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COLOR SUPERCONDUCTIVITY and MAGNETIC FIELD: Strange Bed Fellows in the Core of Neutron Stars?. Vivian de la Incera Western Illinois University. IRGAC 2006. Barcelona, Spain, July 11-15, 2006. Neutron Stars. Diameter:. Mass:. Density:. Magnetic fields:.

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COLOR SUPERCONDUCTIVITY and MAGNETIC FIELD:

Strange Bed Fellows in the Core of Neutron Stars?

Vivian de la Incera

Western Illinois University

IRGAC 2006

Barcelona, Spain, July 11-15, 2006


Neutron Stars

Diameter:

Mass:

Density:

Magnetic fields:

B~ 1012 – 1014 G in the surface of pulsars

B~ 1015 – 1016 G in the surface of magnetars

IRGAC 2006


Outline

  • Color Superconductivity

  • Magnetic Field and Color Superconductivity

  • MCFL: Symmetry, gap structure, gap solutions

  • Conclusions and Outlook

  • E.J. Ferrer, V.I. and C. Manuel,

  • PRL 95, 152002 ; NPB 747, 88.

IRGAC 2006


ColorSuperconductivity

Bailin and Love ‘84

IRGAC 2006


Three flavors at very high density: CFL phase

Pairs: spin zero, antisymmetric in flavor and color

Rapp, Schafer, Shuryak

and Velkovsky, ‘98

Alford, Rajagopal and Wilczek, ‘98

IRGAC 2006


Magnetic Field Inside a Color Superconductor

In spin-zero color superconductivity a linear combination of the photon and one gluon remains massless (in-medium electromagnetic field). An external magnetic field penetrates the superconductor in the form of a “rotated” field (no Meissner effect)

- CHARGES

s

s

s

d

d

d

u

u

u

All-chargedquarks have integer charges

All pairs are -neutral

IRGAC 2006


ColorSuperconductivity & B

Will a magnetic field reinforce color superconductivity?

IRGAC 2006


Dominant attractive interactions in 3-flavor QCD lead to a general order parameter of the form

CFL:

SU(3)CX SU(3)L X SU(3)R

X U(1)BX U(1)e.m.

SU(3)C+L+RX U(1)e.m

Rapp, Schafer, Shuryak

and Velkovsky, PRL 81 (1998)

Alford, Rajagopal and Wilczek,

PLB 422 (1998)

B 0

B = 0

MCFL:

SU(3)C X SU(2)LX SU(2)R

X U(1)B X U(1)e.mX U(-)(1)ASU(2)C+L+R X U(1)e.m

Ferrer, V.I. and Manuel

PRL 95,152002

IRGAC 2006


Three-flavor NJL Theory general order parameter of the form

with Rotated Magnetic Field


MCFL ansatz including subdominant interactions general order parameter of the form

only get contributions from pairs of neutral quarks

get contributions from pairs of neutral and pairs of

charged quarks

IRGAC 2006


The mean-field action can be written as: general order parameter of the form

where the Gorkov fields are defined by:

and the Gorkov inverse propagators are

IRGAC 2006


IRGAC 2006 general order parameter of the form


Gap Equations general order parameter of the form

IRGAC 2006



Gap Solutions reduced to

IRGAC 2006

Ferrer, V.I. and Manuel, NPB 747, 88


  • The magnetic field “ reduced tohelps” CS. The field reinforces the gap that gets contributions from pairs of -charged quarks.

  • The physics behind MCFL is different from the phenomenon of magnetic catalysis. In MCFL the field reinforces the diquark condensate through the modification of the density of state

IRGAC 2006


Cfl vs m cfl
CFL reduced tovs MCFL

  • 9 Goldstone modes: charged and neutral.

  • 5 Goldstone modes: all neutral

  • Low energy similar to low density QCD in a magnetic field.

  • Ferrer, VI and Manuel, NPB’06

  • Low energy similar to low density QCD.Schafer & Wilzcek’ PRL 82 (1999)

IRGAC 2006


Conclusions and outlook
CONCLUSIONS and OUTLOOK reduced to

  • Neutron stars provide a natural lab to explore the effects of B in CS

  • Is MCFL the correct state at intermediate, more realistic, magnetic fields? Gluon condensates?

  • What is the correct ground state at intermediate densities; is it affected by the star’s magnetic field?

  • Explore possible signatures of the CS-in-B phase in neutron stars: neutrino cooling, thermal conductivity, etc.

IRGAC 2006


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