Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity

Massimo Mannarelli; Krishna Rajagopal; Rishi Sharma

doi:10.1103/PhysRevD.73.114012

paper

Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity

arXiv:hep-ph/0603076 · doi:10.1103/PhysRevD.73.114012

Abstract

It is an open challenge to analyze the crystalline color superconducting phases that may arise in cold dense, but not asymptotically dense, three-flavor quark matter. At present the only approximation within which it seems possible to compare the free energies of the myriad possible crystal structures is the Ginzburg-Landau approximation. Here, we test this approximation on a particularly simple "crystal" structure in which there are only two condensates $< u s >\sim Δ exp (i q_{2} \cdot r)$ and $< u d >\sim Δ exp (i q_{3} \cdot r)$ whose position-space dependence is that of two plane waves with wave vectors $q_{2}$ and $q_{3}$ at arbitrary angles. For this case, we are able to solve the mean-field gap equation without making a Ginzburg-Landau approximation. We find that the Ginzburg-Landau approximation works in the $Δ \to 0$ limit as expected, find that it correctly predicts that $Δ$ decreases with increasing angle between $q_{2}$ and $q_{3}$ meaning that the phase with $q_{2} ∥ q_{3}$ has the lowest free energy, and find that the Ginzburg-Landau approximation is conservative in the sense that it underestimates $Δ$ at all values of the angle between $q_{2}$ and $q_{3}$ .

arXiv comment16 pages, 6 figures. Small changes only. Version to appear in Phys. Rev. D

Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity

Abstract

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