1. Efrain J. Ferrer Paramagnetism in Compact Stars
Western Illinois University
IRGAC 2006, Barcelona, Spain

2. OUTLINE Gluons in Magnetized Color Superconductors
Gluon Vortices and Magnetic Antiscreening
Chromomagnetic Instabilities in Color Superconductivity and Magnetic Field Induction
Conclusions and Future Directions
Ferrer and de la Incera, hep-ph/
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3. CFL Pairing & Magnetic Field Penetrationu d u u d s s s
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4. Effects on the Gluons
Ferrer & de la Incera hep-ph/
Because of the modified electromagnetism, gluons are charged in the color superconductor 1 -1
Effective action for the charged gluons within CFL at asymptotic densities
where
IRGAC 2006.

5. with corresponding eigenvector:
Assuming that there is an external magnetic field in the z-direction, one mode becomes unstable when
with corresponding eigenvector:
“Zero-mode problem” for spin-1 non-Abelian gauge fields whose solution is the formation of a vortex condensate of charged gluons
Skalozub, Sov.JNP23 (1978); Nielsen & Olesen NPB 144 (1978)
Skalozub, Sov.JNP243 (1986); Ambjorn & Olesen, NPB315 (1989)
Ferrara & Porrati, MPLA8 (1993); Ferrer& de la Incera, IJMPA 11 (1996)
IRGAC 2006.

6. We can use the Gibbs free-energy
To obtain the equations for the gluon condensate and the induced magnetic field due to the G condensate’s backreaction on the electromagnetic field
Look alike Ginzburg-Landau equations for conventional superconductivity, except for the sign of the anomalous magnetic moment term which leads to antiscreening of the applied magnetic field thus the system behaves as a paramagnet.
IRGAC 2006.

7. Surface Energy Density and Vortex Nucleation
CFL Normal Phase
Condensed Phase
Since we have that which is the required condition for vortex nucleation.

8. Penetration Length λ and Coherence Length ξ in Type I Superconductors
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9. Variation of internal magnetic field (B) with applied external magnetic field (H) for Type I, Type II, and Color Superconductors B Hc H
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10. One can linearize the equations around the critical field
where
to find the solution
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11. The vortex lattice induces a magnetic field that forms a
fluxoid along the z-direction.
The first pictures of a vortex lattice were taken in 1967 by U. Essmann and H. Trauble who sprinkled their sample surfaces with a ferromagnetic powder that arranges itself in a pattern reflecting the magnetic flux line structure.
First image of Vortex lattice, 1967
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12. Meissner Screening Masses & Chromomagnetic Instabilities
in Neutral Dense Two-Flavor Quark Matter
Huang/Shovkovy, PRD 70 (2004)
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13. Meissner Screening Masses & Chromomagnetic Instabilities
in Gapless Three-Flavor Quark Matter
Fukushima, PRD 72 (2005) ; Casalbouni et al, PLB 605 (2005) 362; Alford/Wang JPG 31 (2005) 719.
IRGAC 2006.

14. We can use the Gibbs free-energy
To obtain the equations for the gluon condensate and the induced magnetic field due to the G condensate’s backreaction on the electromagnetic field
Look alike Ginzburg-Landau equations for conventional superconductivity, except for the sign of the anomalous magnetic moment term which leads to antiscreening of the applied magnetic field thus the system behaves as a paramagnet.
IRGAC 2006.

15. Origin of the Galactic Magnetic Field
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16. Some reasons and some implications…
Same gluon effective action, but with imaginary Meissner mass and zero external magnetic field. Same nonlinear equations will produce SSB of rotational symmetry.
Because of the anomalous magnetic moment the gluon vortices would provide a source of magnetic fields in the star.
Inhomogeneous gluon condensate would imply an inhomogeneous gap.
IRGAC 2006.

17. Conclusions and Future Tasks
Exploring color superconductivity in a magnetic field can help to understand CS in realistic systems as compact stars.
Investigate the consequences of the gluon vortices on the gap, as well as the field strengths at which this is relevant.
Determine whether the paramagnetic phase of gluon vortices corresponds to the stable ground state in gapless CS.
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