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Freeze-out and constituent quark formation in a space-time layer

Freeze-out and constituent quark formation in a space-time layer. Constant pre FO temperature contour from hydro for the upper hemisphere, x>0. Matching Conditions for pre/post FO change :. Conservation laws !!! Nondecreasing entropy.

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Freeze-out and constituent quark formation in a space-time layer

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  1. Freeze-out and constituent quark formation in a space-time layer L.P. Csernai

  2. Constant pre FO temperature contour from hydro for the upper hemisphere, x>0 L.P. Csernai

  3. Matching Conditions for pre/post FO change: • Conservation laws !!! • Nondecreasing entropy If the final state is out of Eq., the energy-momentum tensor and f(x,p) have to be evaluated, and the above eqs. solved!!! [L.P. Csernai, Sov. JETP, 65 (l987) 216.][ Anderlik et al. Phys.Rev.C 59 (1999) 3309] [ Tamosiunas and Csernai, Eur. Phys. J. A20 (2004) 269] L.P. Csernai

  4. Rapid FO and recombination into Constituent Quarks A: Hydro history [file] > QGP (q,g)  BAMPS  CQ-s B: Hydro history [file] > QGP (q,g)  FO model in a layer  CQ-s L.P. Csernai

  5. The choices of post FO distributions are: • Jüttner - distr. / Timelike FO • Cut - Jüttner - distr. / Spacelike FO - No physical ground for these choices, although conservation laws can be enforced. - Post FO distr. must not be an eq. distr. - Physical, transport processes must create the post FO distribution  takes space and time! L.P. Csernai

  6. Sudden FO at a sharp 3-dimensional space-time hyper-surface Gradual FO in an extended 4-dimensional space-time volume [J.Knoll] For large systems (vs. mfp) this space-time volume is a “layer”,  there is a dominant direction (gradient) of this change of f(x,p). Let that be: “t” or “s” (It must not be time-like!) From kinetic theory: L.P. Csernai

  7. Mod. Bolz. Tr. Eq. [Csernai et al.,Eur. Phys. J. A 25, 65-73 (2005)] Projected to the direction of dominant change this leads to: where [E. Molnar, et al., PHYSICAL REVIEW C 74, 024907 (2006)] L.P. Csernai

  8. Freeze out in a finite layer • The corresponding equations for both space-like and time-like freeze out /wo re-thermalization • The solution: Space-like Time-like [ E. Molnar, et al., J.Phys.G34 (2007) 1901; Phys.Rev.C74 (2006) 024907; Acta Phys.Hung. A27 (2006) 359; V.K. Magas, et al., Acta Phys. Hung.A27 (2006) 351. ] This should be supplemented with a recombination process into hadrons / constituent quarks. L.P. Csernai

  9. The invariant “ Escape” probability A B C t’ x’ D E F [RFG] Escape probability factors for different points on FO hypersurface, in the RFG. Momentum values are in units of [mc] L.P. Csernai

  10. Freeze out distribution with rescattering from kinetic model across a layer V=0 [V. Magas, et al.,] Heavy Ion Phys.9:193-216,1999 L.P. Csernai

  11. Analytic fit to Kinetic Model Solution: . [ K. Tamosiunas and L.P. Csernai, Eur. Phys. J. A20 (2004) 269] . L.P. Csernai

  12. Cancelling Juttner Distribution[Karolis Tamosiunas et al.] L.P. Csernai

  13. This was up to 2005 – 2006 • New developments from 2006: • v1 confirmed at RHIC • Indication of Mach Cones around jets • CNQ scaling of flow : FO & Hadronization L.P. Csernai

  14. Freeze Out Rapid and simultaneous FO and “hadronization” • Improved Cooper-Frye FO: • - Conservation Laws: • - Post FO distribution: • Hadronization ~ CQ-s • - Pre FO: Current and , QGP • - Post FO: Constituent and • - are conserved in FO!!! • Choice of F.O. hyper-surface / layer [L.P. Csernai, Sov. JETP, 65 (l987) 216.] [Cancelling Juttner orCut Juttner distributions.] L.P. Csernai

  15. CNQ scaling Constituent quark number scaling of v2 (KET ) Collective flow of hadrons can be described in terms of constituent quarks. Observed nq – scaling Flow develops in quark phase, there is no further flow development after hadronization R. A. Lacey (2006), nucl-ex/0608046. L.P. Csernai

  16. Simultaneous FO & recombination • Thermal smearing is influenced by the pre-FO parton distribution  strong • BTE does not take this into account correctly: LOCAL molecular chaos fails • Modified BTE with non-local Collision term is vital: • [Modified Boltzmann Transport Equation, • V.K. Magas, L.P. Csernai, E. Molnar, A. Nyiri and K. Tamosiunas, • Nucl. Phys. A 749 (2005) 202-205. / hep-ph/0502185] • [Modified Boltzmann Transport Equation and Freeze Out, • L.P. Csernai, V.K. Magas, E. Molnar, A. Nyiri and K. Tamosiunas, • Eur. Phys. J. A 25 (2005) 65 -73. / hep-ph/0505228] • FO description should include, (i) partonic thermal smearing, (ii) conservation & entropy increase, (iii) Cooper-Frye type of evaluation of post FO distribution(iv) constituent quarks or Quarkyonic Matter L.P. Csernai

  17. Flow in hydro, before F.O. b= 0 b=30% b-max. b=70% b-max. L.P. Csernai

  18. Freeze Out Flow in hydro, after appr.(*) F.O. b=30% b-max. Correct FO description is of Vital Importance ! (*) Thermal smoothing in z-direction only with TFO = 170 MeV and mFO = 139 MeV (both fixed). Transverse smoothing would furtherreduce the magnitude of v1 (and v2). L.P. Csernai

  19. Hadronization via recombination  /nq Momentum distribution of mesons in simple recombination model: Local fq(pµuµ) is centered at the local u, & meson Wigner function: momentum conservation comoving quark and antiquark: for the momentum distribution of mesons we get: flow moments: for baryons, 2 3 [Molnar D. -NPA774(06)257] L.P. Csernai

  20.  Elliptic flow of mesons: For baryons: Scaling Variables of Flow: 1st step: Flow asymmetry: V2 / n qV2 scales with nq i.e., flow develops in QGP phase, following the common flow velocity, u, of all q-s and g-s. Mass here does not show up (or nearly the same mass for all constituent quarks). Then flow asymmetry does not change any more. In a medium pT is not necessarily conserved, K ET = mT – m might be conserved  scaling in the variable K ET [J. Jia & C. Zhang, 2007] L.P. Csernai

  21. 2nd step: pt / nq K ET / nq = mo (√(1+u2) - 1) / nq ET  u << 1 : mo uT2 / 2  u >> 1 : mo uT Thus, scaling flow indicates dependence (equilibration) of transverse energy, i.e., not only the flow velocity but the constituent quark mass, mo, participates. Flow momentum changes while energy equilibrates in a finite system (Canonical Ensemble). The final stages of hadronization do not change the flow-asymmetry, but locally the constituent quarks complete their "dress up" in their local region by redistributing energy to reach equilibrium. Quarkyonic Matter: No gluons / Asymptotic freedom (weakly interacting) A new phase between high T QGP and Hadronic Phase, Especially at higher baryon densities (FAIR) L.P. Csernai

  22. From QGP • To CQ matter or Quarkyonic matter • CQ is in chemical equilibrium  Energy-mom. • CQ has the same # of q and q-bar as QGP L.P. Csernai

  23. CQ matter in ch. Eq. L.P. Csernai

  24. CQ matter out of ch. Eq. L.P. Csernai

  25. Acceleration, non-relativitic limit Acceleration if PQGP > Phadr L.P. Csernai

  26. In general the FO hyper-surface is not orthogonal to the flow velocities, so this acceleration (deceleration) is an essential consequence of the correct FO description! In early simplified approach[see mentioned in L.P. Csernai: Introduction to Relativistic Heavy Ion Collisions] it was argued that in a flow one can choose a ragged FO hyper-surface like this to the right: t t P dV x x The simplified approach, violates momentum conservation [!] and decreases flow effects! Acceleration is stronger at the edge near to space-like FO, left side. Fully space-like FO leads to strong acceleration as only outgoing particles can FO! FAIR L.P. Csernai

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  29. OUTLOOK for F. O. • CNQ scaling indicates QGP, simplifies F.O. description to Const. Quarks. This requires, however, Modified BTE description • Space – Time volume or layer Freeze Out required • A rapid process should be quantitatively described. The kinetic approach does not provide a time or spatial scale for the Hadronization of QGP! • Larry McLerran [GSI, 9.2.2009] predicts an intermediate Quarkyonic phase • Igor Mishustin [CPOD, GSI, 9.7.2007] sets an estimate for “Explosive Hadronization”. See also earlier work: [Csernai and Mishustin, PRL 74 (95) 5005] • Choice of FO Surface or Layer  Hydro history L.P. Csernai

  30. The END L.P. Csernai

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