [20]

    G. Baym, C. Pethick, and P. Sutherland, Astrophys. J. 170, 299 (1971)

    1971

  13. [22]

    P. M. Pizzochero, Neutron stars, the most exotic nuclear lab in the universe (2010), 1001.1272, URL https://arxiv.org/abs/1001.1272

    2010 arXiv

  14. [23]

    Cameron, Astrophys

    A. Cameron, Astrophys. J. 130, 884 (1959)

    1959

  15. [24]

    P. A. Zyla et al., Prog. Theor. Exp. Phys. 2020, 083C01 (2020), ISSN 2050-3911, URL https://doi.org/10.1093/ptep/ptaa104

    2020 doi

  16. [25]

    V. A. Ambartsumyan and G. S. Saakyan, Sov. Astron. 4, 187 (1960)

    1960

  17. [26]

    Schaffner-Bielich and A

    J. Schaffner-Bielich and A. Gal, Phys. Rev. C 62, 034311 (2000), URL https://link.aps.org/doi/10.1103/PhysRevC.62.034311

    2000 doi

  18. [27]

    K. A. Maslov, E. E. Kolomeitsev, and D. N. Voskresensky, Phys. Rev. C 92, 052801 (2015), URL https://link.aps.org/doi/10.1103/PhysRevC.92.052801

    2015 doi

  19. [28]

    Thakur, B

    P. Thakur, B. K. Sharma, A. Ashika, S. Srivishnu, and T. K . Jha, Phys. Rev. C 109, 025805 (2024), URL https://link.aps.org/doi/10.1103/PhysRevC.109.025805

    2024 doi

  20. [29]

    Chamel and P

    N. Chamel and P. Haensel, Living Rev. Relativity 11, 10 (2008), URL https://doi.org/10.12942/lrr-2008-10

    2008 doi

  21. [31]

    Cohen and R

    J. Cohen and R. J. Furnstahl, Phys. Rev. C 35, 2231 (1987), URL https://link.aps.org/doi/10.1103/PhysRevC.35.2231

    1987 doi

  22. [32]

    Gell-Mann, Phys

    M. Gell-Mann, Phys. Rev. 125, 1067 (1962), URL https://link.aps.org/doi/10.1103/PhysRev.125.1067

    1962 doi

  23. [33]

    Weissenborn, D

    S. Weissenborn, D. Chatterjee, and J. Schaffner-Bielic h, Nucl. Phys. A 881, 62 (2012), ISSN 0375-9474, URL https://www.sciencedirect.com/science/article/pii/S0375947412000863

    2012

  24. [34]

    Inoue, JPS Conf

    T. Inoue, JPS Conf. Proc 26, 023018 (2019)

    2019

  25. [35]

    Demorest et al., Nature 467, 1081 (2010), URL https://www.nature.com/articles/nature09466#Abs3

    P. Demorest et al., Nature 467, 1081 (2010), URL https://www.nature.com/articles/nature09466#Abs3

    2010

  26. [36]

    Antoniadis, P

    J. Antoniadis, P. C. C. Freire, N. Wex, et al., Science 340, 1233232 (2013), URL https://www.science.org/doi/abs/10.1126/science.1233232

    2013 doi

  27. [38]

    Dover and A

    C. Dover and A. Gal, Prog. Part. Nucl. Phys. 12, 171 (1984), ISSN 0146-6410, URL https://www.sciencedirect.com/science/article/pii/0146641084900048

    1984

  28. [39]

    J. J. Sakurai, Phys. Rev. 132, 434 (1963), URL https://link.aps.org/doi/10.1103/PhysRev.132.434

    1963 doi

  29. [40]

    Greiner and B

    W. Greiner and B. Muller, Quantum Mechanics: Symmetries (2nd Edition, Springer, 2004)

    2004

  30. [41]

    L. L. Lopes and D. P. Menezes, Eur. Phys. J. A 56, 122 (2020)

    2020

  31. [42]

    L. L. Lopes and D. P. Menezes, Astrophys. J. 936, 41 (2022). 40

    2022

  32. [43]

    Gell-Mann, Phys

    M. Gell-Mann, Phys. Lett. 8, 214 (1964), ISSN 0031-9163, URL https://www.sciencedirect.com/science/article/pii/S0031916364

    1964

  33. [44]

    J. J. Sakurai, Modern Quantum Mechanics (Addison Wesley Longman, 1994)

    1994

  34. [45]

    J. J. de Swart, Rev. Mod. Phys. 35, 916 (1963), URL https://link.aps.org/doi/10.1103/RevModPhys.35.916

    1963 doi

  35. [46]

    Weissenborn, D

    S. Weissenborn, D. Chatterjee, and J. Schaffner-Bielic h, Phys. Rev. C 85, 065802 (2012)

    2012

  36. [47]

    L. L. Lopes, Prog. Theor. Exper. Phys. 2023, 113D01 (2023), ISSN 2050-3911

    2023

  37. [48]

    McNAMEE, S

    P. McNAMEE, S. J., and F. CHILTON, Rev. Mod. Phys. 36, 1005 (1964), URL https://link.aps.org/doi/10.1103/RevModPhys.36.1005

    1964 doi

  38. [49]

    Gürsey and L

    F. Gürsey and L. A. Radicati, Phys. Rev. Lett. 13, 173 (1964), URL https://link.aps.org/doi/10.1103/PhysRevLett.13.173

    1964 doi

  39. [50]

    Cavagnoli, D

    R. Cavagnoli, D. Menezes, and C. Providencias, Phys. Re v. C 84, 065810 (2011)

    2011

  40. [51]

    Logoteta, I

    D. Logoteta, I. Vidaña, C. Providência, A. Polls, and I. Bombaci, J. Phys. Conf. Seri. 342, 012006 (2012), URL https://doi.org/10.1088/1742-6596/342/1/012006

    2012 doi

  41. [52]

    Chatterjee and I

    D. Chatterjee and I. Vidana, Eur. Phys. J. A 52, 29 (2016), URL https://doi.org/10.1140/epja/i2016-16029-x

    2016 doi

  42. [53]

    McLerran and R

    L. McLerran and R. D. Pisarski, Nucl. Phys. A 796, 83 (2007), ISSN 0375-9474, URL https://www.sciencedirect.com/science/article/pii/S0375947407006823

    2007

  43. [54]

    Fujimoto, T

    Y. Fujimoto, T. Kojo, and L. McLerran, Phys. Rev. C 113, 035206 (2026), URL https://link.aps.org/doi/10.1103/txbp-t8vm

    2026 doi

  44. [55]

    DeTar and T

    C. DeTar and T. Kunihiro, Phys. Rev. D 39, 2805 (1989), URL https://link.aps.org/doi/10.1103/PhysRevD.39.2805

    1989 doi

  45. [56]

    D. Jido, M. Oka, and A. Hosaka, Prog. Theor. Phys. 106, 873 (2001), ISSN 0033-068X, URL https://doi.org/10.1143/PTP.106.873

    2001 doi

  46. [57]

    Gao, Phys

    B. Gao, Phys. Rev. D 113, 083012 (2026), URL https://link.aps.org/doi/10.1103/vb5r-vdm7

    2026 doi

  47. [58]

    R. F. Sawyer, Astrophys. J. 176, 205 (1972)

    1972

  48. [59]

    Motta, A

    T. Motta, A. Thomas, and P. Guichon, Phys. Lett. B 802, 135266 (2020), ISSN 0370-2693, URL https://www.sciencedirect.com/science/article/pii/S0370269320300708

    2020

  49. [60]

    Bethe and M

    H. Bethe and M. Johnson, Nucl. Phys. A 230, 1 (1974), ISSN 0375-9474

    1974

  50. [61]

    L. L. Lopes, EPJA, in press, arXiv (2026), 2605.30554, U RL https://arxiv.org/abs/2605.30554

    2026 arXiv

  51. [62]

    Rarita and J

    W. Rarita and J. Schwinger, Phys. Rev. 60, 61 (1941), URL https://link.aps.org/doi/10.1103/PhysRev.60.61

    1941 doi

  52. [63]

    Drago, A

    A. Drago, A. Lavagno, G. Pagliara, and D. Pigato, Phys. R ev. C 90, 065809 (2014), URL https://link.aps.org/doi/10.1103/PhysRevC.90.065809

    2014 doi

  53. [64]

    Bodek and T

    A. Bodek and T. Cai, Eur. Phys. J. C 80, 655 (2020), URL https://doi.org/10.1140/epjc/s10052-020-8236-8

    2020 doi

  54. [65]

    J. J. Li, A. Sedrakian, and F. Weber, Phys. Lett. B 783, 234 (2018), ISSN 0370-2693, URL https://www.sciencedirect.com/science/article/pii/S0370269318305070

    2018

  55. [66]

    Sedrakian, J.-J

    A. Sedrakian, J.-J. Li, and F. Weber, Prog. Part. Nucl. P hys. 131, 104041 (2023), ISSN 0146-6410, URL https://www.sciencedirect.com/science/article/pii/S0146641023000224

    2023

  56. [67]

    Baym, Phys

    G. Baym, Phys. Rev. Lett. 30, 1340 (1973), URL https://link.aps.org/doi/10.1103/PhysRevLett.30.1340

    1973 doi

  57. [71]

    Ohnishi, D

    A. Ohnishi, D. Jido, T. Sekihara, and K. Tsubakihara, Ph ys. Rev. C 80, 038202 (2009), URL https://link.aps.org/doi/10.1103/PhysRevC.80.038202

    2009 doi

  58. [72]

    Banik and D

    S. Banik and D. Bandyopadhyay, Phys. Rev. C 64, 055805 (2001), URL https://link.aps.org/doi/10.1103/PhysRevC.64.055805

    2001 doi

  59. [73]

    V. B. Thapa, M. Sinha, J. J. Li, and A. Sedrakian, Phys. Re v. D 103, 063004 (2021), URL https://link.aps.org/doi/10.1103/PhysRevD.103.063004

    2021 doi

  60. [74]

    Thakur, Y

    P. Thakur, Y. Kumaran, L. Sudarsan, K. Kunnampully, B. K . Sharma, and T. K. Jha, Phys. Rev. C 111, 035801 (2025), URL https://link.aps.org/doi/10.1103/PhysRevC.111.035801

    2025 doi

  61. [75]

    L. L. Lopes, Phys. Rev. D 113, 023032 (2026), URL https://link.aps.org/doi/10.1103/nmhy-7f9t

    2026 doi

  62. [76]

    Muto, Phys

    T. Muto, Phys. Rev. C 111, 045802 (2025), URL https://link.aps.org/doi/10.1103/PhysRevC.111.045802

    2025 doi

  63. [77]

    LANDAU and E

    L. LANDAU and E. LIFSHITZ, in Statistical Physics (Third Edition) (Butterworth- Heinemann, Oxford, 1980), pp. 446–516, third edition ed., I SBN 978-0-08-057046-4, URL https://www.sciencedirect.com/science/article/pii/B978008057046450021X

    1980

  64. [78]

    Oset and L

    E. Oset and L. Salcedo, Nucl. Phys. A 468, 631 (1987), ISSN 0375-9474, URL https://www.sciencedirect.com/science/article/pii/0375947487901850

    1987

  65. [79]

    Banik and D

    S. Banik and D. Bandyopadhyay, Phys. Rev. C 66, 065801 (2002), URL https://link.aps.org/doi/10.1103/PhysRevC.66.065801

    2002 doi

  66. [80]

    Thorsson, M

    V. Thorsson, M. Prakash, and J. M. Lattimer, Nucl. Phys. A 572, 693 (1994), ISSN 0375-9474

    1994

  67. [81]

    Lee, Phys

    C.-H. Lee, Phys. Rep. 275, 255 (1996), ISSN 0370-1573, URL https://www.sciencedirect.com/science/article/pii/03701573960

    1996

  68. [83]

    A. S., M. Sinha, V. B. Thapa, and V. Parmar, JCAP 2025, 037 (2025), URL https://doi.org/10.1088/1475-7516/2025/10/037

    2025 doi

  69. [84]

    Typel and H

    S. Typel and H. Wolter, Nucl. Phys. A 656, 331 (1999), ISSN 0375-9474, URL https://www.sciencedirect.com/science/article/pii/S0375947499003103. 41

    1999

  70. [85]

    G. A. Lalazissis, T. Nikšić, D. Vretenar, and P. Ring, Ph ys. Rev. C 71, 024312 (2005), URL https://link.aps.org/doi/10.1103/PhysRevC.71.024312

    2005 doi

  71. [86]

    Chin, Ann

    S. Chin, Ann. Phys. 108, 301 (1977), ISSN 0003-4916, URL https://www.sciencedirect.com/science/article/pii/00034916779

    1977

  72. [87]

    E. K. Heide and S. Rudaz, Phys. Lett. B 262, 375 (1991), ISSN 0370-2693, URL https://www.sciencedirect.com/science/article/pii/037026939190608S

    1991

  73. [88]

    Furnstahl, B

    R. Furnstahl, B. D. Serot, and H.-B. Tang, Nucl. Phys. A 618, 446 (1997), ISSN 0375-9474, URL https://www.sciencedirect.com/science/article/pii/S0375947497000626

    1997

  74. [89]

    J. J. Li, W. H. Long, and A. Sedrakian, Eur. Phys. J. A 54, 133 (2018)

    2018

  75. [90]

    Q. Zhao, B. Y. Sun, and W. H. Long, J. Phys. G 42, 095101 (2015), URL https://doi.org/10.1088/0954-3899/42/9/095101

    2015 doi

  76. [91]

    E. E. Salpeter and H. A. Bethe, Phys. Rev. 84, 1232 (1951), URL https://link.aps.org/doi/10.1103/PhysRev.84.1232

    1951 doi

  77. [92]

    Burgio, H.-J

    G. Burgio, H.-J. Schulze, I. Vidaña, and J.-B. Wei, Prog . Part. Nucl. Phys. 120, 103879 (2021), ISSN 0146-6410, URL https://www.sciencedirect.com/science/article/pii/S0146641021000338

    2021

  78. [93]

    ACHARYA, L

    S. ACHARYA, L. MAHARANA, R. MOHANTY, and P. K. PANDA, Int . J. Mod. Phys. E 08, 107 (1999), URL https://doi.org/10.1142/S0218301399000082

    1999 doi

  79. [94]

    L. L. Lopes, D. P. Menezes, and M. R. Pelicer, Phys. Rev. C 109, 045801 (2024), URL https://link.aps.org/doi/10.1103/PhysRevC.109.045801

    2024 doi

  80. [95]

    Annala, T

    E. Annala, T. Gorda, A. Kurkela, J. Nättilä, and A. Vuori nen, Nat. Phys. 16, 907 (2020)

    2020

  81. [96]

    Olinto, Phys

    A. Olinto, Phys. Lett. B 192, 71 (1987)

    1987

  82. [97]

    Lopes, J

    L. Lopes, J. Jimenez, L. Castro, and C. Flores, Eur. Phys . J. C 85, 515 (2025)

    2025

  83. [98]

    H. C. Das, A. Kumar, S. K. Biswal, and S. K. Patra, Phys. Re v. D 104, 123006 (2021), URL https://link.aps.org/doi/10.1103/PhysRevD.104.123006

    2021 doi

  84. [99]

    Grippa, G

    F. Grippa, G. Lambiase, and T. K. Poddar, Universe 11 (2025), ISSN 2218-1997, URL https://www.mdpi.com/2218-1997/11/3/74

    2025

  85. [100]

    L. L. Lopes, Astrophys Space Sci. 370, 79 (2024), URL https://doi.org/10.1007/s10509-025-04472-1

    2024 doi

  86. [101]

    Hinderer, Astrophys

    T. Hinderer, Astrophys. J. 677, 1216 (2008), URL https://dx.doi.org/10.1086/533487

    2008 doi

  87. [102]

    Chatziioannou, Gen

    K. Chatziioannou, Gen. Rel. Grav 52, 109 (2020)

    2020

  88. [103]

    Flores, L

    C. Flores, L. Lopes, L. Benito, and D. Menezes, Eur. Phy s. J. C 80, 1142 (2020), URL https://doi.org/10.1140/epjc/s10052-020-08705-1

    2020 doi

  89. [104]

    L. L. Lopes et al., Phys. Rev. D 108, 083042 (2023), URL https://link.aps.org/doi/10.1103/PhysRevD.108.083042

    2023 doi

  90. [105]

    B. P. Abbott, R. Abbott, T. D. Abbott, et al., Phys. Rev. Lett. 121, 161101 (2018), URL https://link.aps.org/doi/10.1103/PhysRevLett.121.161101

    2018 doi

  91. [106]

    C. A. Raithel, F. Özel, and D. Psaltis, Astrophys. J. 844, 156 (2017), URL https://doi.org/10.3847/1538-4357/aa7a5a

    2017 doi

  92. [107]

    Drischler, R

    C. Drischler, R. J. Furnstahl, J. A. Melendez, and D. R. Phillips, Phys. Rev. Lett. 125, 202702 (2020), URL https://link.aps.org/doi/10.1103/PhysRevLett.125.202702

    2020 doi

  93. [108]

    S. M. A. Imam and N. K. Patra, Phys. Rev. D 112, 103018 (2025), URL https://link.aps.org/doi/10.1103/2fz9-xlv1

    2025 doi

  94. [109]

    A. M. Santos and D. P. Menezes, Braz. J. Phys. 34, 833 (2004), URL https://doi.org/10.1590/S0103-97332004000500033

    2004 doi

  95. [110]

    Tsiopelas, A

    S. Tsiopelas, A. Sedrakian, and M. Oertel, Eur. Phys. J . A 60, 127 (2024), URL https://doi.org/10.1140/epja/s10050-024-01351-1

    2024 doi

  96. [111]

    Weber and N

    F. Weber and N. Glendenning, Astrophys. J 390, 541 (1992)

    1992

  97. [112]

    Pattersons and A

    M. Pattersons and A. Sulaksono, Eur. Phys. J. C 81, 698 (2021)

    2021

  98. [113]

    L. L. Lopes, Astrophys. J. 966, 184 (2024)

    2024

  99. [114]

    Broderick, M

    A. Broderick, M. Prakash, and J. M. Lattimer, Astrophy s. J. 537, 351 (2000), URL https://doi.org/10.1086/309010

    2000 doi

  100. [115]

    Mallick and S

    R. Mallick and S. Schramm, Phys. Rev. C 89, 045805 (2014), URL https://link.aps.org/doi/10.1103/PhysRevC.89.045805

    2014 doi

  101. [116]

    L. L. Lopes, C. O. V. Flores, and D. P. Menezes, Universe 12 (2026), ISSN 2218-1997, URL https://www.mdpi.com/2218-1997/12/4/117

    2026

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