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Understanding Color Neutrality Effects in the PNJL Model

Explore the impact of color neutrality in the PNJL model on strongly interacting matter at finite temperature and density. Investigate quark matter models and phase transitions in the QCD phase diagram.

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Understanding Color Neutrality Effects in 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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