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INDUCED MAGNETISM IN COLOR-SUPERCONDUCTING MEDIA

INDUCED MAGNETISM IN COLOR-SUPERCONDUCTING MEDIA. Efrain J. Ferrer. The University of Texas at El Paso. EJF & de la Incera, PRL 97 (2006) 122301 EJF & de la Incera, PRD 76 (2007) 045011 EJF & de la Incera, PRD 76 (2007) 114012. OUTLINE. Magnetized CS.

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INDUCED MAGNETISM IN COLOR-SUPERCONDUCTING MEDIA

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  1. INDUCED MAGNETISM IN COLOR-SUPERCONDUCTING MEDIA Efrain J. Ferrer The University of Texas at El Paso EJF & de la Incera, PRL 97 (2006) 122301 EJF & de la Incera, PRD 76 (2007) 045011 EJF & de la Incera,PRD 76 (2007) 114012 OUTLINE • Magnetized CS • Gluon Vortices and Magnetic Antiscreening in CS • Chromomagnetic Instabilities & Condensates Compact stars in the QCD phase diagram II (CSQCD II) May 20-24, 2009, Peking University, Beijing, China

  2. Cooper Pair Condensation V. L. Ginzburg L. D. Landau Electric Superconductivity Color Superconductivity Barrois ‘77; Frautschi ’78; Bailin and Love’84; Alford, Rajagopal and Wilczek ’98; Rapp, Schafer, Shuryak and Velkovsky ‘98 J. Bardeen, L. N. Cooper and J. R. Schrieffer • Boson: Zero Spin and opposite momenta • Color Charge • Electric Charge e e d u • Broken Symmetry: SU(3)C, U(1)em • Broken Symmetry: U(1)em

  3. In-Medium Magnetic Field d u d u u d s s s

  4. Neutron Stars Diameter: Mass: Magnetic fields: Temperature: pulsar’s surface: B~ 1012–1014G magnetar’s surface: B~ 1015–1016G

  5. Magnetic Phases at High Density Chromomagnetic Instability

  6. Magnetic CFL B=0 CFL SU(3)C × SU(3)L × SU(3)R × U(1)B × U(1)e.m B 0 MCFL SU(3)C×SU(2)L×SU(2)R ×U(1)B × U(-)(1)A× U(1)e.m. 9 GB E.J. Ferrer, V.I. and C. Manuel, PRL ‘05; NPB’06 5GB

  7. Magnetic Effects on the Gluon Sector EJF & de la Incera,PRL 97 (2006) 122301 Because of the modified electromagnetism, gluons are charged in the color superconductor Gluon Mean-Field-Effective Action in the CFL Phase:

  8. Charged Gluons Effective Action Effective action for the charged gluons within CFL at asymptotic densities where

  9. Magnetic Instability for Charged Spin-1 Fields Assuming that there is an external magnetic field in the z-direction, one mode becomes unstable when with corresponding eigenvector: “Zero-mode problem” for non-Abelian gauge fields whose solution is the formation of a vortex condensate of charged spin-1 fields. Nielsen & Olesen NPB 144 (1978) Skalozub, Sov.JNP23 (1978);ibid 43 (1986) Ambjorn & Olesen, NPB315 (1989)

  10. Gibbs Free-Energy: Minimum Equations: In the approximation:

  11. Minimum Equations: =0 + Magnetic Antiscreening Abrikosov's Equation

  12. Conventional Superconductor vs Color Superconductor Conventional Superconductor H < Hc H ≥ Hc Color Superconductor H ≥ Hc H < Hc

  13. Variation of internal magnetic field (B) with applied magnetic field (H) for Type I, Tipe II and Color Superconductors B Hc H

  14. Solution of the Linear Condensate Equation The linear minimum equation for G* around the critical field is where The solution is given by

  15. Vortex Solution From the experience with conventional type II superconductivity, it is known that the inhomogeneous condensate solutions prefer periodic lattice domains to minimize the energy. Then, putting on periodicity in the y-direction: The periodicity is also transferred to the x-direction: Vortex lattice, First image1967 Then, the general solution is given by the superposition: The vortex lattice induces a magnetic field that forms a fluxoid along the z-direction. The magnetic flux through each periodicity cell in the vortex lattice is quantized

  16. Neutrality Conditions

  17. Cooper Pairing and Neutrality Conditions • The optimal Cooper pairing occurs when • Matter inside a star should be electrically neutral to guarantee the star stability and to minimize the system energy • There are no enough electrons in β equilibrium to balance the charge deficit Cooper pairing is consequently distorted by the Fermi sphere mismatch.

  18. Chromomagnetic Instabilities in 2SC Color Neutrality and beta equilibrium Gluons Masses Stable Gapped 2SC a=1,2,3massless a=4,5,6,7 positive a=8positive Unstable Gapped 2SC a=1,2,3massless a=4,5,6,7 negative a=8positive Gapless 2SC a=1,2,3massless a=4,5,6,7 negative a=8 negative Huang/Shovkovy, PRD 70 (2004) 051501

  19. Some Suggestions • Crystalline Superconductivity • Alford, Bowers & Rajagopal, PRD 63 (2001) 074016 • Phases with Additional Bose Condensates • Bedaque & Schäfer, NPA 697 (2002) 802 • Homogeneous Gluon Condensate • Gorbar, Hashimoto & Miransky, PLB 632 (2006) 305 • Inhomogeneous Gluon Condensate with an Induced Magnetic Field • Ferrer& Incera, PRD 76 (2007) 114012

  20. Chromomagnetic Instabilities & G-B Condensates in 2SC EJF & de la Incera, PRD 76 (2007) 114012

  21. Neutrality Conditions Stable Phase: Huang/Shovkovy, PLB 564 (2003) 205

  22. Effective Action -

  23. Weakly First-Order Phase transition µ8 Tachyonic Mode of Charged Gluons At

  24. Free-Energy: Minimum Equations:

  25. Linear Equations

  26. Gluon-Condensate Solution

  27. Condensate Free-Energy Inhomogeneous Condensate: EJF & de la Incera, hep-ph/0705.2403 0.1ξ Homogeneous Condensate: Gorbar/Hashimoto/Miransky, PLB 632 (2006) 305

  28. Meissner Masses & Chromomagnetic Instabilities in Gapless-Three Flavor Quark Matter Fukushima, PRD 72 (2005) 074002; Casalbouni et al, PLB 605 (2005) 362; Alford/Wang JPG 31 (2005) 719.

  29. Origin of Stellar Magnetic Fields

  30. Difficulties of the Standard Magnetar Model Supernova remnants associated with magnetarsshould be an order of magnitude more energetic. Recent calculations indicate that their energies are similar. When a magnetar spins down, the rotational energy output should go into a magnetized wind of ultra-relativistic electrons and positrons that radiate via synchrotron emission. So far nobody has detected the expected luminous pulsar wind nebulae around magnetars. Possible Alternative: B induced by the CS core.

  31. Conclusionsand Future Directions Magnetism in Color Superconductivity is totally different from magnetism in Conventional Superconductivity Magnetism is reinforced in Color Superconductivity Magnetars CS Cores (?) Numerically solving the nonlinear equation, looking for the realization of the vortex state Exploring the possibility to induce a magnetic field in a three-flavor system: vortex state in gCFL

  32. Three flavors at very high density: CFL phase Diquark condensate O=ODirac⊗Oflavor⊗Ocolor in the CFL is:

  33. 3-Flavor QCD B=0 SU(3)C × SU(3)L × SU(3)R × U(1)B × U(1)e.m B 0 SU(3)C×SU(2)L×SU(2)R ×U(1)B × U(-)(1)A× U(1)e.m. 9 GB 5 GB

  34. 3-Flavor QCD B = 0 SU(3)C× SU(3)L× SU(3)R× U(1)B× U(1)e.m B ≠ 0 SU(3)C × SU(2)L ×SU(2)R ×U(1)B ×U(-)(1)A ×U(1)e.m. Miransky & Shovkovy, PRD 66(2002)

  35. Meissner Screening Masses & Chromomagnetic Instabilities in Neutral Dense Two-Flavor Quark Matter Huang/Shovkovy, PRD 70 (2004) 051501 Tachyonic Mode of Charged Gluons At

  36. Baryonic Matter at Very High Density & CS Cooper instability at the Fermi surface Asymptotic freedom plus ColorSuperconductivity Attractive interactions

  37. Haas-van Alphen Oscillations of the Gaps Magnetic Phases at High Density Haas-van Alphen Oscillations of the Magnetization Noronha and Shovkovy, ArXiv: 0708.0307 Fukushima and Warringa, ArXiv: 0707.3785 Chromomagnetic Instability

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