1. Quantum Harmonic Oscillator for J/psi Suppression at RHIC and SPS Carlos Andrés Peña Castañeda Institute of Theoretical Physics, University of Wrocław, Poland Dense Matter in heavy Ion collisions and supernovae Prerow, October 10-14, 2004 Relativistic Heavy Ion Collisions at High Baryon Number Density Wrocław, December 5-6, 2009

2. 1. Physical Motivation 2. Quantum Harmonic oscillator model for J/psi suppression 3. Suppression Factor 4. Comparison with RHIC and SPS 5. Conclusions OUTLINE

3. 1.Overview to J/psi suppression in HIC Charmonia suppression has been proposed, more than 20 years ago, as a signature for QGP formation Physical motivation J/psi SUPRESSION BY QUARK GLUON PLASMA FORMATION T. Matsui and H. Satz Phys.Lett. B178 (1986) 416 Sequential suppression of the resonances is a thermometer of the temperature reached in the collisions T/T C J/  (1S)  c (1P)  ’(2S)

4. 4 1.Overview to J/psi suppression in HIC Results are shown as a function of a the multiplicity of charged particles ( assuming  SPS ~  RHIC ) Good agreement between PbPb and AuAu R. Arnaldi, Scomparin and M.Leitch Heavy Quarkonia production in Heavy-Ion Collisions Trento, 25-29 May 2009

5. 5 2. Quantum mechanical oscillator model for J/psi suppression Calculate the distortion formation amplitude Calculate the asymptotic state for a given hamiltonian. T. Matsui. Annals Phys. 196, 182 (1989).

6. 6 2. Quantum mechanical oscillator model for J/psi suppression

7. 7

8. 8 3. Suppression Factor 1. One dimensional expansion 2. LQCD entropy density Suppression factor 3. Evolution and propagation times Model Assumptions

9. 9 4. Comparison with RHIC and SPS Size of anomalous suppression is obtained No agreement between AuAu and PbPb Discontinuous frequency

10. 10 4. Comparison with RHIC and SPS (complex potential) D. Blaschke, C. Peña. Quantum Harmonic Oscillator Model for J/psi suppression. (In progress) I. Gjaja, A. Bhattacharjee. Phys. Rev lett, 68 (1992) 2413 P. G. L. Leach, K. Andriopoulus. Appl. Ann. Discrete Math. 2 (2008)146 Kleinert Hagen. Path integral in quantum mechanics, statistics, polymer physics and financial markets, 3rd Edition, 2004.

11. 11 4. Comparison with RHIC and SPS (complex potential) Example Control the character of phase transition consistently with a second order phase trasition

12. 12 4. Comparison with RHIC (screening) (Real Potential Temperature Dependence) Continuous frequency

13. 13 4. Comparison with RHIC (Screening and Damping) (Complex Potential Temperature Dependence)

14. 14 4. Comparison with RHIC (Screening and Damping) Agreement between AuAu and PbPb (3D) Damping due to abpsortion cross section Only Screening (Real)Screening and Damping (Complex) C. Wong, Lectures on Landau Hydrodynamics. A. Polleri et al, Phys. Rev C. 70 (2004) 044906 Boris Tomásik et al, Nucl-th/9907096 L. Grandchamp, R. Rapp, Phys. Lett B. 523 (2001) 60 Control the character of phase transition

15. 15 4. Conclusions 1. The QHO model can be solved almost analytically for a given complex potential depending on Temperature (frequency depending on time). 2. The size of anomalous suppression is obtained easily by fitting the model to the experimental data from SPS and RHIC. 3. The model can be made more robust for an accelerated expansion.