ColorSuperconducting Strangelets

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Color-Superconducting Strangelets
Prerow, 2005
O. Kiriyama ITP, J. W. Goethe-Universitaet
Outline

• Introduction
• Model (NJL model finite-size effects)
• Numerical results
• Color-flavor-unlocking transition?
• Summary

hep-ph/0401075 and Phys. Rev. D 72, 054009 (2005)
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1. Introduction
Strangelets (small lumps of strange quark matter)

• electrons mainly stay outside of quark core
• finite-size effects are important

Model (NJL finite-size effects) 1.
Color-superconducting (CSC) gap survives in
small strangelets? 2. Stability of CSC
strangelets
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Stability of color flavor locked (CFL)
strangelets J. Madsen, Phys. Rev. Lett. 87,
172003 (2001).

• CFL strangelets are significantly
• more stable than normal strangelets!

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2. Model
Three-flavor NJL model
Mean-field approximation 2-flavor
color-superconducting (2SC) phase
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Finite size effects
Multiple Reflection Expansion (MRE)
Balian and Bloch, Ann. Phys. 60, 401 (1970) 64,
271 (1971) Berger and Jaffe, Phys. Rev. C 35,
213 (1987) 44, 566(E) (1991) Madsen, Phys. Rev.
D 50, 3328 (1994).
surface
curvature
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Finite size effects (cont.)

• density of states is suppressed (more
  pronounced at low k)
• negative density of states

infrared cutoff
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Finite size effects (cont.)
E/A of normal strangelets
MRE reproduces the overall structure of the
mode-filling calculations (E/A, free energy, )
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Thermodynamic potential (2SC)
Model parameters
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Gap equation, pressure balance, and baryon number
gap equation
pressure balance relation
baryon number
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3. Numerical results
A dependence of D

• sizable 2SC gap survives
• in small strangelets
• 2SC gap is almost constant
• (as long as A is not too small)
• 2SC gap decreases at very small A

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GD dependence of E/A
strong GD large 2SC gap large pairing
energy stabilizes 2SC strangelets
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E/A (2SC versus CFL)

• CFL strangelets are more stable
• than 2SC strangelets
• (all nine quarks participate in
• the Cooper pairing)

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4. Color-flavor-unlocking transition
Fermi gas model finite-size effects
Madsen, Phys. Rev. Lett. 87, 172003 (2001).
(2SC phase)
(CFL phase)
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E/A (2SC versus CFL)
transition from CFL to 2SC
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5. Summary
Results
Outlook

• rigorous treatment of finite-size effects (at
  small radii)
• competition with other phases
• color singlet (or neutral) condition

mode-filling calculation with the MIT bag wave
functions
2SC versus CFL
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Deviation from the solid line
Appearance of finite size effects
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CFL strangelets
E/A of CFL strangelets (ms0)
CFL strangelets (ms0) could be absolutely stable
!
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A dependence of R
Balance between (kinetic energy) and
(volume energy)