Magnetic fields within color superconducting neutron star cores

J. Berges (MIT); K. Rajagopal (MIT); M. Alford (MIT)

RECORD

Magnetic fields within color superconducting neutron star cores

M. Alford (MIT), J. Berges (MIT), K. Rajagopal (MIT)

High Energy Physics - Phenomenology · Submitted 6 Oct 1999

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

The authors' main claim Our results demonstrate that such cores admit magnetic fields without restricting them to quantized flux tubes.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/9910254 (version 2)

Pith IDGU7JHZEC, Pith's permanent record of this paper and its review

CitationJ. Berges (MIT), K. Rajagopal (MIT), M. Alford (MIT). "Magnetic fields within color superconducting neutron star cores." arXiv:hep-ph/9910254 (1999). https://pith.science/paper/GU7JHZEC

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,164 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.30 · compares with prior results 0.09 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We discuss the Meissner effect for a color superconductor formed by cold dense quark matter. Though color and ordinary electromagnetism are broken in a color superconductor, there is a linear combination of the photon and a gluon that remains massless. Consequently, a color superconducting region may be penetrated by an external magnetic field. We show that at most a small fraction of the magnetic field is expelled, and if the screening distance is the smallest length scale in the problem there is no expulsion at all. We calculate the behavior of the magnetic field for a spherical geometry relevant for compact stars. If a neutron star contains a quark matter core, this core is a color superconductor. Our results demonstrate that such cores admit magnetic fields without restricting them to quantized flux tubes. Such magnetic fields within color superconducting neutron star cores are stable on time scales longer than the age of the universe, even if the spin period of the neutron star is changing.

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	We discuss the Meissner effect for a color superconductor formed by cold dense quark matter.	contribution 0.73	0.61	0.03	unclear 0.75
s1	Though color and ordinary electromagnetism are broken in a color superconductor, there is a linear combination of the photon and a gluon that remains massless.	background 0.84	0.21	0.06	asserted 1.00
s2	Consequently, a color superconducting region may be penetrated by an external magnetic field.	result 0.60	0.29	0.14	hedged possibility 1.00
s3	We show that at most a small fraction of the magnetic field is expelled, and if the screening distance is the smallest length scale in the problem there is no expulsion at all.	result 1.00	0.92	0.33	asserted 0.99
s4	We calculate the behavior of the magnetic field for a spherical geometry relevant for compact stars.	method 0.55	0.94	0.05	asserted 0.98
s5	If a neutron star contains a quark matter core, this core is a color superconductor.	background 0.81	0.18	0.07	asserted 0.99
s6	Our results demonstrate that such cores admit magnetic fields without restricting them to quantized flux tubes.	result 0.60	0.90	0.41	asserted 1.00
s7	Such magnetic fields within color superconducting neutron star cores are stable on time scales longer than the age of the universe, even if the spin period of the neutron star is changing.	result 0.94	0.84	0.45	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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

We discuss the Meissner effect for a color superconductor formed by cold dense quark matter. Though color and ordinary electromagnetism are broken in a color superconductor, there is a linear combination of the photon and a gluon that remains massless. Consequently, a color superconducting region may be penetrated by an external magnetic field. We show that at most a small fraction of the magnetic field is expelled, and if the screening distance is the smallest length scale in the problem there is no expulsion at all. We calculate the behavior of the magnetic field for a spherical geometry relevant for compact stars. If a neutron star contains a quark matter core, this core is a color superconductor. Our results demonstrate that such cores admit magnetic fields without restricting them to quantized flux tubes. Such magnetic fields within color superconducting neutron star cores are stable on time scales longer than the age of the universe, even if the spin period of the neutron star is changing.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 8 Pith papers

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

Axial anomaly and magnetism of nuclear and quark matter
hep-ph 2007-10 accept novelty 7.0 of 10

Above roughly 10^19 gauss a stack of neutral-pion domain walls carries more baryon number per unit energy than nuclear matter, and analogous eta or eta-prime walls form in color-superconducting quark matter.
Quantum-Geometric Meissner Effect in Magnetized Color Superconductors
hep-ph 2026-09 conditional novelty 6.0 of 10

In strongly magnetized two-flavor color-superconducting quark matter, the transverse Meissner mass scales with the pairing gap Δ, not the chemical potential μ, due to quantum-geometric effects from Landau quantization.
Properties of neutral mesons in a hot and magnetized quark matter
hep-ph 2012-06 conditional novelty 6.0 of 10

In a magnetized two-flavor NJL model, neutral sigma and pion mesons acquire direction-dependent refraction indices: unity along the magnetic field and greater than unity transverse to it.
Estimate of the magnetic field strength in heavy-ion collisions
nucl-th 2009-07 conditional novelty 6.0 of 10

UrQMD simulations put the magnetic field at the fireball center at roughly 0.1 m_pi^2 for SPS, order m_pi^2 for RHIC, and about 15 m_pi^2 for LHC energies.
Chiral perturbation theory in a magnetic background - finite-temperature effects
hep-ph 2012-05 conditional novelty 5.0 of 10

At finite temperature in a constant magnetic field, the pion decay constants and the quark condensate fall off more slowly with temperature than at zero field, suggesting a higher chiral transition temperature.

Show 3 more citing papers

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.
Dense and Cold Magnetized Quark Matter: A Review of Magnetic-Field-Independent Regularization and the Medium Separation Scheme
hep-ph 2026-06 unverdicted novelty 3.5 of 10

Review of MFIR and MSS schemes showing the superconducting gap stays finite at high chemical potential in magnetized cold quark matter with no zero-temperature transition to normal phase.
Crystalline color superconductors
hep-ph 2013-02 accept novelty 3.0 of 10

Crystalline color superconducting quark matter can be energetically favored over homogeneous phases in compact-star cores and is chromomagnetically stable, with a shear modulus 20 to 1000 times that of the neutron-star crust.

How the literature uses it

18 arXiv papers cite this in 27 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 · 19 sentences without a confident label

Uses its method or tool 1 paper

The organization of this paper is as follows: In Sec. II, starting from an extended Lagrangian density of a gauged NJL model containing two flavors, and following the method presented in [ref] , we introduce the rotated magnetic field $ẽB$ and determine the Lagrangian density containing the $χ$SB and CSC mass gaps, $σ_B$ and $Δ_B$, respectively.

Color neutral 2SC phase of cold and dense quark matter in the presence of constant magnetic fields · Introduction · 1.00

Uses its data or values 1 paper

The mixing coefficients have been determined in [ref] (see also [ref] ) and are given by cosθ= √(3) g/√(3 g^2 + e^2) sinθ= e/√(3 g^2 + e^2) .

Crystalline color superconductors · Meissner masses of gluons in the g2SC phase · 0.90

Compares with it 1 paper

For comparison, the critical magnetic field needed to destroy superconductivity is at least of order $μΔ/e$ [ref] .

Axial anomaly and magnetism of nuclear and quark matter · 2SC phase in a magnetic field · 0.95

Cites it as background 5 papers

The $(3)$ color symmetries and the global $(3)_L$ and $(3)_R$ flavor symmetries are broken by the condensate to a global subgroup consisting of simultaneous color and flavor transformations, [equation] A diagonal subgroup of the $(3)_L×(3)_R$ is weakly gauged by the electric charge $Qe$, where $Qe$ is a diagonal matrix in the flavor space with entries equalling the electric charges of the $u$, $d$ and $s$ quarks, and a linear combination of the $t^8$ and $Q$ (known as $Q̃$) is unbroken [ref] .

The shear viscosity of two-flavor crystalline color superconducting quark matter · Review · 0.95
Possible effects caused by strong magnetic fields include magnetic catalysis [ref] , modification of the nature of electroweak phase transition [ref] , spontaneous creation of axial currents [ref] , formation of $π_0$ domain walls [ref] and chiral density waves [ref] , chiral magnetic effect [ref] , and last but not least the influence on possible color-superconducting phases [ref] .

Phase diagram of hot magnetized two-flavor color superconducting quark matter · Introduction · 0.99
The response of color-superconducting quark matter to a strong magnetic field has also been studied [ref] .

Axial anomaly and magnetism of nuclear and quark matter · Introduction · 1.00

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.