Color–flavor locking

Color–flavor locking (CFL) is a phenomenon that is expected to occur in ultra-high-density strange matter, a form of quark matter. The quarks form Cooper pairs, whose color properties are correlated with their flavor properties in a one-to-one correspondence between three color pairs and three flavor pairs. According to the Standard Model of particle physics, the color-flavor-locked phase is the highest-density phase of three-flavor matter.^[1]

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 ^[2]

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

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

1. M. Alford, K. Rajagopal, T. Schäfer, A. Schmitt (2008). "Color superconductivity in dense quark matter". Reviews of Modern Physics 80 (4): 1455. arXiv:0709.4635. Bibcode:2008RvMP...80.1455A. doi:10.1103/RevModPhys.80.1455.
2. M. Alford, K. Rajagopal and F. Wilczek (1998). "QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity". Physics Letters B 422: 247. arXiv:hep-ph/9711395. Bibcode:1998PhLB..422..247A. doi:10.1016/S0370-2693(98)00051-3.