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Vivian de la Incera

THE ROLE OF MAGNETIC FIELDS IN DENSE QUARK MATTER. Vivian de la Incera. University of Texas at El Paso. OUTLINE. Color Superconductivity Color Superconductivity in a Magnetic Field: Magnetic CFL Magnetic-Field-Induced Gluon Condensate: Paramagnetic CFL

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Vivian de la Incera

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  1. THE ROLE OF MAGNETIC FIELDS IN DENSE QUARK MATTER Vivian de la Incera University of Texas at El Paso

  2. OUTLINE • Color Superconductivity • Color Superconductivity in a Magnetic Field: Magnetic CFL • Magnetic-Field-Induced Gluon Condensate: Paramagnetic CFL • Chromomagnetic Instabilities at Intermediate Densities (unstable gapped 2SC) • Solution to the CI in 2SC: Spontaneous Generation of GC and B • Conclusions

  3. QCD Phases The biggest puzzles lie in the intermediate regions RHIC Crystalline CS, Gluonic Phases, other? Magnetic Field

  4. NEUTRON STARS ? • At the core • Super-High Densities (~ 10 times nuclear density) • Relatively Low Temperatures (T < 10 MeV) • High Magnetic Fields (probably larger than B~ 1015–1016G for core of magnetars)

  5. COLOR SUPERCONDUCTIVITY Cooper instability at the Fermi surface Asymptotic freedom plus Formation ofQuark-Quark Pairs: ColorSuperconductivity Attractive interactions Bailin & Love, Phys Rep. ‘84

  6. COLOR–FLAVOR LOCKED PHASE Rapp, Schafer, Shuryak and Velkovsky, PRL’98 Alford, Rajagopal and Wilczek, PLB ’98 Diquark condensate O=ODirac⊗Oflavor⊗Ocolor If density great enough, Ms can be neglected and

  7. CFL MAIN FEATURES • All quark pair. No gapless fermions, no massless gluons. • Color superconductivity is more robust than conventional superconductivity (no need to resort to phonons). Hence is a high Tc superconductor. • Chiral symmetry is broken in an unconventional way: through the locking of flavor and color symmetries.

  8. ROTATED ELECTROMAGNETISM d u u d u d s s s

  9. ROTATED CHARGES The pairs are all -neutral, but the quarks can be neutral or charged - CHARGES s s s d d d u u u All-chargedquarks have integer charges

  10. CFL SCALES At very large densities

  11. MAGNETISM IN COLOR SUPERCONDUCTIVITY Can a magnetic field modify the Pairing Pattern? Can the CS produce a back reaction on the magnetic field? Can a color superconductor generate a magnetic field?

  12. ColorSuperconductivity & B

  13. Three-flavor NJL in a Rotated Magnetic Field

  14. MCFL Ansatz only get contributions from pairs of neutral quarks get contributions from pairs of neutral and pairs of charged quarks Ferrer, V.I. and Manuel, PRL’05, NPB’06

  15. NAMBU-GORKOV FIELDS IN NONZERO B , where the Gorkov fields separate by their rotated charge as and the corresponding Gorkov inverse propagators and contain the gaps:

  16. GAP EQUATIONS at LARGE MAGNETIC FIELD

  17. GAP SOLUTIONS at LARGE MAGNETIC FIELD Ferrer, V.I. and Manuel, PRL’05, NPB’06

  18. CFLVSMCFL SU(3)C × SU(3)L × SU(3)R × U(1)B SU(3)C × SU(2)L × SU(2)R × U(1)B × U(1)A • 9 Goldstone modes: charged and neutral. • 5 Goldstone modes: all neutral • Low energy MCFL similar to low density hadronic matter in a magnetic field. • Ferrer, VI and Manuel, PRL’05 NPB’06 • Low energy CFL similar to low density hadronic matter. • Schafer & Wilzcek, PRL’99

  19. LOW ENERGY CFL THEORY IN A MAGNETIC FIELD B = 0 B 0 Ferrer & VI, PRD’07

  20. LOW ENERGY THEORY IN A MAGNETIC FIELD The dispersion relations for the charged Goldstone bosons is Showing that the charged Goldstone bosons acquire a magnetic-field-induced mass For a meson to be stable its mass should be less than twice the gap, otherwise it could decay into a particle-antiparticle pair. Hence, CFLMCFL crossover Ferrer & VI, PRD’07

  21. HAAS-VAN ALPHEN OSCILLATIONS OF THE GAP AND MAGNETIZATION Fukushima and Warringa, PRL’08 Noronha and Shovkovy, PRD’07

  22. MAGNETIC EFFECTS ON THE GLUONS EJF & de la Incera,PRL 97 (2006) 122301 Because of the modified electromagnetism, gluons are charged in the color superconductor Charged Gluon Sector of Mean-Field Effective Action in CFL:

  23. MAGNETIC FIELD INDUCED INSTABILITY IN CHARGED SPIN-ONE 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)

  24. PARAMAGNETIC CFL Minimum Equations: + Magnetic Antiscreening Abrikosov's Equation

  25. DIFFERENT BEHAVIOR in a B Conventional Superconductor H < Hc H ≥ Hc PCFL MCFL Color Superconductor H ≥ Hc H < Hc

  26. PHASES IN THREE-FLAVORS THEORY CFL: SU(3)C SU(3)LSU(3)R U(1)B U(1)e.m. SO(3)rot SU(3)C+L+R U(1)e.m  SO(3)rot Rapp, Schafer, Shuryak& Velkovsky, PRL’98 Alford, Rajagopal and Wilczek, PLB ‘98 MCFL: SU(3)C SU(2)LSU(2)R U(1)B U(-)(1)AU(1)e.m SO(2)rotSU(2)C+L+R U(1)e.m  SO(2)rot Ferrer, V.I. and Manuel PRL’05; NPB ’06 PCFL:gluon condensate G4i iG5i& induced SU(3)C SU(2)L SU(2)R U(1)B  U(-)(1)AU(1)e.m SO(2)rot SU(2)C+L+R U(1)e.m Ferrer & V.I. PRL ’06

  27. MAGNETIC PHASES AT HIGH DENSITY E.J. Ferrer and V.I. Phys.Rev.D76:045011,2007 Chromomagnetic Instability

  28. 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

  29. CHROMOMAGNETIC INSTABILITIES IN 2SC Huang/Shovkovy, PRD 70 (2004) 051501 charged gluons 8th gluon µ8 Tachyonic Mode of Charged Gluons At

  30. EFFECTIVE ACTION for CHARGED GLUONS -

  31. GLUON CONDENSATE AND INDUCED MAGNETIC FIELD Solutions: The gluon condensate generates a magnetic field E.J. Ferrer and V.I. , Phys.Rev.D76:114012, 2007.

  32. DIFFICULTIES OF THE STANDARD MAGNETAR MODEL Supernova remnants associated with magnetarsshould be an order of magnitude more energetic, but 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 Alternatives: B can be boosted (Ferrer& VI, PRL’06) or even induced (Ferrer& VI, PRD’07; Son and Stephanov, PRD’08) by a CS core

  33. Neutron stars provide a natural lab to explore the effects of B in CS What is the correct ground state at intermediate densities? Is it affected by the star’s magnetic field? Inhomogeneous Gluon Condensates, other field-related effects… Explore possible signatures of the CS-in-B phase in neutron stars CONCLUSIONS

  34. OUTLOOK • It seems to be a profound connection between magnetism and color superconductivity. More work needs to be done to explore this association at a deeper level and to establish a link between theory and astrophysical observations. • Connections between MCFL/PCFL and Quark-Nova Mechanism? • (CSQCD II conference)

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