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Color superconductivity and the strange quark Mark Alford Washington University Saint Louis, USA
1 Outline
I High density QCD Color-superconducting quark matter, Color- avor locking (CFL) II Quark matter in compact stars
weak interactions, neutrality, Ms; gapless CFL III Signatures of color superconductivity in compact stars Transport properties, mass-radius relationship IV Looking to the future
2 I. High density QCD QCD phase diagram
Conjectured form NJL model calculation T 60
RHIC 50 NQ
40 2SC QGP uSC guSC→ 30 T [MeV] non−CFL χ 20 SB g2SC
CFL 10 gas liq CFL NQ ←gCFL 0 320 340 360 380 400 420 440 460 480 500 µ [MeV] nuclear compact star µ (Ruster, Werth, Buballa, Shovkovy, Rischke, hep-ph/0503184) heavy ion collisions: chiral critical point and rst-order line compact stars: color superconducting quark matter core
3 Cooper pairing of quarks at high density At su ciently high density and low temperature, there is a Fermi sea of almost free quarks.
µ = EF E F = E N p But quarks have attractive QCD interactions.
Any attractive quark-quark interaction causes pairing instability of the Fermi surface. This is the Bardeen-Cooper-Schrie er (BCS) mechanism of superconductivity.
4 High-density QCD calculations Guess a color- avor-spin pairing pattern P ; mini- mize free energy wrt : gap equation for . = hqiaqjbi1P I = Pij ab
1. Weak-coupling methods. First-principles calculations = direct from QCD Lagrangian, valid in the asymptotic regime, currently & 106 MeV. 2. Nambu–Jona-Lasinio models, ie quarks with four- = fermion coupling based on instanton vertex, single gluon exchange, etc. This is a semi-quantitative guide to physics in the compact star regime 400 MeV, not a systematic approximation to QCD. NJL gives 10 100 MeV at 400 MeV. Both methods agree on the favored pairing pattern.
5 Color superconductivity in three avor quark matter: Color- avor locking (CFL) Equal number of colors and avors gives a special pairing pattern (Alford, Rajagopal, Wilczek, hep-ph/9804403)