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Color neutrality effects in the phase diagram of the PNJL model

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. Motivation.

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Color neutrality effects in the phase diagram of the PNJL model

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  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. From RHIC CBM@FAIR (from Jürgen Schaffner-Bielich)

  3. HADRONIC PHASE:“our world” color neutral hadrons, SB For a long time, QCD phase diagram restricted to 2 phases 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 • 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 NJL model is the most simple and widely used model of this type. local interactions

  5. Effective theories Lattice results at μ -> 0 Reproduce ? Chiral symmetry breaking Lattice simulations of P in a pure gauge theory extrapolate at high μ confinement Nambu Jona-Lasinio model + Polyakov loop dynamiccs Higher Tc than NJL • 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 + βdecay

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

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

  8. gluon dynamics, δSE (Φ,T) -> (V/T) U(Φ,T) effective potential, confinement-deconf. transition We considered the polynomial form for the effective potential *: T0 = 270 MeV from lattice crit temp for deconf. with

  9. Then, we obtain the Euclidean effective action over Dirac, flavor and color indices where Matsubara frequencies ωn=(2n+1) π T • MFA -> drop the meson fluctuations • (+ Usual 2SC ansatz Δ5 = Δ7= 0 and Δ2 = Δ) Matsubara frequencies ωn=(2n+1) π T

  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 => μ3 = 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 • mc = 5.5 • a0 = 3.51 • a1 = -2.47 • a2 = 15.2 from lattice • b3 = -1.75 • T0 = 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 = μ8= μr = μb = 0, Mo = 324.11 Mev • for μ ≠ 0 (Δ still 0) Trivially satisfied for a wide range of μ8 Step beyond: μ8 from fin T and then T -> 0 For μ < M0/3

  15. For μ > M0 (before 1st order ph.tr) 2SC -> • T = 0 in region μr = cte f(Δ) ≠ 0 • T ≠ 0 in region μr = cte f(Δ) ≠ 0 until T = 20 MeV, 2nd order If H/G > 0.783 f(Δ) ≠ 0

  16. Summary and outlook • we have studied a chiral quark model at finite T andµ • NJL + diquarks + Polyakov loop + color neutrality • ansatz PRD75, 034007 (2007)ϕ8 = 0 => μ8 ≠ 0, then μ3 = 0 • to enforce color neutrcolor neutrality => μ8 ≠ 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 ϕ3ϕ8 ≠ 0, => μ3μ8 ≠ 0 more general… 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! فرامرز

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