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arxiv: 2605.13934 · v1 · submitted 2026-05-13 · ✦ hep-ph · hep-th· nucl-th

Recognition: 1 theorem link

· Lean Theorem

Diquark Correlators and Phase Structure in the Quark-Meson-Diquark Model beyond Mean Field

Mire Ugo , Schaefer Bernd-Jochen
Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:50 UTC · model grok-4.3

classification ✦ hep-ph hep-thnucl-th
keywords quark-meson-diquark modelfunctional renormalization groupdiquark condensationphase structuremesonic fluctuationsSilver-Blaze propertyfinite density
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The pith

Mesonic fluctuations beyond mean field substantially modify the phase structure of the two-flavor quark-meson-diquark model and allow diquark condensation to dominate at strong couplings.

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

The paper applies the functional renormalization group to the quark-meson-diquark model at finite density and computes the two-point functions of the diquark fields at real-time frequencies. It enforces renormalization-group consistency of the effective potential to remove cutoff artifacts. Once mesonic fluctuations are retained, the phase diagram changes markedly from its mean-field version. For sufficiently large diquark couplings the system is driven into a regime dominated by diquark condensation rather than other ordered phases. These shifts are tracked through the location of the diquark pole mass and the preservation of the Silver-Blaze property.

Core claim

Incorporating mesonic fluctuations in the functional renormalization group treatment of the quark-meson-diquark model produces substantial modifications of the finite-density phase structure relative to mean-field results; for sufficiently strong diquark couplings the dynamics become dominated by diquark condensation, as revealed by the diquark pole mass and the Silver-Blaze property while RG consistency of the effective potential is maintained.

What carries the argument

Functional renormalization group truncation of the quark-meson-diquark model that retains mesonic fluctuations and evaluates diquark two-point functions at finite real-time frequencies.

If this is right

  • The phase structure changes substantially once mesonic fluctuations are retained.
  • Diquark condensation dominates the dynamics for sufficiently strong diquark couplings.
  • The diquark pole mass tracks the location of the condensation transition.
  • The Silver-Blaze property remains intact and helps control cutoff artifacts.
  • RG-consistent treatment of the effective potential eliminates spurious cutoff dependence.

Where Pith is reading between the lines

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

  • Mean-field treatments likely underestimate the role of diquark condensation in dense quark matter.
  • The same fluctuation-driven shift could appear in other low-energy models of QCD at finite baryon density.
  • Results may inform the expected location of color-superconducting phases inside compact stars.

Load-bearing premise

The quark-meson-diquark model together with the chosen functional renormalization group truncation accurately represents the relevant non-perturbative QCD dynamics at finite density.

What would settle it

An independent non-perturbative calculation, for instance via Dyson-Schwinger equations on the identical model Lagrangian and parameters, that yields an unchanged phase structure or no diquark-condensation dominance at strong couplings.

Figures

Figures reproduced from arXiv: 2605.13934 by Mire Ugo, Schaefer Bernd-Jochen.

Figure 1
Figure 1. Figure 1: Diagrammatic flow of the quark-meson-diquark [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Vacuum flow of the diquark two-point function including bosonic (sigma and pion) fluctuations. The flow of the [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Phase diagrams for the quark-meson-diquark model for different diquark couplings [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Quark mass ¯mq = gϕσ¯ and the diquark gap ∆¯ gap = g∆∆ for various diquark couplings ¯ g∆ as functions of the quark chemical potential in MFA (left) and mLPA (right). 𝜇 [MeV] 250 300 350 400 450 s [M e V 3 ] −20 −15 −10 −5 0 × 106 gΔ = 6 gΔ = 5 gΔ = 4 gΔ = 3 gΔ = 0 (quark-meson model) [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Entropy density s as a function of the chemical potential µ for different diquark couplings g∆ in the mLPA, compared with a pure quark-meson FRG calculation. fluence of mesonic and diquark fluctuations. By contrast, in mLPA the onset of diquark condensation is shifted to higher chemical potentials, most prominently at smaller g∆, and is accompanied by a forward bending of the con￾densation line. In additio… view at source ↗
Figure 6
Figure 6. Figure 6: Curvature diquark and meson masses as a function of the quark chemical potential [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Real (solid lines) and imaginary (dashed lines) parts of the vacuum diquark two-point function as a function of the [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Impact of RG consistency on the phase structure of the quark-meson-diquark model at fixed diquark coupling g∆ = 4 in MFA (left) and mLPA (right). Color coding and line conventions are as in [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
read the original abstract

A comprehensive study of the phase structure of the two-flavor quark-meson-diquark model is presented within the nonperturbative functional renormalization group framework. The influence of mesonic fluctuations beyond the mean-field approximation is investigated, and two-point functions of the diquark fields are computed at finite real-time frequencies. Renormalization group consistency of the effective potential is ensured in order to avoid cutoff artifacts. Substantial modifications of the phase structure are found once mesonic fluctuations are included, and for sufficiently strong diquark couplings the dynamics become dominated by diquark condensation. These effects are elucidated through an analysis of the diquark pole mass and the Silver-Blaze property.

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 / 2 minor

Summary. The manuscript presents a comprehensive FRG study of the two-flavor quark-meson-diquark model at finite density. It computes the effective potential with mesonic fluctuations included beyond mean field, evaluates real-time diquark two-point functions, and enforces RG consistency of the potential to remove cutoff artifacts. The central results are that mesonic fluctuations produce substantial modifications to the phase structure and that, for sufficiently strong diquark couplings, the dynamics are dominated by diquark condensation; these conclusions are supported by an analysis of the diquark pole mass and the Silver-Blaze property.

Significance. If the truncation is reliable, the work demonstrates that fluctuations beyond mean field can qualitatively alter the phase diagram of an effective QCD model at finite density and can drive diquark condensation. The explicit computation of real-time correlators and the enforcement of RG consistency are concrete strengths that improve upon standard mean-field treatments and provide a controlled framework for studying diquark degrees of freedom.

major comments (1)
  1. [Numerical results and phase diagrams] The central claim of 'substantial modifications' and diquark dominance rests on the chosen FRG truncation (including the form of the effective potential and the regulator). A direct, quantitative comparison between the mean-field and FRG phase boundaries (e.g., critical chemical potentials or coexistence regions) is needed to establish the size of the effect; without such a comparison the magnitude of the reported changes remains difficult to assess.
minor comments (2)
  1. [Diquark correlators] The definition of the diquark pole mass extraction from the real-time two-point function should be stated explicitly, including any analytic continuation procedure.
  2. [RG consistency section] A brief discussion of the sensitivity of the results to the choice of regulator or to the truncation order would strengthen the robustness statement.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comment on our manuscript. We agree that a direct quantitative comparison will strengthen the presentation of our results and will incorporate it in the revised version.

read point-by-point responses

  1. Referee: [Numerical results and phase diagrams] The central claim of 'substantial modifications' and diquark dominance rests on the chosen FRG truncation (including the form of the effective potential and the regulator). A direct, quantitative comparison between the mean-field and FRG phase boundaries (e.g., critical chemical potentials or coexistence regions) is needed to establish the size of the effect; without such a comparison the magnitude of the reported changes remains difficult to assess.

    Authors: We agree that a direct quantitative comparison is required to clearly establish the magnitude of the modifications induced by mesonic fluctuations. In the revised manuscript we will add a new figure that overlays the mean-field and FRG phase boundaries in the temperature-chemical potential plane, explicitly reporting the shifts in critical chemical potentials and the size of any coexistence regions. This comparison will be performed at the same parameter values used in the original analysis, thereby quantifying the effect size while preserving the existing truncation. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper applies standard functional renormalization group flow equations to the quark-meson-diquark model, computes real-time diquark two-point functions, and enforces RG consistency of the effective potential to remove cutoff artifacts. The reported phase-structure modifications and diquark-condensation dominance follow directly from these flows once mesonic fluctuations are included, with the diquark pole mass and Silver-Blaze property obtained from the resulting propagators. No derivation step reduces by construction to a fitted input, self-citation load-bearing premise, or ansatz smuggled from prior work; the central claims remain independent of the target observables.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The model depends on parameters such as diquark coupling strengths that are varied to explore regimes; the FRG method relies on standard truncations and the assumption of RG consistency to control artifacts. No new particles or forces are introduced.

free parameters (1)
  • diquark coupling strength
    Varied as a key parameter to determine when diquark condensation dominates the dynamics.
axioms (2)
  • domain assumption The functional renormalization group flow equations with the chosen truncation capture the dominant mesonic fluctuations.
    Invoked to justify going beyond mean field while maintaining computational tractability.
  • domain assumption Ensuring renormalization group consistency of the effective potential eliminates cutoff artifacts.
    Stated explicitly in the abstract as a requirement for reliable results.

pith-pipeline@v0.9.0 · 5414 in / 1421 out tokens · 60470 ms · 2026-05-15T02:50:28.985098+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

113 extracted references · 113 canonical work pages · 45 internal anchors

  1. [1]

    (38) simplifies to ∂tUk(σ,∆) = k5 12π2 3 ϵπ + 1 ϵσ − 4Nf ϵq θ(ϵ− q ) + ϵ+ q E+q + ϵ− q E−q

    Zero temperature flows At zero temperature and finite chemical potential, the flow Eq. (38) simplifies to ∂tUk(σ,∆) = k5 12π2 3 ϵπ + 1 ϵσ − 4Nf ϵq θ(ϵ− q ) + ϵ+ q E+q + ϵ− q E−q . (42) For ∆ = 0, the fermionic energy ratios reduce to ϵ+ q E+q →1 and ϵ− q E−q →2θ(ϵ − q )−1,(43) so that the fermionic flowN cθ(ϵ− q ) exhibits the Silver- Blaze property atT= ...

    work page

  2. [2]

    Quark-meson flows For ∆ = 0 and finite temperature, the quasi-particle energies reduce to E+ q →ϵ + q andE − q → |ϵ − q |.(44) Consequently, the flow converges to that of a quark- meson flow withN c = 3 degenerate colors: ∂tUk(σ,∆ = 0) = k5 12π2 −2Nf Nc ϵq tanh ϵ+ q 2T + tanh ϵ− q 2T + 3 ϵπ coth ϵπ 2T + 1 ϵσ coth ϵσ 2T . (45) B. Parameter fixing To solve ...

    work page

  3. [3]

    In principle, the corresponding RGC initial condition follows directly from the definition of the scale-dependent mean-field potential in Eq

    RG consistency in the mean-field flow The implementation of RGC at the mean-field level of a QMD model is straightforward. In principle, the corresponding RGC initial condition follows directly from the definition of the scale-dependent mean-field potential in Eq. (48). However, one important difference is that the initial potential at the UV scale – deno...

    work page

  4. [4]

    Mathematically, RG flows form a semi-group rather than a group: the coarse-graining from the UV to the IR is irreversible and no inverse trans- formation exists

    RG consistency in the mesonic LPA flow Implementing RGC within the LPA is in general more subtle than in the MFA. Mathematically, RG flows form a semi-group rather than a group: the coarse-graining from the UV to the IR is irreversible and no inverse trans- formation exists. While this limitation is less severe in the MFA, enforcing RGC in LPA (or beyond)...

    work page

  5. [5]

    Back-bending of the chiral transition line in mLPA The characteristic back-bending of the chiral transi- tion line at decreasingT(Fig. 3, right panels) has also been observed in other low-energy effective model studies beyond MFA [82–87], as well as in mean-field studies of effective Polyakov-loop theories on the lattice [88]. Due to the Clausius-Clapeyro...

    work page

  6. [6]

    Strong-interaction matter under extreme conditions

    Diquark onset and chiral transition In MFA, the onset of diquark condensation coincides with the chiral transition at low temperature forg ∆ = 3,4. For larger couplings (g ∆ = 5,6), the diquark on- set slightly precedes the chiral transition, which changes from first order to a sharp crossover atg ∆ = 6. This behavior can be seen in Fig. 4, where the quar...

    work page

  7. [7]

    Hebeler, Three-nucleon forces: Implementation and applications to atomic nuclei and dense matter, Phys

    K. Hebeler, Three-nucleon forces: Implementation and applications to atomic nuclei and dense matter, Phys. Rept.890, 1 (2021), arXiv:2002.09548 [nucl-th]

    work page arXiv 2021

  8. [8]

    M. G. Alford, K. Rajagopal, and F. Wilczek, Qcd at fi- nite baryon density: Nucleon droplets and color super- conductivity, Phys. Lett. B422, 247 (1998), arXiv:hep- ph/9711395

    work page arXiv 1998

  9. [9]

    M. G. G. Alford, Color superconducting quark matter, Ann. Rev. Nucl. Part. Sci.51, 131 (2001), arXiv:hep- ph/0102047

    work page arXiv 2001

  10. [10]

    M. G. Alford, A. Schmitt, K. Rajagopal, and T. Sch¨ afer, Color superconductivity in dense quark matter, Rev. Mod. Phys.80, 1455 (2008), arXiv:0709.4635 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  11. [11]

    The phase diagram of dense QCD

    K. Fukushima and T. Hatsuda, The phase diagram of dense qcd, Rept. Prog. Phys.74, 014001 (2011), arXiv:1005.4814 [hep-ph]. 21

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  12. [12]

    Crystalline color superconductors

    R. Anglani, R. Casalbuoni, M. Ciminale, N. Ippolito, R. Gatto, M. Mannarelli, and M. Ruggieri, Crystalline color superconductors, Rev. Mod. Phys.86, 509 (2014), arXiv:1302.4264 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  13. [13]

    Inhomogeneous chiral condensates

    M. Buballa and S. Carignano, Inhomogeneous chiral condensates, Prog. Part. Nucl. Phys.81, 39 (2015), arXiv:1406.1367 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  14. [14]

    W.-j. Fu, J. M. Pawlowski, and F. Rennecke, QCD phase structure at finite temperature and density, Phys. Rev. D101, 054032 (2020), arXiv:1909.02991 [hep-ph]

    work page arXiv 2020

  15. [15]

    R. D. Pisarski and F. Rennecke, Signatures of Moat Regimes in Heavy-Ion Collisions, Phys. Rev. Lett.127, 152302 (2021), arXiv:2103.06890 [hep-ph]

    work page arXiv 2021

  16. [16]

    W.-j. Fu, J. M. Pawlowski, R. D. Pisarski, F. Rennecke, R. Wen, and S. Yin, The qcd moat regime and its real- time properties, (2024), arXiv:2412.15949 [hep-ph]

    work page arXiv 2024

  17. [17]

    T. F. Motta, M. Buballa, and C. S. Fischer, New tool to detect inhomogeneous chiral symmetry break- ing, (2024), arXiv:2411.02285 [hep-ph]

    work page arXiv 2024

  18. [18]

    Schmitt, Phases and properties of color superconduc- tors, (2025), arXiv:2511.07319 [hep-ph]

    A. Schmitt, Phases and properties of color superconduc- tors, (2025), arXiv:2511.07319 [hep-ph]

    work page arXiv 2025

  19. [19]

    J. M. Pawlowski, F. Rennecke, and F. R. Sattler, Inho- mogeneous instabilities in high-density QCD, (2025), arXiv:2512.20510 [hep-ph]

    work page arXiv 2025

  20. [20]

    Bazavovet al.(HotQCD), Chiral crossover in QCD at zero and non-zero chemical potentials, Phys

    A. Bazavovet al.(HotQCD), Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795, 15 (2019), arXiv:1812.08235 [hep-lat]

    work page arXiv 2019

  21. [21]

    Borsanyi, Z

    S. Borsanyi, Z. Fodor, J. N. Guenther, R. Kara, S. D. Katz, P. Parotto, A. Pasztor, C. Ratti, and K. K. Sz- abo, Qcd crossover at finite chemical potential from lat- tice simulations, Phys. Rev. Lett.125, 052001 (2020), arXiv:2002.02821 [hep-lat]

    work page arXiv 2020

  22. [22]

    L. Dini, P. Hegde, F. Karsch, A. Lahiri, C. Schmidt, and S. Sharma, Chiral phase transition in three-flavor QCD from lattice QCD, Phys. Rev. D105, 034510 (2022), arXiv:2111.12599 [hep-lat]

    work page arXiv 2022

  23. [23]

    Namekawa, K

    Y. Namekawa, K. Kashiwa, H. Matsuda, A. Ohnishi, and H. Takase, Improving efficiency of the path opti- mization method for a gauge theory, Phys. Rev. D107, 034509 (2023), arXiv:2210.05402 [hep-lat]

    work page arXiv 2023

  24. [24]

    Aartset al., Phase transitions in particle physics: Results and perspectives from lattice quantum chromo- dynamics, Prog

    G. Aartset al., Phase transitions in particle physics: Results and perspectives from lattice quantum chromo- dynamics, Prog. Part. Nucl. Phys.133, 104070 (2023), arXiv:2301.04382 [hep-lat]

    work page arXiv 2023

  25. [25]

    C. S. Fischer, Qcd at finite temperature and chemical potential from dyson-schwinger equations, Prog. Part. Nucl. Phys.105, 1 (2019), arXiv:1810.12938 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  26. [26]

    Fu, QCD at finite temperature and density within the fRG approach: an overview, Commun

    W.-j. Fu, QCD at finite temperature and density within the fRG approach: an overview, Commun. Theor. Phys. 74, 097304 (2022), arXiv:2205.00468 [hep-ph]

    work page arXiv 2022

  27. [27]

    Dupuis, L

    N. Dupuis, L. Canet, A. Eichhorn, W. Metzner, J. M. Pawlowski, M. Tissier, and N. Wschebor, The nonper- turbative functional renormalization group and its ap- plications, Phys. Rept.910, 1 (2021), arXiv:2006.04853 [cond-mat.stat-mech]

    work page arXiv 2021

  28. [28]

    C. S. Fischer and J. M. Pawlowski, Phase structure and observables at high densities from first principles QCD, (2026), arXiv:2603.11135 [hep-ph]

    work page arXiv 2026

  29. [29]

    Quark Confinement from Color Confinement

    J. Braun, H. Gies, and J. M. Pawlowski, Quark confine- ment from color confinement, Phys. Lett. B684, 262 (2010), arXiv:0708.2413 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  30. [30]

    From Quarks and Gluons to Hadrons: Chiral Symmetry Breaking in Dynamical QCD

    J. Braun, L. Fister, J. M. Pawlowski, and F. Rennecke, From Quarks and Gluons to Hadrons: Chiral Symmetry Breaking in Dynamical QCD, Phys. Rev. D94, 034016 (2016), arXiv:1412.1045 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  31. [31]

    Chiral symmetry breaking in continuum QCD

    M. Mitter, J. M. Pawlowski, and N. Strodthoff, Chiral symmetry breaking in continuum QCD, Phys. Rev. D 91, 054035 (2015), arXiv:1411.7978 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  32. [32]

    A. K. Cyrol, L. Fister, M. Mitter, J. M. Pawlowski, and N. Strodthoff, Landau gauge Yang-Mills corre- lation functions, Phys. Rev. D94, 054005 (2016), arXiv:1605.01856 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  33. [33]

    A. K. Cyrol, M. Mitter, J. M. Pawlowski, and N. Strodthoff, Nonperturbative quark, gluon, and me- son correlators of unquenched qcd, Phys. Rev. D97, 054006 (2018), arXiv:1706.06326 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  34. [34]

    Braun and B

    J. Braun and B. Schallmo, From quarks and gluons to color superconductivity at supranuclear densities, Phys. Rev. D105, 036003 (2022), arXiv:2106.04198 [hep-ph]

    work page arXiv 2022

  35. [35]

    Renormalization group consistency and low-energy effective theories

    J. Braun, M. Leonhardt, and J. M. Pawlowski, Renor- malization group consistency and low-energy effective theories, SciPost Phys.6, 056 (2019), arXiv:1806.04432 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  36. [36]

    J. O. Andersen and M. P. Nødtvedt, Color supercon- ductivity in the two-flavor quark-meson diquark model, (2024), arXiv:2408.12361 [hep-ph]

    work page arXiv 2024

  37. [37]

    Gholami, L

    H. Gholami, L. Kurth, U. Mire, M. Buballa, and B.- J. Schaefer, Renormalizing the Quark-Meson-Diquark Model, (2025), arXiv:2505.22542 [hep-ph]

    work page arXiv 2025

  38. [38]

    J. O. Andersen and M. P. Nødtvedt, Pion condensa- tion versus 2SC, speed of sound, and charge neutral- ity effects in the quark-meson diquark model, (2025), arXiv:2502.10229 [hep-ph]

    work page arXiv 2025

  39. [39]

    J. O. Andersen and M. P. P. Nødtvedt, Quark-meson di- quark model and color superconductivity in dense quark matter, (2026), arXiv:2602.18256 [hep-ph]

    work page arXiv 2026

  40. [40]

    J. B. Kogut, M. A. Stephanov, and D. Toublan, On two color QCD with baryon chemical potential, Phys. Lett. B464, 183 (1999), arXiv:hep-ph/9906346

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  41. [41]

    J. O. Andersen and T. Brauner, Phase diagram of two- color quark matter at nonzero baryon and isospin den- sity, Phys. Rev. D81, 096004 (2010), arXiv:1001.5168 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  42. [42]

    Quark-meson-diquark model for two-color QCD

    N. Strodthoff, B.-J. Schaefer, and L. von Smekal, Quark- meson-diquark model for two-color QCD, Phys. Rev. D 85, 074007 (2012), arXiv:1112.5401 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  43. [43]

    N. Khan, J. M. Pawlowski, F. Rennecke, and M. M. Scherer, The Phase Diagram of QC2D from Functional Methods, (2015), arXiv:1512.03673 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  44. [44]

    N. J. Evans, S. D. H. Hsu, and M. Schwetz, Nonper- turbative couplings and color superconductivity, Phys. Lett. B449, 281 (1999), arXiv:hep-ph/9810514

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  45. [45]

    Sch¨ afer and F

    T. Sch¨ afer and F. Wilczek, High density quark mat- ter and the renormalization group in qcd with two and three flavors, Phys. Lett. B450, 325 (1999), arXiv:hep- ph/9810509

    work page arXiv 1999

  46. [46]

    Renormalization Flow of Bound States

    H. Gies and C. Wetterich, Renormalization flow of bound states, Phys. Rev. D65, 065001 (2002), arXiv:hep-th/0107221

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  47. [47]

    W.-j. Fu, X. Luo, J. M. Pawlowski, F. Rennecke, R. Wen, and S. Yin, Hyper-order baryon number fluc- tuations at finite temperature and density, Phys. Rev. D104, 094047 (2021), arXiv:2101.06035 [hep-ph]

    work page arXiv 2021

  48. [48]

    Fukushima, J

    K. Fukushima, J. M. Pawlowski, and N. Strodthoff, Emergent hadrons and diquarks, Annals Phys.446, 169106 (2022), arXiv:2103.01129 [hep-ph]

    work page arXiv 2022

  49. [49]

    Stoll, N

    J. Stoll, N. Zorbach, and J. Braun, Nonperturba- tive fluctuation effects of charged bosonic fields: A 22 quark-diquark model study at nonzero density, (2025), arXiv:2510.01066 [hep-ph]

    work page arXiv 2025

  50. [50]

    Leonhardt, M

    M. Leonhardt, M. Pospiech, B. Schallmo, J. Braun, C. Drischler, K. Hebeler, and A. Schwenk, Symmetric nuclear matter from the strong interaction, Phys. Rev. Lett.125, 142502 (2020), arXiv:1907.05814 [nucl-th]

    work page arXiv 2020

  51. [51]

    Braun and B

    J. Braun and B. Schallmo, Zero-temperature thermo- dynamics of dense asymmetric strong-interaction mat- ter, Phys. Rev. D106, 076010 (2022), arXiv:2204.00358 [nucl-th]

    work page arXiv 2022

  52. [52]

    Fermion Interactions and Universal Behavior in Strongly Interacting Theories

    J. Braun, Fermion Interactions and Universal Behavior in Strongly Interacting Theories, J. Phys. G39, 033001 (2012), arXiv:1108.4449 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  53. [53]

    Braun, M

    J. Braun, M. Leonhardt, and M. Pospiech, Fierz- complete njl model study iii: Emergence from quark- gluon dynamics, Phys. Rev. D101, 036004 (2020), arXiv:1909.06298 [hep-ph]

    work page arXiv 2020

  54. [54]

    D. T. Son, Superconductivity by long range color mag- netic interaction in high density quark matter, Phys. Rev. D59, 094019 (1999), arXiv:hep-ph/9812287

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  55. [55]

    R. D. Pisarski and D. H. Rischke, Gaps and critical temperature for color superconductivity, Phys. Rev. D 61, 051501 (2000), arXiv:nucl-th/9907041

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  56. [56]

    Buballa, NJL model analysis of quark matter at large density, Phys

    M. Buballa, NJL model analysis of quark matter at large density, Phys. Rept.407, 205 (2005), arXiv:hep- ph/0402234

    work page arXiv 2005

  57. [57]

    Berges, D

    J. Berges, D. U. Jungnickel, and C. C. Wetterich, Two flavor chiral phase transition from nonperturbative flow equations, Phys. Rev. D59, 034010 (1999), arXiv:hep- ph/9705474

    work page arXiv 1999

  58. [58]

    The Phase Diagram of the Quark-Meson Model

    B.-J. Schaefer and J. Wambach, The Phase diagram of the quark meson model, Nucl. Phys. A757, 479 (2005), arXiv:nucl-th/0403039

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  59. [59]

    Susceptibilities near the QCD (tri)critical point

    B.-J. Schaefer and J. Wambach, Susceptibilities near the qcd (tri)critical point, Phys. Rev. D75, 085015 (2007), arXiv:hep-ph/0603256

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  60. [60]

    Fluctuation-induced modifications of the phase structure in (2+1)-flavor QCD

    F. Rennecke and B.-J. Schaefer, Fluctuation-induced modifications of the phase structure in (2+1)- flavor QCD, Phys. Rev. D96, 016009 (2017), arXiv:1610.08748 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  61. [61]

    Mass sensitivity of the three-flavor chiral phase transition

    S. Resch, F. Rennecke, and B.-J. Schaefer, Mass sensi- tivity of the three-flavor chiral phase transition, Phys. Rev. D99, 076005 (2019), arXiv:1712.07961 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  62. [62]

    K. Otto, M. Oertel, and B.-J. Schaefer, Nonperturbative quark matter equations of state with vector interactions, Eur. Phys. J. ST229, 3629 (2020), arXiv:2007.07394 [hep-ph]

    work page arXiv 2020

  63. [63]

    Grossi, F

    E. Grossi, F. J. Ihssen, J. M. Pawlowski, and N. Wink, Shocks and quark-meson scatterings at large density, Phys. Rev. D104, 016028 (2021), arXiv:2102.01602 [hep-ph]

    work page arXiv 2021

  64. [64]

    Ihssen, J

    F. Ihssen, J. M. Pawlowski, F. R. Sattler, and N. Wink, Towards quantitative precision for QCD at large densi- ties, (2023), arXiv:2309.07335 [hep-th]

    work page arXiv 2023

  65. [65]

    Exact evolution equation for the effective potential

    C. Wetterich, Exact evolution equation for the effec- tive potential, Phys. Lett. B301, 90 (1993), two identi- cal pdf papers original 1993 and 2017, arXiv:1710.05815 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  66. [66]

    Gor’kov, Microscopic derivation of the ginzburg- landau equations in the theory of superconductivity, Sov

    L. Gor’kov, Microscopic derivation of the ginzburg- landau equations in the theory of superconductivity, Sov. Phys. JETP36(9), 1364 (1959)

    work page 1959

  67. [67]

    Nambu, Quasi-particles and gauge invariance in the theory of superconductivity, Phys

    Y. Nambu, Quasi-particles and gauge invariance in the theory of superconductivity, Phys. Rev.117, 648 (1960)

    work page 1960

  68. [68]

    M. L. Bellac,Thermal Field Theory, Cambridge Mono- graphs on Mathematical Physics (Cambridge University Press, 2011)

    work page 2011

  69. [69]

    W.-j. Fu, X. Luo, J. M. Pawlowski, F. Rennecke, and S. Yin, Ripples of the QCD Critical Point, (2023), arXiv:2308.15508 [hep-ph]

    work page arXiv 2023

  70. [70]

    M. Hess, F. Karsch, E. Laermann, and I. Wetzorke, Diquark masses from lattice QCD, Phys. Rev. D58, 111502 (1998), arXiv:hep-lat/9804023

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  71. [71]

    Nucleon Properties in the Covariant Quark-Diquark Model

    M. Oettel, R. Alkofer, and L. von Smekal, Nucleon prop- erties in the covariant quark diquark model, Eur. Phys. J. A8, 553 (2000), arXiv:nucl-th/0006082

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  72. [72]

    Effective masses of diquarks

    P. Maris, Effective masses of diquarks, Few Body Syst. 32, 41 (2002), arXiv:nucl-th/0204020

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  73. [73]

    Gholami, U

    H. Gholami, U. Mire, F. Rennecke, B.-J. Schaefer, and S. Yin, (to be published) (2026)

    work page 2026

  74. [74]

    B. J. Schaefer and M. Wagner, QCD critical region and higher moments for three flavor models, Phys. Rev. D 85, 034027 (2012), arXiv:1111.6871 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  75. [75]

    Skokov, B

    V. Skokov, B. Friman, E. Nakano, K. Redlich, and B.-J. Schaefer, Vacuum fluctuations and the thermodynamics of chiral models, Phys. Rev. D82, 034029 (2010)

    work page 2010

  76. [76]

    J. M. Pawlowski, Aspects of the functional renormalisa- tion group, Annals Phys.322, 2831 (2007), arXiv:hep- th/0512261

    work page arXiv 2007

  77. [77]

    J. M. Pawlowski, M. M. Scherer, R. Schmidt, and S. J. Wetzel, Physics and the choice of regulators in func- tional renormalisation group flows, Annals Phys.384, 165 (2017), arXiv:1512.03598 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  78. [78]

    T. K. Herbst, M. Mitter, J. M. Pawlowski, B.-J. Schae- fer, and R. Stiele, Thermodynamics of QCD at vanishing density, Phys. Lett. B731, 248 (2014), arXiv:1308.3621 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  79. [79]

    Gholami, M

    H. Gholami, M. Hofmann, and M. Buballa, Renormalization-group consistent treatment of color superconductivity in the NJL model, (2024), arXiv:2408.06704 [hep-ph]

    work page arXiv 2024

  80. [80]

    Koenigstein, M

    A. Koenigstein, M. J. Steil, N. Wink, E. Grossi, J. Braun, M. Buballa, and D. H. Rischke, Numer- ical fluid dynamics for FRG flow equations: Zero- dimensional QFTs as numerical test cases. I. The O(N) model, Phys. Rev. D106, 065012 (2022), arXiv:2108.02504 [cond-mat.stat-mech]

    work page arXiv 2022

Showing first 80 references.