Crystallography of three-flavor quark matter

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Krishna Rajagopal^1,2 and Rishi Sharma¹
¹Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Nuclear Science Division, MS 70R319, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

Received 5 June 2006; published 17 November 2006

Weanalyze and compare candidate crystal structures for the crystalline colorsuperconducting phase that may arise in cold, dense but notasymptotically dense, three-flavor quark matter. We determine the gap parameterDelta and free energy Omega(Delta) for many possible crystal structureswithin a Ginzburg-Landau approximation, evaluating Omega(Delta) to order Delta⁶. Incontrast to the two-flavor case, we find a positive Delta⁶term and hence an Omega(Delta) that is bounded from belowfor all the structures that we analyze. This means thatwe are able to evaluate Delta and Omega as afunction of the splitting between Fermi surfaces for all thestructures we consider. We find two structures with particularly robustvalues of Delta and the condensation energy, within a factorof 2 of those for the CFL phase which isknown to characterize QCD at asymptotically large densities. The robustnessof these phases results in their being favored over wideranges of density. However, it also implies that the Ginzburg-Landauapproximation is not quantitatively reliable. We develop qualitative insights intowhat makes a crystal structure favorable, and use these towinnow the possibilities. The two structures that we find tobe most favorable are both built from condensates with face-centeredcubic symmetry: in one case, the <ud> and <us> condensatesare separately face-centered cubic; in the other case <ud> and<us> combined make up a face-centered cube.

URL:	http://link.aps.org/doi/10.1103/PhysRevD.74.094019
DOI:	10.1103/PhysRevD.74.094019
PACS:	12.38.-t; 12.38.Mh; 26.60.+c; 74.20.-z 12.38.-t Quantum chromodynamics 12.38.Mh Quark–gluon plasma 26.60.+c Nuclear matter aspects of neutron stars 74.20.-z Theories and models of superconducting state YEAR: 2006

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