pith. sign in

arxiv: 2602.14113 · v2 · pith:UF2VJ44Wnew · submitted 2026-02-15 · ⚛️ nucl-th · astro-ph.HE· cond-mat.quant-gas· cond-mat.supr-con· hep-ph

Quarkyonic matter and hadron-quark crossover from an ultracold atom perspective

Hiroyuki Tajima , Kei Iida , Toru Kojo , Haozhao Liang This is my paper

Pith reviewed 2026-05-21 12:59 UTC · model grok-4.3

classification ⚛️ nucl-th astro-ph.HEcond-mat.quant-gascond-mat.supr-conhep-ph
keywords quarkyonic matterhadron-quark crossoverspeed of soundBEC-BCS crossovertripling fluctuationsneutron star equation of stateultracold atomsfield theory
0
0 comments X

The pith

The tripling fluctuation effect accounts for both the speed of sound peak and baryon momentum shells in the hadron-quark crossover.

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

The paper constructs a field-theoretical description of the continuous transition from hadrons to quarks in dense matter by drawing an analogy to the BEC-BCS crossover observed in ultracold atom gases. Within a simplified model, the tripling fluctuation effect produces a peak in the speed of sound while also generating a shell-like structure in the baryon momentum distribution. These two features together match the expectations of the quarkyonic matter picture that has been proposed for neutron star interiors. A sympathetic reader cares because the work supplies a microscopic mechanism for how pressure rises rapidly without a sharp phase boundary, directly affecting the equation of state that governs neutron star structure and gravitational-wave signals.

Core claim

In a simplified field-theoretical framework inspired by the BEC-BCS crossover in ultracold atoms, the tripling fluctuation effect simultaneously produces a peak in the speed of sound and a baryon momentum-shell structure, thereby providing a microscopic derivation of the quarkyonic matter model for the hadron-quark crossover.

What carries the argument

The tripling fluctuation effect, which arises in the quantum many-body treatment of the crossover and generates the peak in sound velocity together with the shell structure in the baryon momentum distribution.

If this is right

  • The hadron-quark crossover proceeds continuously without requiring a first-order phase transition.
  • The quarkyonic matter scenario receives a field-theoretical microscopic foundation from many-body fluctuation physics.
  • The speed-of-sound peak functions as a direct signature of tripling fluctuations rather than other proposed mechanisms.
  • The baryon momentum distribution develops shell-like features at high densities as a natural outcome of the same effect.

Where Pith is reading between the lines

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

  • The same fluctuation mechanism could be tested by mapping nuclear-matter observables onto controllable ultracold-atom setups.
  • Incorporating the effect into more realistic interactions would allow refined predictions for neutron-star radii and tidal deformability.
  • Analogous tripling or higher-order fluctuations may govern crossover physics in other strongly coupled systems such as the quark-gluon plasma.

Load-bearing premise

The tripling fluctuation mechanism identified in ultracold-atom BEC-BCS systems transfers directly to the authors' simplified field-theoretical model of the hadron-quark crossover.

What would settle it

A lattice QCD simulation or neutron-star observation that finds no peak in the speed of sound near the expected crossover density, or that shows a smooth baryon momentum distribution without shell structure.

Figures

Figures reproduced from arXiv: 2602.14113 by Haozhao Liang, Hiroyuki Tajima, Kei Iida, Toru Kojo.

Figure 1
Figure 1. Figure 1: Calculated momentum distributions of (a) quark-like fermions fQ(k) and (b) baryon-like trimers fB(K) at several µ/T, where kF = √ 2mµ is the Fermi momentum. The temperature is fixed at T = 0.1B. quarkyonic matter picture [10]. At small K, the cancellation between the bound and scattering contributions in Eq. (18) leads to the strong suppression of fB(K). On the other hand, just above k = 3kF, the negative … view at source ↗
Figure 2
Figure 2. Figure 2: Isothermal speed of sound cs normalized by the Fermi velocity vF = kF/m. The temperature is taken as T = 0.125B. baryon-baryon and quark-quark interactions except for the confinement force [13]. While quarks behave as relativistic particles, baryons are assumed to be non-relativistic particles. In such a case, we obtain the net baryon number density ρ/Nc in symmetric matter (where Nc = 3 is the color degre… view at source ↗
read the original abstract

The dense matter equation of state is of great interest due to the recent development of astrophysical observations for neutron stars. A rapid increase in pressure indicates a continuous crossover from a hadron phase to a quark phase without any phase transitions, yet its microscopic mechanism remains elusive. Recently, a peak in the speed of sound and a baryon momentum-shell structure, which are predicted from a quarkyonic matter picture, have been regarded as key features of the hadron-quark crossover. In this work, we explore a field-theoretical framework to describe the hadron-quark crossover, drawing an analogy with the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover established in ultracold atomic experiments. Strikingly, a peak in the speed of sound and the baryon momentum-shell structure can simultaneously be explained by the tripling fluctuation effect arising from a different context of quantum many-body physics. We demonstrate these properties in a simplified model and provide a microscopic derivation of the quarkyonic matter model within our field-theoretical framework.

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

1 major / 1 minor

Summary. The manuscript develops a field-theoretical model for the hadron-quark crossover in dense matter, inspired by the BEC-BCS crossover in ultracold atoms. It argues that a tripling fluctuation effect can simultaneously produce a peak in the speed of sound and a baryon momentum-shell structure, thereby supplying a microscopic derivation of the quarkyonic matter picture within the authors' simplified framework.

Significance. If the analogy and its implementation prove robust, the approach could furnish a concrete microscopic link between controlled atomic many-body physics and the equation of state relevant to neutron-star observations. The use of a simplified model to demonstrate both features at once is a clear strength, though the result's broader impact depends on showing that the fluctuation mechanism survives the differences between atomic and QCD interactions.

major comments (1)
  1. The central claim requires that the tripling fluctuation mechanism identified in the atomic BEC-BCS context directly generates both the speed-of-sound peak and the baryon momentum-shell structure when mapped onto hadron-quark degrees of freedom. The manuscript implements this via a simplified Lagrangian/Hamiltonian but does not report explicit checks that isolate the tripling term and verify survival of the shell structure under deformations away from the atomic limit (e.g., longer-range interactions or added confinement). This robustness test is load-bearing for the transferability argument.
minor comments (1)
  1. Notation for the fluctuation spectrum and the precise definition of the tripling term could be clarified with an explicit equation early in the model section to aid readers unfamiliar with the atomic literature.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the potential impact of our work. We address the major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: The central claim requires that the tripling fluctuation mechanism identified in the atomic BEC-BCS context directly generates both the speed-of-sound peak and the baryon momentum-shell structure when mapped onto hadron-quark degrees of freedom. The manuscript implements this via a simplified Lagrangian/Hamiltonian but does not report explicit checks that isolate the tripling term and verify survival of the shell structure under deformations away from the atomic limit (e.g., longer-range interactions or added confinement). This robustness test is load-bearing for the transferability argument.

    Authors: We agree that demonstrating robustness under deformations is valuable for strengthening the transferability argument. Our manuscript employs a minimal field-theoretical model to show that the tripling fluctuation effect, adapted from the BEC-BCS context, can simultaneously produce both the speed-of-sound peak and the baryon momentum-shell structure in a simplified hadron-quark framework. While we have not included explicit numerical isolations of the tripling term or tests with longer-range interactions or confinement in the present version, the mechanism originates from general features of quantum many-body fluctuations that are not tied exclusively to short-range atomic potentials. In the revision, we will add a new subsection discussing the expected persistence of these features, supported by perturbative arguments and references to analogous robustness in related crossover models. This will clarify why the core results are not artifacts of the atomic limit while maintaining the paper's focus on the simplified demonstration. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is an independent analogy implemented in a simplified model

full rationale

The paper constructs a field-theoretical model by explicit analogy to the BEC-BCS crossover in ultracold atoms, then demonstrates that the tripling fluctuation effect produces both a speed-of-sound peak and baryon momentum-shell structure. This is presented as an exploratory mapping and microscopic derivation of quarkyonic features rather than a reduction of outputs to inputs by construction. No equations or sections in the provided text show parameters fitted to the target observables and then relabeled as predictions, nor do self-citations serve as the sole load-bearing justification for the central mapping. The derivation remains self-contained as a modeling choice whose validity rests on the analogy's qualitative robustness, which is external to any internal fitting loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on the transferability of the tripling fluctuation concept and on the validity of the simplified model; no explicit free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption The tripling fluctuation effect from ultracold-atom BEC-BCS physics applies to the hadron-quark crossover.
    This is the central analogy invoked to derive the quarkyonic features.

pith-pipeline@v0.9.0 · 5742 in / 1173 out tokens · 48701 ms · 2026-05-21T12:59:57.208516+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

43 extracted references · 43 canonical work pages · 3 internal anchors

  1. [1]

    Fukushima K and Hatsuda T 2010 Reports on Progress in Physics 74 014001

    work page 2010

  2. [2]

    Özel F and Freire P 2016 Annual Review of Astronomy and Astrophysics 54 401–440

    work page 2016

  3. [3]

    Li B A, Cai B J, Xie W J and Zhang N B 2021 Universe 7 182

    work page 2021

  4. [4]

    Baym G, Hatsuda T, Kojo T, Powell P D, Song Y and Takatsuka T 2018 Rep. Prog. Phys. 81 056902 URL https://dx.doi.org/10.1088/1361-6633/aaae14 7 IOP Publishing Journal vv (yyyy) aaaaaa Author et al

    work page doi:10.1088/1361-6633/aaae14 2018

  5. [5]

    Masuda K, Hatsuda T and Takatsuka T 2013 Astrophys. J. 764 12 ( Preprint 1205.3621)

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  6. [6]

    Schäfer T and Wilczek F 1999 Phys. Rev. Lett. 82(20) 3956–3959 URL https://link.aps.org/doi/10.1103/PhysRevLett.82.3956

    work page doi:10.1103/physrevlett.82.3956 1999

  7. [7]

    Kojo T 2021 AAPPS Bulletin 31 11

    work page 2021

  8. [8]

    Fujimoto Y, Fukushima K, Kamata S and Murase K 2024 Phys. Rev. D 110(3) 034035 URL https://link.aps.org/doi/10.1103/PhysRevD.110.034035

    work page doi:10.1103/physrevd.110.034035 2024

  9. [9]

    Huang Y J, Baiotti L, Kojo T, Takami K, Sotani H, Togashi H, Hatsuda T, Nagataki S and Fan Y Z 2022 Phys. Rev. Lett. 129(18) 181101 URL https://link.aps.org/doi/10.1103/PhysRevLett.129.181101

    work page doi:10.1103/physrevlett.129.181101 2022

  10. [10]

    Fujimoto Y, Fukushima K, Hotokezaka K and Kyutoku K 2023 Phys. Rev. Lett. 130(9) 091404 URL https://link.aps.org/doi/10.1103/PhysRevLett.130.091404

    work page doi:10.1103/physrevlett.130.091404 2023

  11. [11]

    McLerran L and Pisarski R D 2007 Nucl. Phys. A 796 83–100 ( Preprint 0706.2191)

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  12. [12]

    McLerran L and Reddy S 2019 Phys. Rev. Lett. 122(12) 122701 URL https://link.aps.org/doi/10.1103/PhysRevLett.122.122701

    work page doi:10.1103/physrevlett.122.122701 2019

  13. [13]

    Fujimoto Y, Kojo T and McLerran L D 2024 Phys. Rev. Lett. 132(11) 112701 URL https://link.aps.org/doi/10.1103/PhysRevLett.132.112701

    work page doi:10.1103/physrevlett.132.112701 2024

  14. [14]

    Chin C, Grimm R, Julienne P and Tiesinga E 2010 Rev. Mod. Phys. 82(2) 1225–1286 URL https://link.aps.org/doi/10.1103/RevModPhys.82.1225

    work page doi:10.1103/revmodphys.82.1225 2010

  15. [15]

    Zwerger W 2011 The BCS-BEC crossover and the unitary Fermi gas vol 836 (Springer Science & Business Media)

    work page 2011

  16. [16]

    Strinati G C, Pieri P, Röpke G, Schuck P and Urban M 2018 Phys. Rep. 738 1–76

    work page 2018

  17. [17]

    Ohashi Y, Tajima H and van Wyk P 2020 Prog. Part. Nucl. Phys. 111 103739 ISSN 0146-6410 URL https://www.sciencedirect.com/science/article/pii/S0146641019300742

    work page 2020

  18. [18]

    2014 Proc

    Kasahara S, Watashige T, Hanaguri T, Kohsaka Y, Yamashita T, Shimoyama Y, Mizukami Y, Endo R, Ikeda H, Aoyama K et al. 2014 Proc. Natl. Acad. Sci. 111 16309–16313

    work page 2014

  19. [19]

    Nakagawa Y, Kasahara Y, Nomoto T, Arita R, Nojima T and Iwasa Y 2021 Science 372 190–195

    work page 2021

  20. [20]

    Suzuki Y, Wakamatsu K, Ibuka J, Oike H, Fujii T, Miyagawa K, Taniguchi H and Kanoda K 2022 Phys. Rev. X 12(1) 011016 URL https://link.aps.org/doi/10.1103/PhysRevX.12.011016

    work page doi:10.1103/physrevx.12.011016 2022

  21. [21]

    Iida K and Itou E 2022 Progress of Theoretical and Experimental Physics 2022 111B01

    work page 2022

  22. [22]

    High Energ

    Iida K, Itou E, Murakami K and Suenaga D 2024 J. High Energ. Phys. 2024 22

    work page 2024

  23. [23]

    Kojo T and Suenaga D 2022 Phys. Rev. D 105(7) 076001 URL https://link.aps.org/doi/10.1103/PhysRevD.105.076001

    work page doi:10.1103/physrevd.105.076001 2022

  24. [24]

    Chiba R and Kojo T 2024 Phys. Rev. D 109(7) 076006 URL https://link.aps.org/doi/10.1103/PhysRevD.109.076006

    work page doi:10.1103/physrevd.109.076006 2024

  25. [25]

    Fukushima K and Minato S 2025 Phys. Rev. D 111(9) 094006 URL https://link.aps.org/doi/10.1103/PhysRevD.111.094006

    work page doi:10.1103/physrevd.111.094006 2025

  26. [26]

    Low Temp

    Nozieres P and Schmitt-Rink S 1985 J. Low Temp. Phys. 59 195–211

    work page 1985

  27. [27]

    Tajima H, Iida K, Kojo T and Liang H 2025 Phys. Rev. Lett. 135(4) 042701 URL https://link.aps.org/doi/10.1103/4ywp-752m

    work page doi:10.1103/4ywp-752m 2025

  28. [28]

    Dashen R, Ma S K and Bernstein H J 1969 Phys. Rev. 187 345–370

    work page 1969

  29. [29]

    Tajima H, Tsutsui S, Doi T M and Iida K 2022 Phys. Rev. Res. 4(1) L012021 URL https://link.aps.org/doi/10.1103/PhysRevResearch.4.L012021 8 IOP Publishing Journal vv (yyyy) aaaaaa Author et al

    work page doi:10.1103/physrevresearch.4.l012021 2022

  30. [30]

    Tajima H, Tsutsui S, Doi T M and Iida K 2023 Symmetry 15 333

    work page 2023

  31. [31]

    Sá de Melo C A R, Randeria M and Engelbrecht J R 1993 Phys. Rev. Lett. 71(19) 3202–3205 URL https://link.aps.org/doi/10.1103/PhysRevLett.71.3202

    work page doi:10.1103/physrevlett.71.3202 1993

  32. [32]

    Drut J E, McKenney J R, Daza W S, Lin C L and Ordóñez C R 2018 Phys. Rev. Lett. 120(24) 243002 URL https://link.aps.org/doi/10.1103/PhysRevLett.120.243002

    work page doi:10.1103/physrevlett.120.243002 2018

  33. [33]

    Daza W S, Drut J E, Lin C L and Ordóñez C R 2019 Modern Physics Letters A 34 1950291

    work page 2019

  34. [34]

    Maki J and Ordóñez C R 2019 Phys. Rev. A 100(6) 063604 URL https://link.aps.org/doi/10.1103/PhysRevA.100.063604

    work page doi:10.1103/physreva.100.063604 2019

  35. [35]

    McKenney J R, Jose A and Drut J E 2020 Phys. Rev. A 102(2) 023313 URL https://link.aps.org/doi/10.1103/PhysRevA.102.023313

    work page doi:10.1103/physreva.102.023313 2020

  36. [36]

    Tajima H, Iida K and Liang H 2024 Phys. Rev. C 109(5) 055203 URL https://link.aps.org/doi/10.1103/PhysRevC.109.055203

    work page doi:10.1103/physrevc.109.055203 2024

  37. [37]

    Hryhorchak O, Panochko G and Pastukhov V 2025 Annals of Physics 170296

    work page 2025

  38. [38]

    Röpke G, Schmidt M, Münchow L and Schulz H 1983 Nuclear Physics A 399 587–602

    work page 1983

  39. [39]

    Generalized Beth--Uhlenbeck approach to mesons and diquarks in hot, dense quark matter

    Blaschke D, Buballa M, Dubinin A, Roepke G and Zablocki D 2014 Annals Phys. 348 228–255 (Preprint 1305.3907)

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  40. [40]

    Klempt E and Richard J M 2010 Rev. Mod. Phys. 82(2) 1095–1153 URL https://link.aps.org/doi/10.1103/RevModPhys.82.1095

    work page doi:10.1103/revmodphys.82.1095 2010

  41. [41]

    Nakano E and Tatsumi T 2005 Phys. Rev. D 71(11) 114006 URL https://link.aps.org/doi/10.1103/PhysRevD.71.114006

    work page doi:10.1103/physrevd.71.114006 2005

  42. [42]

    Akagami S, Tajima H and Iida K 2021 Phys. Rev. A 104(4) L041302 URL https://link.aps.org/doi/10.1103/PhysRevA.104.L041302

    work page doi:10.1103/physreva.104.l041302 2021

  43. [43]

    Gao B and Yoshida K 2025 Phys. Rev. C 112(6) 065203 URL https://link.aps.org/doi/10.1103/95dn-656y 9

    work page doi:10.1103/95dn-656y 2025