Two alternatives of spontaneous chiral symmetry breaking in QCD

Jan Stern (IPN-Orsay)

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Two alternatives of spontaneous chiral symmetry breaking in QCD

Jan Stern (IPN-Orsay)

High Energy Physics - Phenomenology · Submitted 13 Jan 1998

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

The authors' main claim SB$\chi$S can be realized either with $<\bar q q > =0$, provided the low density of states is compensated by a high mobility, or with a non-vanishing condensate, provided the mobility is suppressed.

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What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.11 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Considering QCD in an Euclidean box, the mechanism of spontaneous breaking of chiral symmetry (SB$\chi$S) is analyzed in terms of average properties of lowest eigenstates of the Dirac operator. A formal analogy between the pion decay constant and conductivity in disordered systems is established. It follows that SB$\chi$S results from a subtle balance between the density of Euclidean quark states and their mobility. SB$\chi$S can be realized either with $<\bar q q > =0$, provided the low density of states is compensated by a high mobility, or with a non-vanishing condensate, provided the mobility is suppressed. It is conjectured that the first case corresponds to extended whereas the latter case to (weakly) localized quark states.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Considering QCD in an Euclidean box, the mechanism of spontaneous breaking of chiral symmetry (SB$\chi$S) is analyzed in terms of average properties of lowest eigenstates of the Dirac operator.	contribution 0.53	0.77	0.04	asserted 0.90
s1	A formal analogy between the pion decay constant and conductivity in disordered systems is established.	contribution 0.70	0.83	0.04	asserted 1.00
s2	It follows that SB$\chi$S results from a subtle balance between the density of Euclidean quark states and their mobility.	interpretation 0.65	0.71	0.47	asserted 1.00
s3	SB$\chi$S can be realized either with $<\bar q q > =0$, provided the low density of states is compensated by a high mobility, or with a non-vanishing condensate, provided the mobility is suppressed.	result 0.92	0.65	0.73	hedged possibility 0.58
s4	It is conjectured that the first case corresponds to extended whereas the latter case to (weakly) localized quark states.	interpretation 1.00	0.30	0.22	speculative 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from argument 0.63.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Considering QCD in an Euclidean box, the mechanism of spontaneous breaking of chiral symmetry (SB$\chi$S) is analyzed in terms of average properties of lowest eigenstates of the Dirac operator. A formal analogy between the pion decay constant and conductivity in disordered systems is established. It follows that SB$\chi$S results from a subtle balance between the density of Euclidean quark states and their mobility. SB$\chi$S can be realized either with $<\bar q q > =0$, provided the low density of states is compensated by a high mobility, or with a non-vanishing condensate, provided the mobility is suppressed. It is conjectured that the first case corresponds to extended whereas the latter case to (weakly) localized quark states.

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References

Forward citations

Cited by 12 Pith papers

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

Inverse meson mass ordering in color-flavor-locking phase of high density QCD
hep-ph 1999-10 accept novelty 8.0 of 10

In the color-flavor-locking phase of dense QCD, meson masses depend only on bare quark masses and are partly inverted, with the eta-prime the lightest state.
Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
hep-th 2018-07 conditional novelty 6.0 of 10

A new mixed 't Hooft anomaly in massless QCD, involving baryon number, discrete chiral symmetry, and flavor symmetry, rules out the Stern phase of chiral symmetry breaking.
Massive fermions without fermion bilinear condensates
hep-lat 2014-10 conditional novelty 6.0 of 10

Monte Carlo simulations of a two-flavor staggered fermion model in three dimensions show a direct second-order transition between a massless phase and a massive phase with no fermion bilinear condensate.
Novel phase in SU(3) lattice gauge theory with 12 light fermions
hep-lat 2011-11 conditional novelty 6.0 of 10

A previously unobserved intermediate phase in 12-flavor SU(3) lattice gauge theory breaks single-site shift symmetry, confines, and is chirally symmetric, and likely arises from staggered-fermion lattice artifacts rat...
N_f Dependence of the Quark Condensate from a Chiral Sum Rule
hep-ph 1999-09 conditional novelty 6.0 of 10

A chiral sum rule built from experimental pion-kaon scattering data yields L6 between 0.4 and 0.8 times 10^-3, implying the quark condensate drops by roughly a factor of two as the strange quark mass goes to zero.

Show 7 more citing papers

Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
hep-th 2019-05 conditional novelty 5.0 of 10

In the charge-q N-flavor Schwinger model on a cylinder with flavor-twisted boundary conditions, the chiral condensate has fractional theta dependence e^{i theta / Nq}, produced by fractional quantum instantons with ac...
QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
hep-ph 2001-01 conditional novelty 5.0 of 10

Including quark-mass isospin breaking at next-to-next-to-leading order in chiral perturbation theory leaves the low-energy constants essentially unchanged and yields m_u/m_d = 0.46 +/- 0.09.
The phase diagram of nuclear and quark matter at high baryon density
hep-ph 2013-01 conditional novelty 3.0 of 10

The review argues that a third regime, quarkyonic matter, sits between confined nuclear matter and deconfined quark matter in large-Nc QCD, with pressure scaling as O(Nc).
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...
Modern Theory of Nuclear Forces
nucl-th 2008-11 accept novelty 3.0 of 10

Chiral effective field theory, ordered by a momentum expansion, yields nuclear forces tied to QCD symmetries, and at fourth order reproduces two-nucleon data to about 200 MeV lab energy with a quantified error band.
Chiral Perturbation Theory and Baryon Properties
hep-ph 2007-06 accept novelty 2.0 of 10

Chiral perturbation theory, matched to lattice QCD, gives a controlled description of baryon properties only for pion masses below roughly 350 MeV, and this review maps where that description works and where it fails.
Chiral perturbation theory
hep-ph 2006-11 accept novelty 2.0 of 10

Chiral perturbation theory supplies model-independent, systematically improvable formulas for the quark-mass dependence of low-energy hadron observables, and this review surveys its foundations, applications, and limi...

How the literature uses it

15 arXiv papers cite this in 19 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

Papers citing it · 15 sentences without a confident label

Contests it 1 paper

In Sec. [ref], we also examine and rule out an exotic scenario of chiral symmetry breaking, originally proposed by Stern [ref] .

Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking · Introduction · contest 0.84

Compares with it 2 papers

The presence of a new second order critical point makes the mechanism interesting even in the continuum.[The fermion mass generation mechanism we explore in this work is different from the one proposed in [ref] where chiral symmetry is spontaneously broken due to four-fermion condensates instead of fermion bilinear condensates and massless bosons are present.

Fermion masses through four-fermion condensates · Introduction · 0.88
[Intriguingly, a similar unusual scaling $∼1/√(V_4)$ also appears in color-superconducting phases of QCD at high density [ref] , in the superfluid phase of two-color QCD [ref] and in an exotic phase proposed by Stern [ref] .] Then [ref] becomes ∫_-∞^∞ ζ 1/iζ+ μ_uρ_(ζ;μ_u,μ_d) = f_2/f_A μ_u + μ_d I_'(μ_uμ_d)/I_(μ_uμ_d) .

U(1) axial symmetry and Dirac spectra in QCD at high temperature · Spectral sum rules II: microscopic limit · 0.82

Cites it as background 1 paper

In the context of $4$-dimensional QCD with fundamental fermions, this operator was important to discuss the exotic scenario of chiral symmetry breaking, called Stern phase [ref] .

Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model · Discrete 't Hooft anomaly and four-fermion interaction · 0.96

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