A Brief Introduction to ColorSuperconductivity

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A Brief Introduction to Color-Superconductivity
Xinyang Wang

• Department of Physics, Western Illinois
  University, Macomb, IL 61455

Macomb, February 20,2008
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Outline

• Introduction
• Neutron stars
• Superconductivity
• Color-Superconductivity
• Summary

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Introduction

• QCD phase diagram

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Introduction

• Phase diagram of water.

• They are similar.

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Neutron stars

• Created after supernova
• Mass 1.4 Mass of the Sun
• Radius 10 km
• Density of the center region is very high (0.15
  fm-3)
• Temperature during the deleptonization (via
  neutrino emission) process from 10 MeV to 1 MeV

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Neutron stars
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Superconductivity

• In 1911, Kammerling Onnes found the first
  superconductor mercury.

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Meissner effect

• In 1933 Meissner and Ochsenfeld discovered
  Meissner effect The expulsion of a magnetic
  field from a superconductor.

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Specific heat in Superconductor

• The electronic specific heat increases
  discontinuously at Tc and vanishes exponentially
  near T 0
• This is the evidence for the existence of an
  energy gap existing in the single particle
  electronic energy spectrum.

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Cooper pair

• Many-electron system
• Attractive interaction
• Cooper pairs

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Gap equation
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Color superconductivity

• The dominant interaction is strong interaction.
  It is described by the color group SU(3)
  non-Abelian gauge theory in QCD.
• At sufficiently high density and low temperature,
  the quarks are almost free.
• Attraction between pairs of quarks lead to the
  formation of Cooper pairs.

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Color superconductivity phases

• Quark Cooper pair quark has three different
  colors, three different flavors and two different
  spin direction.
• There is a 9?9 matrix of possible BCS patterns.

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Color superconductivity

• A problem
• Which quarks pair to form Cooper pairs?

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Color-flavor locking(CFL) phase (1/2)

• In the ultra high density quark matter, the mass
  of strange quark can be neglect by comparison
  with the chemical potential.
• In CSL phase, there is an equal number of colors
  and flavors.

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The quark Cooper pairs in CFL
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Pairing pattern in CFL phase
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Color-flavor locking (CFL) phase (2/2)

• Quarks in pairs have different colors and
  flavors.
• Breaks chiral symmetry.
• Need no phase transition between low and high
  density phases.
• Unbroken rotated electromagnetism. No usual,
  electromagnetic Meissner effect. But there is
  color Meissner effect.

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CFL phase in neutron stars
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Spin-one Color superconductivity

• Single-flavor pair
• Angular momentum J 1 for Cooper pairs.
• Gaps smaller than J 0.

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R-modes Gravitational spin-down of compact stars

• R-mode is a quadrupole flow that emits
  gravitational radiation. It arises spontaneously
  when a star spins fast enough, and if the shear
  and bulk viscosity are low enough.

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Bulk viscosity

• The bulk viscosity is a measure of the energy
  density dissipation during the expansion and
  compression of a fluid.
• If the expansion or compression drives the system
  out of chemical equilibrium, the microscopic
  processes which give bulk viscosity will
  re-equilibrate the system.

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Weak process in Color-Superconductivity matters

• Urca process, e.g.,
• Cooling the stars.
• Dominant in non-strange quark matter.
• Non-lepton process
• Dominant in strange quark matter.

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Summary

• Cold and dense quark matter is a color
  superconductor.
• This matter should be found in neutron stars.
• There are several different phases of
  color-superconductor.
• Weak processes play an important role in neutron
  stars.

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Acknowledge

• Thank you for Dr. Igor Shokovy adapt this lecture.

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Thank you