# Color–flavor locking

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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 colored matter.[1]

## Color-flavor-locked Cooper pairing

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

${\displaystyle \langle \psi _{i}^{\alpha }C\gamma _{5}\psi _{j}^{\beta }\rangle \propto \delta _{i}^{\alpha }\delta _{j}^{\beta }-\delta _{j}^{\alpha }\delta _{i}^{\beta }=\epsilon ^{\alpha \beta A}\epsilon _{ijA}}$

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[clarification needed] symmetry group.

## Physical properties

The CFL phase has several remarkable properties.

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; 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.