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

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 OUTLINE

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

? 4 At the core Super-High Densities (~ 10 times nuclear density) Relatively Low Temperatures (T < 10 MeV) High Magnetic Fields (probably larger than B~ –10 16 G for core of magnetars) NEUTRON STARS

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

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

7 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. CFL MAIN FEATURES

d s u d d u u s s ROTATED ELECTROMAGNETISM

uuudddsss CHARGES All -charged quarks have integer charges The pairs are all -neutral, but the quarks can be neutral or charged ROTATED CHARGES

CFL SCALES At very large densities

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?

Color Superconductivity & B

Three-flavor NJL in a Rotated Magnetic Field

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

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

GAP EQUATIONS at LARGE MAGNETIC FIELD

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

CFL VS MCFL 9 Goldstone modes: charged and neutral. 5 Goldstone modes: all neutral Low energy CFL similar to low density hadronic matter. Schafer & Wilzcek, PRL’99 Low energy MCFL similar to low density hadronic matter in a magnetic field. Ferrer, VI and Manuel, PRL’05 NPB’06 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

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

Showing that the charged Goldstone bosons acquire a magnetic-field-induced mass The dispersion relations for the charged Goldstone bosons is Ferrer & VI, PRD’07 LOW ENERGY THEORY IN A MAGNETIC FIELD 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, CFL MCFL crossover

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

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

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) MAGNETIC FIELD INDUCED INSTABILITY IN CHARGED SPIN-ONE FIELDS

Minimum Equations: Magnetic Antiscreening + 24 PARAMAGNETIC CFL

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

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 MCFL: 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  SO(2) rot PCFL: gluon condensate G 4 i  iG 5 i & 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 PHASES IN THREE-FLAVORS THEORY Rapp, Schafer, Shuryak& Velkovsky, PRL’98 Alford, Rajagopal and Wilczek, PLB ‘98 Ferrer, V.I. and Manuel PRL’05; NPB ’06 Ferrer & V.I. PRL ’06

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

Color Neutrality and beta equilibrium Unstable Gapped 2SC a=1,2,3 massless a=4,5,6,7 negative a=8 positive Gapless 2SC a=1,2,3 massless a=4,5,6,7 negative a=8 negative Stable Gapped 2SC a=1,2,3 massless a=4,5,6,7 positive a=8 positive Gluons Masses Huang/Shovkovy, PRD 70 (2004) CHROMOMAGNETIC INSTABILITIES IN 2SC

At Tachyonic Mode of Charged Gluons µ8µ8 CHROMOMAGNETIC INSTABILITIES IN 2SC charged gluons 8 th gluon Huang/Shovkovy, PRD 70 (2004)

- EFFECTIVE ACTION for CHARGED GLUONS

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.

Supernova remnants associated with magnetars should 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 DIFFICULTIES OF THE STANDARD MAGNETAR MODEL

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

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) OUTLOOK