Quantum Harmonic Oscillator for

J/psi Suppression at RHIC and SPS

Carlos Andrés Peña CastañedaInstitute of Theoretical Physics,

University of Wrocław, Poland

Dense Matter in heavy Ion collisions and supernovaePrerow, October 10-14, 2004

Relativistic Heavy Ion Collisions at High Baryon Number DensityWrocław, December 5-6, 2009

1. Physical Motivation

2. Quantum Harmonic oscillator model for J/psi suppression

3. Suppression Factor

4. Comparison with RHIC and SPS

5. Conclusions

OUTLINE

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. SatzPhys.Lett. B178 (1986) 416

Sequential suppression of the resonances is a thermometer of the temperature reached in the collisions

T/TC

J/(1S)

c(1P)

’(2S)

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.LeitchHeavy Quarkonia production in Heavy-Ion Collisions

Trento, 25-29 May 2009

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

2. Quantum mechanical oscillator model for J/psi suppression

7

2. Quantum mechanical oscillator model for J/psi suppression

8

3. Suppression Factor

1. One dimensional expansion

2. LQCD entropy density

Suppression factor

3. Evolution and propagation times

Model Assumptions

9

4. Comparison with RHIC and SPS

Size of anomalous suppression is obtained

No agreement between AuAu and PbPb

Discontinuous frequency

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) 2413P. G. L. Leach, K. Andriopoulus. Appl. Ann. Discrete Math. 2 (2008)146Kleinert Hagen. Path integral in quantum mechanics, statistics, polymer physics and financial markets, 3rd Edition, 2004.

11

4. Comparison with RHIC and SPS (complex potential)Example

Control the character of phase transition consistently with a second order phase trasition

12

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

Continuous frequency

13

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

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) 044906Boris Tomásik et al, Nucl-th/9907096 L. Grandchamp, R. Rapp, Phys. Lett B. 523 (2001) 60

Control the character of phase transition

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.