1. Color neutrality effects in the phase diagram of the PNJL model A. Gabriela Grunfeld Tandar Lab. – Buenos Aires - Argentina In collaboration with D. Blaschke D. Gomez Dumm N. N. Scoccola

2. Motivation Understanding of the behavior of strongly interacting matter at finite T and/or density is of fundamental interest and has important applications in cosmology, in the astrophysics of neutron stars and in the physics of URHIC. CBM@FAIR From RHIC (from Jürgen Schaffner-Bielich)

3. For a long time, QCD phase diagram restricted to 2 phases HADRONIC PHASE: “our world” color neutral hadrons,  SB QGP:  S is restored In recent years phase diagram richer and more complex structure Rajagopal

4. The treatment of QCD at finite densities and temperatures is a problem of very high complexity for which rigorous approaches are not yet available NJL model is the most simple and widely used model of this type. Development of effective models for interacting quark matter that obey the symmetry requirements of the QCD Lagrangian Inclusion of simplified quark interactions in a systematic way local interactions

5. Effective theoriesLattice results at μ -> 0 Reproduce ? extrapolate at high μ Nambu Jona-Lasinio model + Polyakov loop dynamiccs Lattice simulations of P in a pure gauge theory Chiral symmetry breaking confinement It reasonable to ask what happens with color neutrality in presence of PL important in URHIC could be extended to compact stars imposing electric charge neutrality + β decay Higher Tc than NJL

6. The model NJL SU(2) flavor + quarks with a background color field related to the Polyakov loop Φ: m c (current q mass), G and H parameters of the model In our case: SU(2) flavor + diquarks + color neutrality H/G = ¾ from Fierz tr. OGE diquarks *S. Rößner, C. Ratti and W. Weise, PRD75, 034007 (2007)

7. Polyakov loop: quarks with a background color field then Polyakov gauge => diag representation order parameter for confinement

8. We considered the polynomial form for the effective potential *: with T 0 = 270 MeV from lattice crit temp for deconf. δSE (Φ,T) -> (V/T) U(Φ,T) gluon dynamics, effective potential, confinement-deconf. transition

9. over Dirac, flavor and color indices Matsubara frequencies ω n =(2n+1) π T Then, we obtain the Euclidean effective action whereMatsubara frequencies ω n =(2n+1) π T MFA -> drop the meson fluctuations (+ Usual 2SC ansatz Δ 5 = Δ 7 = 0 and Δ 2 = Δ)

10. Then, the thermodynamic potential per volume reads:

11. Thermodynamic equilibrium -> minimum of thermodynamic potential. The mean fields and are obtained from the coupled gap equations together with We impose color charge neutrality We consider * To Ω be real => μ 3 = 0

12. NUMERICAL RESULTS we use the set of parameters from PRD75, 034007 (2007) G = 10.1 GeV -2 Λ = 0.65 GeV effective theory, fluctuations, at T = μ = 0 H = ¾ G, 0.8G m c = 5.5 a 0 = 3.51 a 1 = -2.47 a 2 = 15.2 from lattice b 3 = -1.75 T 0 = 270. Phase diagram: Low μ -> XSB and XSB + 2SC High μ -> 2SC

13. Phase diagrams

14. Low temperature expansion T = 0 for μ ≠ 0 (Δ still 0) Trivially satisfied for a wide range of μ 8 for μ = 0, Δ = μ 8 = μ r = μ b = 0, M o = 324.11 Mev Step beyond: μ 8 from fin T and then T -> 0 For μ < M 0 /3

15. For μ > M 0 (before 1st order ph.tr) 2SC -> T = 0 If H/G > 0.783 f(Δ) ≠ 0 in region μ r = cte f(Δ) ≠ 0 T ≠ 0 in region μ r = cte f(Δ) ≠ 0 until T = 20 MeV, 2nd order

16. Summary and outlook we have studied a chiral quark model at finite T and µ NJL + diquarks + Polyakov loop + color neutrality ansatz PRD75, 034007 (2007) ϕ 8 = 0 => μ 8 ≠ 0, then μ 3 = 0 to enforce color neutr color neutrality => μ 8 ≠ 0 without PL, symmetric case, with PL non symmetric densities in color space different quark matter phases can occur at low T and intermediate µ coexisting phase XSB + 2SC region Next step: starting with ϕ 3 ϕ 8 ≠ 0, => μ 3 μ 8 ≠ 0 more general… فرامرز Some References S. Rößner, C. Ratti and W. Weise, PRD75, 034007 (2007) F. Karsch and E. Laermann, Phys. Rev. D 50, 6954 (1994) [arXiv:hep-lat/9406008]. C. Ratti, M. A. Thaler and W. Weise, Phys. Rev. D 73, 014019 (2006) [arXiv:hep-ph/0506234]. M. Buballa, Phys. Rept. 407, 205 (2005) [arXiv:hep-ph/0402234]. K. Fukushima Physics Letters B 591 (2004) 277–284 S. Rößner, T. Hell, C. Ratti and W. Weise, arXiv:0712.3152v1 hep-ph THANKS!