# Physics: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 colored matter.^{[1]}

## Color-flavor-locked Cooper pairing

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

- [math]\displaystyle{ \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} }[/math]

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.

- 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.

## See also

## References

- ↑
M. Alford; K. Rajagopal; T. Schäfer; A. Schmitt (2008). "Color superconductivity in dense quark matter".
*Reviews of Modern Physics***80**(4): 1455–1515. doi:10.1103/RevModPhys.80.1455. Bibcode: 2008RvMP...80.1455A. - ↑
M. Alford; K. Rajagopal; F. Wilczek (1998). "QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity".
*Physics Letters B***422**(1–4): 247–256. doi:10.1016/S0370-2693(98)00051-3. Bibcode: 1998PhLB..422..247A.

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