Color–flavor locking

Color-flavor-locked Cooper pairing

If each quark is represented as \psi^\alpha_i, with color index \alpha taking values 1, 2, 3 corresponding to red, green, and blue, and flavor index i taking values 1, 2, 3 corresponding to up, down, and strange, then the color-flavor-locked pattern of Cooper pairing is

:\langle \psi^\alpha_i C \gamma_5 \psi^\beta_j \rangle \propto \delta^\alpha_i\delta^\beta_j - \delta^\alpha_j\delta^\beta_i = \epsilon^{\alpha\beta A}\epsilon_{ij A}

This means that a Cooper pair of an up quark and a down quark must have colors red and green, and so on. This pairing pattern is special because it leaves a large unbroken symmetry group.

Physical properties

The CFL phase has several remarkable properties.

• It breaks chiral symmetry.
• It is a superfluid.
• It is an electromagnetic insulator, in which there is a "rotated" photon, containing a small admixture of one of the gluons.
• It has the same symmetries as sufficiently dense hyperonic matter.

There are several variants of the CFL phase, representing distortions of the pairing structure in response to external stresses such as a difference between the mass of the strange quark and the mass of the up and down quarks.

References