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DYNAMICS OF QUARK HADRON PHASE TRANSITION PRASHANT SHUKLA Nuclear Physics Division

DYNAMICS OF QUARK HADRON PHASE TRANSITION PRASHANT SHUKLA Nuclear Physics Division Bhabha Atomic Research Center Mumbai 400085, India. INTRODUCTION Building Blocks Leptons Hadrons

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DYNAMICS OF QUARK HADRON PHASE TRANSITION PRASHANT SHUKLA Nuclear Physics Division

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  1. DYNAMICS OF QUARK HADRON PHASE TRANSITION PRASHANT SHUKLA Nuclear Physics Division Bhabha Atomic Research Center Mumbai 400085, India

  2. INTRODUCTION Building Blocks Leptons Hadrons ( e, m ...) p, n … p (qqq) (qq) 1.    Freely moving inside 2.    Forbidden to come outside qqq p ·Increase hadron Density --- Compressing ·Or increase K. E. of hadrons --- Heating   pi n p ECqqg n p n p gq gq pi p qq Hadrons Phase Transition QGP The unverse is supposed to have started from this soup

  3. Phase Diagrams

  4. g, e+e-, m+m- p, K, h, r, w, p, n, f, L, D, X, W, D, d, J/Y,… PARTICLES!

  5. NEED TO DO DYNAMICS ·To describe experimental data sensitive to dynamics, namely photons and dileptons, which will alow us to trace back the history ·Any Proof of quark hadron phase transition will be a proof of QGP formation. ·Use the results of pQCD models for initial stage conditions ·Take the parameters from first principle calculations of Lattice QCD around phase transition region

  6. LATTICE QCD RESULTS: OUR GUIDELINE 2 Flavour QCD TC = 171 + 4 MeV 3 Flavour QCD TC = 154 + 8 MeV We take TC = 160 MeV Energy density calculated with Lattice QCD of size 163 X 4 with µ = 0.

  7. m =0 T F. Karsch, Quark Matter 2001

  8. Hadronization (Nucleation) Above TC Below TC QGP Critical Hadron Bubbles 1. Get the fluctuation rate 2. Couple with suitable expansion dynamics

  9. INGREDIENTS OF THE MODEL The phase conversion rate from QGP to hadrons (Nucleation rate) I = I0 e-Fc/T The free energy FC of a critical bubble of radius is FC = (4p /3) s RC2 RC = 2 s / ( Dp + Fsc ) s is the surface tension and Dp= ph-pq We have worked on the prefactor I0 for quark hadron phase transition. Fsc is the contribution due to subcritical bubbles derived by us.  1. Shukla et al, PRC 62 (2000). 2. Shukla et. al PRD 63 (2001).

  10. DYNAMICS Fraction of hadrons at a proper time t is h(t) = tc t dt' I (T(t')) [1 - h(t')] V(t', t) Expansion scenario de/dt + D (e+p)/t = (4 h /3 + z)/t 2 = m/t2 Where D=1 for (1+1) dimension (slowest cooling) Where D=3 for (3+1) dimension (fastest cooling) Shukla et. al, PRC59 (1999)

  11. HadronicFraction At T=TC Early Universe RHIC

  12. Mixed Phase Hadron Phase QGP

  13. QGP Hadron Phase Mixed Phase

  14. NUCLEATION VS SPINODAL DECOMPOSITION A generic form (Ginzberg Landau free energy) f(f) = a 0 + a(T) f2 - b T f3 + c f4 (b, c > 0) All parameters are obtained in terms of Surface tension s, Correlation length x and Bag constant B. The temperature where the hadron phase starts appearing T1 = [B / (B – 81s/256 x)]1/4 TC. The spinodal temperature where only one minimum corresponding to hadron phase exists and the quark phase becomes unstable TS = [B/ (B + 81s/16 x)]1/4 TC. Shukla et al, PRC 62 (2000).

  15. SPINODAL DECOMPOSITION: SUDDEN HADRONIZATION At RHIC QGP has to supercool. How long ? The spinodal temperature is TS= [B/ (B + 81s/16 x)] 1/4 TC. If the minimum temperature reached during supercooling > TS nucleation is favoured < TS spinodal decomposition is favoured Mixed Phase Hadron Phase QGP Shukla and Mohanty, Phys. Rev. bf C64, 054910 (2001).

  16. At late stage of hadronization

  17. THE PHOTON DISTRIBUTIONS: The photon (dilepton) emission rate E dN/d3p =  [ (1-h) RQGP(T) + h Rhad (T) ] d4x The temperature T and hadronic fraction h are obtained from different scenario of our model.

  18. Supercooling curve SPS Photon Data

  19. CONCLUSIONS OF THE STUDY : ·The Dynamics of quark hadron phase transition is quite different inURHIC as compared to that in Early universe. ·In case of slow cooling: Nucleation also Small supercooling expected. · For the case of URHIC strong supercooling. We explicitly show that it will go through spinodal instability. · The photon data of SPS are found by us to be consistent with the scenario of supercooling and fragmentation at late stage of hadronization.

  20. Publications to the work presented : • A. K. Mohanty, P. Shukla, and M. Gleiser, Phys. Rev. C65, 034908 (2002). • P. Shukla and A. K. Mohanty, Phys. Rev. C64, 054910 (2001). • P. Shukla, A. K. Mohanty and S. K. Gupta, Phys. Rev. D63, 014012 (2001). • P. Shukla, A. K. Mohanty, S. K. Gupta, and M. Gleiser, Phys. Rev. C62, 054904 (2000). • P. Shukla, S. K. Gupta and A. K. Mohanty, Phys. Rev. C59, 914 (1999); 62, 039901 (2000). • P. Shukla and A. K. Mohanty, Pramana, J. of Phys 60, 1117 (2003). • First order quark-hadron phase transition and photon spectrum in relativistic heavy ion collisions, submitted to PRC.

  21. My Collaborators: 1. A. K. Mohanty 2. S. K. Gupta 3. M. Gleiser

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