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Recent Results on the Quark Coalescence Model

Károly Ürmössy and Tamás S. Bíró MTA KFKI RMKI , ELTE Fürstenfeld 15-17 April 2009. Recent Results on the Quark Coalescence Model. Content. Thermalized Hadrons and Quarks at RHIC ? Hadronisation by Coalescence, quasi-particles of the quark-gluon matter Comparison with pQCD

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Recent Results on the Quark Coalescence Model

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  1. Károly Ürmössy and Tamás S. Bíró MTA KFKI RMKI, ELTE Fürstenfeld 15-17 April 2009 Recent Results on the Quark Coalescence Model

  2. Content • Thermalized Hadrons and Quarks at RHIC ? • Hadronisation by Coalescence, quasi-particles of the quark-gluon matter • Comparison with pQCD • Why power-laws?

  3. Intro: From thermal quarks to hadron spectra The detector sees - Cooper-Fry formula Instant hadronisation at propertime τ, radial flow v║r (Blastwave)

  4. Ansatzfor the Transverse Spectra Ansatz: Co-moving Energy:

  5. Flow In the co-moving system the energy is minimal at the maximal yield: The value of the maximum is proportional to the mass :

  6. Antiproton spektrum (RHIC) Adler S S, et al. (PHENIX Collaboration) 2004 Phys. Rev. C69 034909 dN/pTdpT PT [GeV] Max:

  7. Thermal hadrons at RHIC (Qmesons – 1)*2 = 3*(Qbaryons - 1) Vflow = 0.42 – 0.55 Thermal up to 6-10 GeV

  8. Thermalisation at the Level of Quarks? Instant hadronisation → no time evollution of the fqs during the hadronization IF for pT» m coalescence constraint quark disp no p pick-up from the plasma THEN → Quarks, hadrons have power-law asymptotics → The hadron power scales with the quark number: (Qmesons – 1)*2 = 3*(Qbaryons - 1)

  9. Non-Extensivity q Scaling T.S.Biro, K. Ürmössy: Pions and kaons from stringy quark matter arXiv:0812.2985v1 [hep-ph] Qquark - 1= (Qmeson – 1)2 = 3(Qbaryon - 1)

  10. Tslope - m Scaling T.S.Biro, K. Ürmössy: Pions and kaons from stringy quark matter arXiv:0812.2985v1 [hep-ph] Tslope = T0+ (Qhadron- 1)m

  11. Quasi-particles at Low pT Simple product does not work! mi << M. We need something like P

  12. Let’s Try Quarks With Mass-distribution! J Zimányi et al 2005 J. Phys. G: Nucl. Part. Phys.31 711-718 To achieve that have a maximum around M/2 for mesons

  13. Power-law quasi-particles, with distrbuted mass: T.S.Biró,P.Lévai,P.Ván,J.Zimányi: PRC,vol.75,Issue3,id.034910,03/2007.

  14. Coalescence - pQCD T.S.Bíró,G.G.Barnaföldi,K.Ürmössy: J.Phys.G:Nucl.Part.Phys.35044012, 2008.

  15. Why Power Laws? Superstatistics C. Beck, E. Cohen, H. L. Swinney:Phys. Rev. E 72, 056133 (2005) Tamás Bíró’ Talk

  16. Kinetic model Langevin problem:

  17. Kinetic model The equivalent Fokker-Planck problem: Let G, D depend on p through the energy! To get our power-law distribution as stacionary sollution we have to enter a linear spectral slope T(E)

  18. Kinetc model T. S. Biró, G. Györgyi, A. Jakovác, G. Purcsel 2005 J.Phys.G:Nucl.Part.Phys.31 S759-S763 into the equation for G and D. All D(E) – G(E) pairs result in our power-law distribution. Then we know what stochastic equation drives the quasi-particles of the plasma.

  19. Non-additiveEnergy Composition T. S. Biró, G. Purcsel 2008Phys. Lett A 3721174

  20. Equilibration

  21. Variationand energydistribution: konst The termodynamic temperature is the intercept of the spectral slope:

  22. Conclusion • There can be thermalisation at RHIC at the quark level, because: Under 6-8 GeV the power of Mesonic to Baryonic spectra goes as 2 to 3. • T(hadron) scales with m linearly: T(m) = To + (q - 1)m • Our calculations are in qualitative agreement with pQCD calculations • We use power-law distributed quarks because: pQCD, Addition Rules, T fluctuations, Fokker-Planck with D(E)

  23. Refrences T.S.Bíró,G.G.Barnaföldi,K.Ürmössy:PionandKaonspectrafromdistributedmassquarkmatter,J.Phys.G:Nucl.Part.Phys.35044012(6pp)doi:10.1088/0954-3899/35/4/044012,2008. T.S.Bíró,K.Ürmössy:Fromquarkcombinatoricstospectral coalescence,TheEuropeanPhysicalJournal,SpecialTopics,Volume155,Number1/March,2008. T.S.Biro, K. Ürmössy: Pions and kaons from stringy quark matter arXiv:0812.2985v1 [hep-ph] Submitted: 16 Dec 2008. Tamas S. Biro, Gabor Purcsel and Karoly Urmossy: Non-Extensive Approach to Quark Matter arXiv:0812.2104 Submitted: December 2008.

  24. Coalescence Factor

  25. Lattice EOS – Mass Distribution

  26. Lattice-EOS with u, d, s Quarks (μ=0) T.S.Biró,P.Lévai,P.Ván,J.Zimányi: PRC,vol.75,Issue3,id.034910,03/2007.

  27. T.S.Biró,P.Lévai,P.Ván,J.Zimányi:J.Phys.G:Nucl.Part.Phys.32No12(Dec. 2006) S205-S212. ThermodynamicConsistency

  28. T.S. Biró, A. László, P. Ván: http://arxiv.org/abs/heph-ph/0612085v1 μandT IndependentMass-distribution from Lattice EOS

  29. T.S. Biró, A. László, P. Ván: http://arxiv.org/abs/heph-ph/0612085v1 Mass-Distribution from the Inversion of the Meier-transform

  30. T.S.Biró,P.Lévai,P.Ván,J.Zimányi: PRC,vol.75,Issue3,id.034910,03/2007. μ,TIndependency→Mass-Gap

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