First-order phase transition from hypernuclear matter to deconfined quark matter obeying new constraints from compact star observations

A. G. Grunfeld; D. Blaschke; H. R. Moshfegh; M. Shahrbaf

REVIEW 4 major objections 4 minor 86 references

First-order phase transition from hypernuclear matter to deconfined quark matter obeying new constraints from compact star observations

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper argues that a first-order transition to color-superconducting quark matter solves the hyperon puzzle and produces hybrid stars reaching 2.2 solar masses while meeting the new observational constraints.

desk verdict Worth engaging: a clear model-construction paper that makes a specific new prediction—the layered hypernuclear-quark star—but that layer sits in a chemical-potential window the authors themselves say their hadronic EoS should not be trusted in. read the letter →

arxiv 1908.04740 v3 pith:D6XOQ7G5 submitted 2019-08-13 nucl-th astro-ph.HEhep-ph

M. Shahrbaf , D. Blaschke , A. G. Grunfeld , H. R. Moshfegh This is my paper · ORCID

classification nucl-thastro-ph.HEhep-ph PACS 13.75.Ev12.38.Aw21.65.+f97.60.Jd26.60.+c25.75.Nq

keywords hyperonpuzzlehybridneutronstarsquarkdeconfinementMaxwellconstructionnonlocalNambu-Jona-Lasiniomodelcolorsuperconductivityequationofstatecompactstarconstraints

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 takes on the hyperon puzzle: adding hyperons to the dense matter inside a neutron star softens the equation of state so much that ordinary hadronic models cannot reach the observed two-solar-mass maximum. The proposed way out is a first-order phase transition, built by a Maxwell construction, from this hypernuclear matter to deconfined, color-superconducting quark matter. With the density-dependent quark model nlNJLB the transition happens at a high enough chemical potential that the star keeps an intermediate hypernuclear shell, and the maximum mass reaches 2.2 solar masses while satisfying the PSR J0740+6620 and GW170817 constraints. A sympathetic reader would take this as evidence that quark deconfinement, not exotic hadronic stiffening, can resolve the puzzle, and that compact stars in the observed mass range may have three distinct layers of matter.

What carries the argument

The argument is carried by a Maxwell construction between two equations of state, in which the phase with the higher pressure at a given baryon chemical potential is the stable one. The hadronic side is the LOCV hypernuclear equation of state, a lowest-order constrained variational calculation with realistic two- and three-body nuclear forces, and with Lambda and Sigma-minus hyperons added as noninteracting particles in beta equilibrium. The quark side is a nonlocal Nambu-Jona-Lasinio model with a color-superconducting diquark condensate; in the nlNJLB variant the bag pressure and vector coupling are made density-dependent by interpolating among three constant-parameter pressures, which confines quarks at low density and keeps the matter stiff at high density. A constant-speed-of-sound extrapolation extends the quark equation of state to the energy densities needed for the maximum mass. Together these pieces push the deconfinement crossing above the hyperon threshold, creating the intermediate hypernuclear phase.

What would settle it

Recompute the same Maxwell construction with a hadronic phase that includes interacting hyperons and check whether the hyperon-onset chemical potential moves above the quark-deconfinement chemical potential near 1090 to 1110 MeV; if it does, the claimed hypernuclear layer is gone. A radius measurement of a 1.4 to 1.6 solar-mass neutron star that rules out the predicted hybrid branch would also settle the question.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the quark matter model determines whether deconfinement pre-empts strangeness or coexists with it. With the constant-coupling model nlNJLA, the hadron-quark pressure crossing lies below the hyperon threshold, so quark matter replaces nuclear matter directly. With the generalized model nlNJLB, whose bag pressure and vector coupling depend on density, the crossing shifts to roughly 1090 to 1110 MeV, above the hyperon onset at 1063 MeV; the result is a hybrid star equation of state with an intermediate hypernuclear phase between the nuclear outer core and the color-superconducting quark inner core. This equation of state reaches maximum masses up to 2.2 solar masses, above the one-sigma PSR J0740+6620 lower bound, while radii comply with the GW170817-derived constraints: a 1.6-solar-mass star must have radius above 10.7 km and a 1.4-solar-mass star below 13.6 km. All stars in the observed mass range from about 1.2 to 2.2 solar masses would then contain a hypernuclear shell around a quark core.

Load-bearing premise

The paper's new hypernuclear layer lives in a chemical-potential window between the hyperon onset near 1063 MeV and the deconfinement transition near 1090 to 1110 MeV, while Section II A itself says the hadronic equation of state should not be applied above about 1050 MeV. If that hadronic model is not reliable in this window, or if treating hyperons as noninteracting particles shifts the onset, the intermediate phase may disappear.

Editorial extensions

If this is right

If the nlNJLB hybrid equation of state is right, the maximum mass of a compact star is about 2.2 solar masses, satisfying the PSR J0740+6620 lower limit.
Neutron stars in the observed mass range, about 1.2 to 2.2 solar masses, would contain three matter layers: a nuclear outer core, a hypernuclear shell, and a color-superconducting quark inner core.
Quark deconfinement would begin already at star masses between about 0.99 and 1.14 solar masses, so quark cores would be common rather than limited to the most massive stars.
For isospin-symmetric matter, the model predicts a deconfinement onset between 2.2 and 2.7 times nuclear saturation density for all nlNJLB parameter sets, a target range for future heavy-ion collision experiments.
Because the energy-density jump at the transition is not large enough, this class of models does not produce a disconnected third family of stable hybrid stars.

Reading between the lines

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

The intermediate hypernuclear layer is the paper's most fragile outcome: it occupies the chemical-potential region where the hadronic model is stated to lose validity, so a hadronic treatment with interacting hyperons is the natural check that could erase it.
If the layered structure is real, it should leave a distinctive mass-radius signature near 1.4 to 1.6 solar masses, where the hypernuclear shell softens the equation of state before the quark core stiffens it; current and future radius measurements can look for this nonmonotonic behavior.
The density-dependent bag pressure acts as a phenomenological stand-in for confinement, and independent information about the quark matter speed of sound from gravitational-wave or radius data would test whether this mechanism is the right one.
The predicted symmetric-matter onset of 2.2 to 2.7 times nuclear saturation density is a concrete target for collision experiments, but a fair comparison will require the finite-temperature extension that the paper says is still to be built.

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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

First, the one thing to know: this is a model-construction paper, not a discovery paper, and it reads like one. It does something genuinely new: it builds a two-phase hybrid EoS in which deconfinement occurs after hyperon onset, so compact stars can develop a nuclear → hypernuclear → quark-matter layered structure, and it reaches maximum masses above 2.1 solar masses. It also gives specific predictions for deconfinement in symmetric matter (2.2–2.7 n0) that heavy-ion experiments at FAIR or NICA could try to test.

What it does well: the Maxwell construction and TOV integrations are standard and look correctly handled; the paper presents four parameter sets and shows how the results depend on them; it compares the constant-coupling nlNJLA model (deconfinement before hyperon onset) with the density-dependent nlNJLB model (intermediate hypernuclear shell). The authors are also unusually candid about limitations. They state that the LOCVY hadronic EoS should not be applied beyond a chemical potential of about 1050 MeV, then use it up to 1090–1110 MeV for the nlNJLB transition, with hyperon onset at 1063 MeV. That is exactly where the paper's most novel result, the intermediate hypernuclear phase, lives. The hyperons are treated as non-interacting, and the hadronic EoS is explicitly flagged as unjustified there. If hyperon interactions shift the onset, or if chiral symmetry restoration softens the EoS, the layered structure could disappear. So the 2.2-solar-mass hybrid star with a hyperon shell is best read as a demonstration of consistency, not a prediction.

The qualitative conclusion, that quark deconfinement can resolve the hyperon puzzle under current mass constraints, is more robust, because nlNJLA already satisfies the constraint with a transition before hyperons appear. The paper also honestly notes the no-reconfinement assumption and the constant-speed-of-sound extrapolation above 690 MeV/fm³. No code or EoS tables are provided, and several key inputs come from earlier work by the same group, so the numbers are not independently reproducible from the text. That is a moderate weakness, not a fatal one.

Verdict: this deserves a serious referee. The claims are clearly stated, limitations are flagged, and the paper gives the subfield a concrete, testable construction. I would send it to review, then ask the authors to provide the EoS tables and to address the 1050 MeV validity issue head-on, either by extending the hadronic model or by clearly labeling the layered-star result as exploratory.

Referee Report

4 major / 4 minor

Summary. The paper constructs hybrid compact-star equations of state by combining the LOCV hypernuclear hadronic EoS with a color-superconducting nonlocal NJL quark-matter EoS, using a Maxwell construction for the deconfinement transition. Two quark-model variants are considered: nlNJLA with constant couplings, and nlNJLB with density-dependent vector coupling and bag pressure, the latter matched to a constant-speed-of-sound extrapolation at high density. The authors find that nlNJLA deconfines before hyperon onset, whereas their four nlNJLB parameter sets produce deconfinement after hyperon onset, leading to stars with an intermediate hypernuclear shell and maximum masses up to about 2.2 Msun. They interpret this as a viable solution of the hyperon puzzle under the PSR J0740+6620 and GW170817 constraints, and additionally discuss the deconfinement transition in isospin-symmetric matter for heavy-ion applications.

Significance. If the central result is robust, the paper provides a concrete, observationally constrained scenario in which massive hybrid stars contain a layered structure of nuclear matter, hypernuclear matter, and color-superconducting quark matter, and it connects this scenario to measurable deconfinement transition densities in symmetric matter. The work is timely, clearly structured, and transparent about the model dependence through four parameter sets. Its main strength is the demonstration that a sufficiently stiff quark-matter EoS with a delayed first-order transition can satisfy the 2 Msun constraint even when hyperons soften the hadronic phase. However, the most novel claim, the existence of an intermediate hypernuclear phase, relies on the LOCVY EoS in a regime where the authors themselves caution against its use, and the quantitative maximum-mass value depends on a CSS extrapolation whose parameters are not systematically varied.

major comments (4)

[Section II A and Fig. 8] The central new result, the intermediate hypernuclear phase in model nlNJLB, is obtained by applying the LOCVY hadronic EoS in the chemical-potential window from hyperon onset at mu = 1063 MeV to the deconfinement transition at roughly 1090-1110 MeV, yet the paper states in Section II A that the LOCVY EoS should not be applied when the chemical potential exceeds about 1050 MeV and that hyperons are treated as non-interacting particles. This is exactly the window in which the claimed new phase lives, so the existence of the hypernuclear shell is not established unless the authors demonstrate robustness against the identified limitations, for example by including repulsive hyperon mean fields or by varying the YN interaction and showing that the crossing point and the layer structure survive.
[Section IV, Figs. 6 and 7] The quantitative statement that the maximum mass reaches about 2.2 Msun is obtained after replacing the nlNJLB EoS with a constant-speed-of-sound extrapolation above the matching point epsilon = 690 MeV/fm3, but the paper does not report the value of c_s^2 used in the extrapolation or the sensitivity of M_max to the matching point and to c_s^2. Since this extrapolated EoS determines the maximum mass, the authors should provide such a sensitivity analysis or explicitly state that the 2.2 Msun value is a consequence of the CSS assumption rather than a prediction of the underlying quark model.
[Abstract and Introduction (Ref. [27])] The abstract claims that model nlNJLB provides 'for the first time' a hybrid star EoS with an intermediate hypernuclear matter phase between nuclear and color-superconducting quark matter, but the introduction itself describes Ref. [27] as having shown that a compact-star structure with a hypernuclear shell and a color-superconducting quark core is possible while fulfilling the 2 Msun constraint. The novelty claim therefore appears to conflict with the authors' own cited literature and needs to be clarified or qualified, for instance by specifying that the present work is the first to obtain this structure with the LOCVY and generalized nlNJL combination.
[Section II B, Eqs. (21)-(24) and Table I] The appearance of the intermediate hypernuclear phase is controlled by the choice of the switching parameters mu_<, Gamma_<, mu_<<, Gamma_<< and the couplings eta_<, eta_> in the density-dependent nlNJLB model, with mu_< values near 1070-1090 MeV placed close to the hyperon onset. The paper should make explicit that the intermediate phase is a consequence of this parameter choice rather than an inevitable prediction of the model, and should show how the phase structure changes when mu_< is varied across the hyperon-onset window.

minor comments (4)

[Section II A, Eq. (20)] The text states f_pi = 0.093 MeV for the pion decay constant, which appears to be a typo; the intended value is likely 0.093 GeV or 93 MeV, since the combination f_pi^2 M_pi^2 in the denominator would otherwise have incorrect dimensions.
[Fig. 10 caption] The figure caption and axis label contain 'PSR J0740+6220', which should read PSR J0740+6620 as in the abstract and the rest of the paper.
[Section IV, paragraph after Fig. 10] There is a typo in 'sufficiently large jump in the energy density tat the deconfinement transition'; 'tat' should be 'at'.
[Section II B, paragraph after Eq. (8)] The word 'wich' in 'a covariant formfactor wich accounts' should be 'which'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the intermediate hypernuclear phase is a computed model outcome; the flagged LOCVY validity and CSS matching issues are extrapolation risks, not circular reductions.

full rationale

The paper's derivation chain is a two-phase model study: it takes the LOCVY hadronic EoS (from the authors' prior variational calculations), the nlNJL quark EoS with density-dependent coefficients (introduced in Ref. [33] and calibrated to the density-functional quark matter approach of Ref. [42]), applies a Maxwell construction, and solves the TOV equations. The claimed new intermediate hypernuclear phase is a computed consequence of the chosen Table I parameters, not a quantity that was fitted to produce itself: no step in Eqs. (19)-(24) or in the TOV integration uses the existence of the intermediate hypernuclear phase as an input. The switching parameters µ< = 1070-1090 MeV are model inputs adopted from prior work, and they are indeed larger than the hyperon onset at 1063 MeV, which makes the appearance of an intermediate phase plausible; however, the actual deconfinement crossing is still determined by the pressure equality P_H = P_Q, and the paper explicitly contrasts model nlNJLA, where no such phase is realized, to display the model sensitivity. The self-citations to Refs. [33] and [42] supply an openly adopted phenomenological quark EoS, not a hidden theorem; the tanh-interpolation ansatz for η(µ) and B(µ) is stated explicitly in Eqs. (21)-(24). The manuscript also flags its own limitations: in Section II A it states that 'we should abstain from applying' the LOCVY EoS 'when the chemical potential exceeds about 1050 MeV', even though the intermediate phase resides in the 1063-1110 MeV window, and it notes that the CSS matching point is 'a matter of choice'. These are extrapolation and correctness risks, not circular reductions: they weaken the robustness of the central new claim but do not make it equivalent to its inputs. No quoted equation reduces to its own input by construction, and no fitted parameter is renamed as a prediction. Therefore the paper shows no significant circularity.

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

The central claim depends on the LOCVY hypernuclear EoS (with non-interacting hyperons), the nlNJL quark EoS (two flavors, color superconducting), a Maxwell construction with an explicit no-reconfinement rule, and a set of hand-chosen parameters including the bag function B(mu), the vector couplings eta_< and eta_>, the switching scales mu_<, Gamma_<, mu_<<, Gamma_<<, and the CSS matching point at 690 MeV/fm3. The main new structural result, the intermediate hypernuclear phase, is sensitive to these choices.

free parameters (6)

Vector coupling eta in model nlNJLA = 0.12, 0.13, 0.14, 0.15
Constant vector coupling controls quark EoS stiffness; only eta > 0.12 avoids reconfinement and gives the hybrid sequences in Figs. 2-4. The maximum mass and transition density shift with eta.
Bag pressure constant B in model nlNJLB = 20, 25, 30, 30 MeV/fm3 for sets 1-4
The amplitude in Eq. (22) suppresses quark pressure at low chemical potential; it is the main ingredient that pushes deconfinement above the hyperon threshold, creating the intermediate hypernuclear phase.
Low-density vector coupling eta_< (nlNJLB) = 0.05 (sets 1, 2), 0.07 (sets 3, 4)
Input to the interpolation in Eq. (23); softens the low-density quark EoS and influences the transition window.
High-density vector coupling eta_> (nlNJLB) = 0.09, 0.12, 0.12, 0.16 for sets 1-4
Controls high-density stiffness of the quark phase; larger eta_> raises the maximum mass, which must clear the PSR J0740+6620 bound.
Switching scales and widths (mu_<, Gamma_<, mu_<<, Gamma_<<) = mu_< = 1070-1090 MeV, Gamma_< = 150-170 MeV, mu_<< = 1500-1600 MeV, Gamma_<< = 270-300 MeV
Define where the three nlNJL parametrizations are switched in Eq. (23); these choices set the chemical potential window of the phase transition.
CSS matching energy density epsilon_CSS = 690 MeV/fm3
Above this density the quark EoS is replaced by a constant speed of sound extrapolation; the matching point choice contributes to setting Mmax near 2.2 Msun.

assumptions (6)

ad hoc to paper The LOCVY hadronic EoS is used in a chemical potential range where the paper itself declares it invalid (above about 1050 MeV).
Section II A says 'we should abstain from applying it when the chemical potential exceeds about 1050 MeV', but hyperon onset is at 1063 MeV and the nlNJLB transition is nearby; the intermediate hypernuclear phase rests on this extrapolated EoS.
domain assumption Hyperons in the hadronic phase are treated as non-interacting particles.
Section II A states that hyperons are non-interacting; the hyperon onset and the softening that defines the puzzle depend on this simplification.
domain assumption After deconfinement, the hadronic EoS is no longer considered, so reconfinement crossings are ignored (no reconfinement paradigm).
Section II C: second crossings in P(mu) are excluded by assumption, which shapes the hybrid star sequences and the choice of 'physical' nlNJLA cases.
domain assumption The quark matter EoS is restricted to two flavors (u,d) and contains no strange quarks.
Section II B uses the two-flavor nlNJL model, while the hadronic phase contains Lambda and Sigma- hyperons; strangeness from dissolving hyperons is not represented in the quark phase.
domain assumption The nlNJL mean-field model with a diquark condensate adequately describes cold deconfined quark matter at neutron star densities.
The quark EoS is taken from refs. [33,40,41] with the covariant form factor and couplings; its applicability at these densities is assumed.
standard math Standard general relativity (TOV equations) and the chosen crust EoS describe the star's structure.
Section III solves TOV with Negele-Vautherin and Harrison-Wheeler crust EoS; this is standard practice and not the main source of uncertainty.

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Pith. "Pith review of First-order phase transition from hypernuclear matter to deconfined quark matter obeying new constraints from compact star observations." pith.science (2026). https://pith.science/paper/D6XOQ7G5

@misc{pith2026190804740,
  author       = {Pith},
  title        = {Pith review of: First-order phase transition from hypernuclear matter to deconfined quark matter obeying new constraints from compact star observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D6XOQ7G5}},
  note         = {Machine review of arXiv:1908.04740}
}

abstract

We reconsider the problem of the hyperon puzzle and its suggested solution by quark deconfinement within the two-phase approach to hybrid compact stars with recently obtained hadronic and quark matter equations of state. For the hadronic phase we employ the hypernuclear equation of state from the lowest order constrained variational method and the quark matter phase is described by a sufficiently stiff equation of state based on a color superconducting nonlocal Nambu-Jona-Lasinio model with constant (model nlNJLA) and with density-dependent (model nlNJLB) parameters. We study the model dependence of the phase transition obtained by a Maxwell construction. Our study confirms that also with the present set of equations of state quark deconfinement presents a viable solution of the hyperon puzzle even for the new constraint on the lower limit of the maximum mass from PSR J0740+6620. In this work we provide with model nlNJLB for the first time a hybrid star EoS with an intermediate hypernuclear matter phase between the nuclear and color superconducting quark matter phases, for which the maximum mass of the compact star reaches $2.2~M_\odot$, in accordance with most recent constraints. In model nlNJLA such a phase cannot be realised because the phase transition onset is at low densities, before the hyperon threshold density is passed. We discuss possible consequences of the hybrid equation of state for the deconfinement phase transition in symmetric matter as it will be probed in future heavy-ion collisions at FAIR, NICA and corresponding energy scan programs at the CERN and RHIC facilities.

Figures

Figures reproduced from arXiv: 1908.04740 by the authors.

**Figure 1.** Chiral symmetry restoration in the hadronic phase of matter leads to a parity doubling of hadronic states. For the applications to compact stars this concerns in particular the chiral partner state of the nucleon, the N(1535) which at a density exceeding nχSR will become degenerate in mass with the nucleon. This scenario, supported by lattice QCD simulations at finite temperatures [37], has been investigated, e.g., … view at source ↗

**Figure 1.** FIG. 1. Nuclear and hypernuclear matter EoS obtained from the LOCV method, compared [PITH_FULL_IMAGE:figures/full_fig_p025_1.png] view at source ↗

**Figure 2.** FIG. 2. Pressure as a function of chemical potential for the Maxwell construction of the deconfine [PITH_FULL_IMAGE:figures/full_fig_p026_2.png] view at source ↗

Figures from the paper (11 more)

**Figure 3.** Figure 3: FIG. 3. Pressure as a function of energy density for Maxwell construction of the deconfine [PITH_FULL_IMAGE:figures/full_fig_p027_3.png]

**Figure 4.** Figure 4: FIG. 4. Mass-radius relation of hybrid star for Maxwell construction of the deconfinement PT [PITH_FULL_IMAGE:figures/full_fig_p028_4.png]

**Figure 5.** Figure 5: FIG. 5. Hybrid star EoS (bold solid line) obtained by a Maxwell construction between the [PITH_FULL_IMAGE:figures/full_fig_p029_5.png]

**Figure 6.** Figure 6: FIG. 6. Quark matter EoS for which we have used the nlNJLB quark matter model with density [PITH_FULL_IMAGE:figures/full_fig_p030_6.png]

**Figure 7.** Figure 7: FIG. 7. The squared speed of sound [PITH_FULL_IMAGE:figures/full_fig_p031_7.png]

**Figure 8.** Figure 8: FIG. 8. Pressure as a function of chemical potential for the Maxwell construction of the de [PITH_FULL_IMAGE:figures/full_fig_p032_8.png]

**Figure 9.** Figure 9: FIG. 9. Pressure as a function of energy density for the Maxwell construction of the deconfinement [PITH_FULL_IMAGE:figures/full_fig_p033_9.png]

**Figure 10.** Figure 10: FIG. 10. Mass-radius relation of hybrid star for Maxwell construction of the deconfinement PT [PITH_FULL_IMAGE:figures/full_fig_p034_10.png]

**Figure 11.** Figure 11: FIG. 11. Profiles of energy densities for model nlNJLA (upper panel) with four cases of vector cou [PITH_FULL_IMAGE:figures/full_fig_p035_11.png]

**Figure 12.** Figure 12: FIG. 12. Profiles of energy densities for model nlNJLA (upper panel) with four cases of vector [PITH_FULL_IMAGE:figures/full_fig_p036_12.png]

**Figure 13.** Figure 13: FIG. 13. Pressure versus baryon chemical potential in the isospin-symmetric case for the LOCVY [PITH_FULL_IMAGE:figures/full_fig_p037_13.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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Mukherjee, S

A. Mukherjee, S. Schramm, J. Steinheimer and V. Dexheimer, Astron. Astrophys. 608 (2017) A110

work page 2017

[2] [1]

a microscopic method in conﬁguration space which is purely variational

[3] [2]

simply generalizable to ﬁnite temperature

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In fact, the two-body energy in LOCV method is a functional of correlation function

correlation functions for baryon-baryon interactions as well as structure functions which are important quantities of interest in scattering studies, are obtained directly 7 in our formulation. In fact, the two-body energy in LOCV method is a functional of correlation function. Thus, by a minimization of the energy with respect to the correlation function...

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tensor correlation functions are employed

[6] [5]

considering Eq.(4), the energy per baryon and correlation functions are state-dependent and can be obtained for each state which is deﬁned by α ={J,L,S,T,T z,s}

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Recently, we have extended the work of Goudarzi et al

numerical calculations are not a time consuming, so that they can be performed on standard desktop or laptop computers. Recently, we have extended the work of Goudarzi et al. [58] by including hyperons, and studied the composition and EoS of a charged neutral, equilibrated mixture of neutrons, protons, electrons, muons, free Σ− as well as Λ hyperons at ze...

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Γfψ(x− z 2), (6) ja D(x) = ∫ d4z g(z) ¯ψC(x + z

work page