IRGAC 2006
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Transcript of IRGAC 2006
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IRGAC 2006
COLOR SUPERCONDUCTIVITY and MAGNETIC FIELD:
Strange Bed Fellows in the Core of Neutron Stars?Vivian de la Incera
Western Illinois University
Barcelona, Spain, July 11-15, 2006
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IRGAC 2006
B~ 1012 – 1014 G in the surface of pulsars
B~ 1015 – 1016 G in the surface of magnetars
Neutron Stars
20R km (12 miles)
Diameter:
Mass:
30 010 , 0.15 fm
Magnetic fields:
Density:
?
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• 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
Outline
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( )
High baryon density
quark deconfined matter
Attractive
one-gluon-exchange
interactions
Cooper instability
quark-quark pairing
IRGAC 2006Color Superconductivity
Bailin and Love ‘84
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IRGAC 2006
Three flavors at very high density: CFL phase
C L R BSU( ) X SU( ) X S
U
Symmetry Br
( ) X U(
eaki
)3
n
g
3 3 1
:
Pairs: spin zero, antisymmetric in flavor and color
CFLib bi
j jia a
i
C+L+R( )S 3URapp, Schafer, Shuryak and Velkovsky, ‘98 Alford, Rajagopal and Wilczek, ‘98
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Magnetic Field Inside a Color Superconductor
BB8G
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)
u u ud d ds s s
0 0 -1 0 0 -1 1 1 0
- CHARGES
All -charged quarks have integer charges All pairs are -neutralQ
Q
Q
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IRGAC 2006
Color Superconductivity & B
Will a magnetic field reinforce color superconductivity?
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CFL:SU(3)C X SU(3)L X SU(3)R
X U(1)B X U(1)e.m.
SU(3)C+L+R X U(1)e.m
Rapp, Schafer, Shuryak
and Velkovsky, PRL 81 (1998)
Alford, Rajagopal and Wilczek,
PLB 422 (1998)
1 2 331 2 31 2~j j
a a ab b b bi
aji i ij
MCFL:
SU(3)C X SU(2)L X SU(2)R
X U(1)B X U(1)e.m X U(-)(1)A
SU(2)C+L+R X U(1)e.m
Ferrer, V.I. and Manuel
PRL 95,152002
1 2 3
Dominant attractive interactions in 3-flavor QCD lead to a general order parameter of the form
1 2 3
IRGAC 2006
B = 0 B 0
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0 0 01 1 1
( )0 ( )0 ( )0
5 0 5
5
0
( )[ ] ( ) ( )[ ] ( ) ( )[ ] ( )
1 [ ( ) ( ) ( ) ( )
2
( ) ( ) h.c.
{
]}
B
C
xy
MCFL MCFL
MCFL
C
C
x G y x G y x G y
x y x y
x
I
y
2 3 3
0 0
0
1 2 11 3 2( , , , , , , , , )
, ,
0
s s s d d d u u
Q
u
Q
0
0
' '
(1,1,0,1,1,0,0,0,1)
(0,0,0,0,0,0,1,1,0)
(0,0,1,0,0,1,0,0,0)
1
diag
diag
d
Q
iag
( )0
( )00
10
10
[ ] ( )
[ ] ( )
G i
G i
eA
Three-flavor NJL Theory
with Rotated Magnetic Field
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MCFL ansatz including subdominant interactions
MCFL
and S A only get contributions from pairs of neutral quarks
IRGAC 2006
2 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 2 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 2
S S A S A
S A
S A
S A
S A S S A
S A
S
B B
B B
B B
B B
B BA
S A
S A S
B
BA S
B
B B B
and B BS A get contributions from pairs of neutral and pairs of
charged quarks
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0 0 01 1 11
[ , ] [2
]xy
S SI S
00
0
C C C
where the Gorkov fields are defined by:
The mean-field action can be written as:
and the Gorkov inverse propagators are
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( )
( )
(
( )0
( )0
)
( )
(0
0
( )0
( )0
( )0
( 0
0)
( ) )0
1
1
1
1
1
1
1
1
10
[ ] ( , )
[ ] ( , )
[ ] ( , )
[ ] ( , )
[ ] ( , )
[ ] ( , )
G x y
G x y
G x y
G x y
G x y
G x y
S
S
S
00
0
C
C C
(0)
( )
( )
0 0MCFL
MCFL
MCFL
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Gap Equations
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2 3 2
2 3 2 22 22 23 (2 ) 3 (2 )( ) 2( ) ( ) ( )
B BB
B
AA
A AB
Aeg d g
q
Bq dq
q
For fields the gap equations can be reduced to
2Be
2
2 2
3
2 3 2 2
17 7
9 94 (2 ) ( ) ( ) 2( )B
A AA
A A
g d q
q q
2 3
2 3 2 22 218 (2 ) ( ) ( ) 2( )B
A AS
A A
g d q
q q
2 2 3
2 2 2 32 22 26 (2 ) 6 (2 )( ) ( ) ( ) 2( )
A A
A
BB
S
A
B
B B
g dq g d q
q
eB
q
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2
2
2
2 2
0.3, 0.2
~
~ B
1A8
A
g
=3/2, ,
1
eB
B 0
yx
=
yx
G
Gap Solutions
2 2
2 2
3 1exp( )
1 2( )
36 21 1 2 2exp 1
17 17 (1 ) 74
1 1
4A S
A
B B
S A
BA
eg
x
y
y
x y y
B
2
2
1exp( ),
(2 2 )
2 2
3
~
2
2
B
B 2
AB
G
= , = ,
g
N N
N N
Be
G
Ferrer, V.I. and Manuel, NPB 747, 88IRGAC 2006
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IRGAC 2006
The magnetic field “helps” CS. The field reinforces the gap that gets contributions from pairs of -charged quarks.
Q
1exp( )~
(2 2 )AB
BG N N
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
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CFL vs MCFL
• 9 Goldstone modes: charged and neutral.
• 5 Goldstone modes: all neutral
• Low energy similar to low density QCD. Schafer & Wilzcek’ PRL 82 (1999)
• Low energy similar to low density QCD in a magnetic field.
Ferrer, VI and Manuel, NPB’06
IRGAC 2006
C L+ R+ 3
( )SU
( ) , ( ) 2
8 1
8 1
R+C +L(2)
SU
221 12 2
221 12 2
( ) , ( ) ,
( )
3 4 1 1
3 4
( 81
81
)
B
B
B
A
A
A
A
A A
A
A
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CONCLUSIONS and OUTLOOK
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