On two-color QCD with baryon chemical potential

D. Toublan; J.B. Kogut; M.A. Stephanov

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On two-color QCD with baryon chemical potential

J.B. Kogut, M.A. Stephanov, D. Toublan

High Energy Physics - Phenomenology · Submitted 11 Jun 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim First, using QCD inequalities we show that at finite baryon chemical potential mu, condensation must occur in the channel with scalar diquark quantum numbers.

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.05 · mentions code or data availability 0.01.

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We study SU(2) color QCD with even number of quark flavors. First, using QCD inequalities we show that at finite baryon chemical potential mu, condensation must occur in the channel with scalar diquark quantum numbers. This breaks the U(1) symmetry generated by baryon charge (baryon superconductivity). Then we derive the effective Lagrangian describing low lying meson and baryon excitations using extended local chiral symmetry of the theory. This enables us to determine the leading term in the dependence of the masses on mu exactly.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study SU(2) color QCD with even number of quark flavors.	contribution 0.58	0.67	0.03	asserted 0.87
s1	First, using QCD inequalities we show that at finite baryon chemical potential mu, condensation must occur in the channel with scalar diquark quantum numbers.	result 0.87	0.94	0.58	asserted 1.00
s2	This breaks the U(1) symmetry generated by baryon charge (baryon superconductivity).	interpretation 0.73	0.63	0.25	asserted 1.00
s3	Then we derive the effective Lagrangian describing low lying meson and baryon excitations using extended local chiral symmetry of the theory.	method 0.91	0.95	0.07	asserted 1.00
s4	This enables us to determine the leading term in the dependence of the masses on mu exactly.	result 0.87	0.94	0.19	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We study SU(2) color QCD with even number of quark flavors. First, using QCD inequalities we show that at finite baryon chemical potential mu, condensation must occur in the channel with scalar diquark quantum numbers. This breaks the U(1) symmetry generated by baryon charge (baryon superconductivity). Then we derive the effective Lagrangian describing low lying meson and baryon excitations using extended local chiral symmetry of the theory. This enables us to determine the leading term in the dependence of the masses on mu exactly.

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References

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Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Fractional Superfluid Vortices and Worldsheet Wess--Zumino--Witten Models in Two-Color QCD and $Sp(2N)$ Gauge Theories
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Minimal superfluid vortices in even-flavor pseudoreal gauge theories wind only 1/m of the baryon circulation quantum and localize Sp(2m)_N WZW conformal field theories with central charge Nm(2m+1)/(N+m+1).
Phase-diagram of two-color lattice QCD in the chiral limit
hep-lat 2006-02 conditional novelty 7.0 of 10

The strongly coupled two-color QCD chiral limit shows a weak first-order finite-temperature transition at zero chemical potential, an XY-universality second-order transition at nonzero chemical potential, and a mean-f...
Diquark Correlators and Phase Structure in the Quark-Meson-Diquark Model beyond Mean Field
hep-ph 2026-05 unverdicted novelty 6.0 of 10

Including mesonic fluctuations beyond mean field substantially modifies the phase structure of the quark-meson-diquark model, with diquark condensation dominating for strong couplings as analyzed via diquark pole mass...
Renormalizing the Quark-Meson-Diquark Model
hep-ph 2025-05 conditional novelty 6.0 of 10

Renormalized and two RG-consistent versions of the Quark-Meson-Diquark model reproduce the BCS relation and Stefan-Boltzmann limit at high density, while the sigma-delta scheme violates the BCS relation.
Fate of $\Sigma_c$, $\Xi_c'$ and $\Omega_c$ baryons at high temperature with chiral restoration
hep-ph 2024-11 conditional novelty 6.0 of 10

At high temperature, parity partners of singly charmed baryons become degenerate, Sigma_c and Omega_c masses converge, and the Sigma_c to Lambda_c pi width closes.

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Study of the phase diagram of dense two-color QCD within lattice simulation
hep-lat 2016-05 conditional novelty 6.0 of 10

Two-color QCD with two quark flavors shows a hadronic phase, a diquark Bose-Einstein condensate above half the pion mass, and a dense BCS-like quark phase that remains confined.
The SIMPlest Miracle
hep-ph 2014-11 conditional novelty 6.0 of 10

Strongly coupled QCD-like gauge theories with the Wess-Zumino-Witten term provide explicit, calculable realizations of the SIMP dark matter mechanism, predicting pion dark matter in the MeV-to-GeV range with self-scat...
Quark-meson-diquark model for two-color QCD
hep-ph 2011-12 accept novelty 6.0 of 10

Once bosonic diquark baryons are included alongside mesons, the two-color QCD phase diagram loses the chiral critical endpoint that quark-meson models produce, and the mean-field tricritical point on the diquark-conde...
The Condensed Matter Physics of QCD
hep-ph 2000-11 accept novelty 5.0 of 10

Dense three-flavor quark matter forms a color-flavor locked superconductor whose broken symmetries, gapped spectrum, and modified electromagnetism mirror those of confined hadronic matter.
FRG analysis of dense two-color QCD within the linear sigma model
hep-ph 2026-06 unverdicted novelty 4.0 of 10

FRG analysis in the linear sigma model for QC2D shows enhanced meson U(1)_A anomaly couplings with increasing mu_q but suppressed topological susceptibility following chiral restoration at high density or temperature.
A quarkyonic matter model
hep-ph 2026-05 unverdicted novelty 4.0 of 10

The IdylliQ model uses quark saturation to generate stiff equations of state and effective baryon repulsions that mitigate hyperon softening in neutron star matter.
Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
hep-th 2006-04 accept novelty 4.0 of 10

The paper derives the microscopic two-point eigenvalue correlation functions for QCD with imaginary isospin chemical potential, in quenched and two-flavor cases, from the epsilon-regime chiral Lagrangian.
The phase diagram of dense QCD
hep-ph 2010-05 accept novelty 3.0 of 10

A structured survey of the QCD phase diagram that separates firmly established results (lattice QCD at small baryon density, weak-coupling colour superconductivity at asymptotically high density) from conjectured phas...

How the literature uses it

62 arXiv papers cite this in 119 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Compares with it 4 papers

The critical chemical potential ([ref]) is the same as the result from chiral perturbation theory [ref] and NJL model [ref] , and suggested numerically by lattice simulations [ref] .

Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model · Linear sigma model · 0.98
In Sec. [ref], we have numerically seen that the phase transition from the hadronic phase to the baryon superfluid phase takes place just when $μ_q$ coincides with $m_π^(H)/2$, similarly to other chiral models ignoring spin-$1$ hadrons [ref] .

Mass spectrum of spin-one hadrons in dense two-color QCD: Novel predictions by extended linear sigma model · Analytic derivation of $μ_q^cr = m_π^(H)/2$ in the eLSM · 0.98
For $I=0$, $0^+$ channel, this is consistent with the results of ChPT [ref] .

Measurement of hadron masses in 2-color finite density QCD · Mass spectrum · 0.85

Cites it as support 2 papers

The exact chiral effective field theory results [ref] from the symmetries and breaking patterns as reviewed in Sec. [ref] tell us that we must include the diquark condensate along with the chiral condensate and base our mean-field analysis on Eqs. ([ref]), ([ref]) in order to describe the superfluid diquark phase starting at a critical line $μ_c(T)$ with $μ_c(0) = m_π/2$ (or $μ_B = m_B$).

Quark-meson-diquark model for two-color QCD · Diquark condensation · 0.98
Based on this observation we also neglect the latter condensate in the following.[In [ref] it was rigorously shown by QCD inequalities, which hold even at nonzero chemical potential owing to the positivity of the Euclidean path-integral measure of two-color QCD, that for massless quarks the lightest meson is the $0^+$ diquark, and thus a condensation (if it occurs) must occur in the channel $ψ^TCγ_5ψ$.]

Chiral Lagrangian and spectral sum rules for dense two-color QCD · Symmetry breaking patterns · 1.00

Cites it as background 29 papers

The main examples are QCD with an isospin chemical potential $μ_I$ (i.e. $N_f$ is even, $μ_1=-μ_2=μ_3=-μ_4=⋯=μ_I/2$; we call this theory as QCD$_I$) and degenerate mass [ref] , two-color QCD of even number of flavors and degenerate mass [ref] , QCD with adjoint fermions [ref] , and $SO(2N_c)$ and $Sp(2N_c)$ Yang-Mills theories [ref] .

Large-Nc equivalence and the sign problem at finite baryon density · Introduction · 0.95
Moreover, the pseudoreality allows us to extend $SU(2)_L×SU(2)_R$ chiral symmetry to the so-called Pauli-Gürsey $SU(4)$ symmetry [ref] , and then, the chiral condensate induces the symmetry breaking of $SU(4)→Sp(4)$.

Mass spectrum of spin-one hadrons in dense two-color QCD: Novel predictions by extended linear sigma model · Introduction · 0.88
Absence of sign problem.—We consider the class of QCD-like theories where quarks transform in a (pseudo)real representation of the gauge group [ref] , restricting ourselves for simplicity to two degenerate quark flavors $u,d$ with the common current mass $m$.

Anomaly-Induced Inhomogeneous Phase in Quark Matter without the Sign Problem · Introduction · 0.84

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