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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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slide1

THE ROLE OF MAGNETIC FIELDS IN DENSE QUARK MATTER

Vivian de la Incera

University of Texas at El Paso

slide2

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
slide3

QCD Phases

The biggest puzzles lie in the intermediate regions

RHIC

Crystalline CS, Gluonic Phases, other?

Magnetic Field

slide4

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)
slide5

COLOR SUPERCONDUCTIVITY

Cooper instability

at the Fermi surface

Asymptotic freedom

plus

Formation ofQuark-Quark Pairs: ColorSuperconductivity

Attractive interactions

Bailin & Love, Phys Rep. ‘84

slide6

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

slide7

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.
slide9

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

slide10

CFL SCALES

At very large densities

slide11

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?

slide14

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

slide15

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:

slide17

GAP SOLUTIONS at LARGE MAGNETIC FIELD

Ferrer, V.I. and Manuel, PRL’05, NPB’06

cfl vs m cfl
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
slide19

LOW ENERGY CFL THEORY IN A MAGNETIC FIELD

B = 0

B 0

Ferrer & VI, PRD’07

slide20

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

slide21

HAAS-VAN ALPHEN OSCILLATIONS OF THE GAP AND MAGNETIZATION

Fukushima and Warringa, PRL’08

Noronha and Shovkovy, PRD’07

slide22

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:

slide23

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)

slide24

PARAMAGNETIC CFL

Minimum Equations:

+

Magnetic Antiscreening

Abrikosov's Equation

slide25

DIFFERENT BEHAVIOR in a B

Conventional Superconductor

H < Hc

H ≥ Hc

PCFL

MCFL

Color Superconductor

H ≥ Hc

H < Hc

slide26

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

slide27

MAGNETIC PHASES AT HIGH DENSITY

E.J. Ferrer and V.I. Phys.Rev.D76:045011,2007

Chromomagnetic Instability

slide28

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

slide29

CHROMOMAGNETIC INSTABILITIES IN 2SC

Huang/Shovkovy, PRD 70 (2004) 051501

charged gluons

8th gluon

µ8

Tachyonic Mode of Charged Gluons

At

slide31

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.

slide32

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

conclusions
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
slide34

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)