1. Mean Field Effect on J/psi Production in Heavy Ion Collisions Baoyi Chen Physics Department Tsinghua University Cooperators: Kai Zhou Yunpeng Liu Pengfei Zhuang (Professor) Tsinghua University WeiHai July 23 2012

2. Outline 1. Motivation 2. Transport Model & Hydrodynamics 3. Mean Field Effect on J/psi Mass 4. Numerical Results and Analysics 5. Summery Tsinghua University WeiHai July 23 2012

3. In order to understand the properties of the QGP, we consider interactions between Jpsi and the medium -----> collisions( inelastic, elastic) Tsinghua University WeiHai July 23 2012 Motivation Inelastic collisions: nuclear absorption, gloun dissociation and regeneration Elastic collisions : mean field effect

4. In order to understand the properties of the QGP, we consider interactions between Jpsi and the medium -----> collisions( inelastic, elastic) Tsinghua University WeiHai July 23 2012 Motivation Inelastic collisions: nuclear absorption, gloun dissociation and regeneration Elastic collisions : mean field effect Inelastic collisions affect Jpsi yield, pt-spectrum, v2 largely, will elastic collisions change these too?

5. Tsinghua University WeiHai July 23 2012 Motivation Mean field effect changes Jpsi mass Jpsi mass shift second-order stark effect QCD sum rules (PRD 79, 011501) mass shift reduces shreshold of Jpsi regeneration and makes easy regeneration -200MeV

6. Tsinghua University WeiHai July 23 2012 Motivation The mean field force Inhomogeneous medium makes space gradients of temperature (calculated by hydrodynamics) none-zero. The attractive mean field force pulls Jpsi to the center of the fireball. and leads to a shift from high pt to low pt (PRD 79, 01150)

7. Transport Model & Hydrodynamics 1. Evolution of Medium (Energy-momentum Conservation) 2+1 demensional boost invariant Tsinghua University WeiHai July 23 2012 with + EOS 2. J/psi Transport Equation ( J/psi are so heavy, hard to be thermalied ) suppression regeneration both inelsatic elastic

8. Transport Model & Hydrodynamics without elastic collisions the analytic solution is Tsinghua University WeiHai July 23 2012 Two competition mechanism: Initial Production V.S. Regeneration with glouns 、 c quark are totally thermalized

9. width J/psi decay (gloun dissociaition) mass shift mean field effect Mean Field Effect on Jpsi Mass After considering the mass shift effect of Jpsi, we should also consider Jpsi width. In dynamically evolutive QGP Tsinghua University WeiHai July 23 2012 1.J/psi width

10. Tsinghua University WeiHai July 23 2012 Mean Field Effect on J/psi Mass Qualitatively estimate J/psi width choose typical medium velocity 2 times Jpsi width increases with T, duo to higher gloun density at higher T

11. Tsinghua University WeiHai July 23 2012 Mean Field Effect on J/psi Mass Qualitatively estimate J/psi width choose typical medium velocity 2 times Jpsi width increases with T, duo to higher gloun density at higher T (PRD 82, 054008) Jpsi width Jpsi width in our model(left) is qualitatively consistent with the right figure

12. Tsinghua University WeiHai July 23 2012 Mean Field Effect on J/psi Mass assuming small elastic cross section for charmonia at hadron level is still true at parton level. It can be solved perturbatively with (PRD 79, 01150) reduced threshold of J/psi makes regeneration more easily; the mean field force induced by inhomogeneous property of the medium pulls J/psi to the center of the fireball

13. Tsinghua University WeiHai July 23 2012 Mean Field Effect on J/psi Mass assuming small elastic cross section for charmoniaat hadron level is still true at parton level. It can be solved perturbatively leaving mean field force first, but keeping the temperature dependence of the mass The first-order solution

14. Tsinghua University WeiHai July 23 2012 Mean Field Effect on J/psi Mass assuming small elastic cross section for charmoniaat hadron level is still true at parton level. It can be solved perturbatively leaving mean field force first, but keeping the temperature dependence of the mass The first-order solution the second-order solution effective regeneration

15. Tsinghua University WeiHai July 23 2012 Mean Field Effect on J/psi Mass assuming small elastic cross section for charmoniaat hadron level is still true at parton level. It can be solved perturbatively leaving mean field force first, but keeping the temperature dependence of the mass The first-order solution the second-order solution effective regeneration The iteration converges rapidly !

16. Tsinghua University WeiHai July 23 2012 Numerical Results and Analysics 1. Results below only expands to second- order, 2. neglecting mass shift effect on excited states of J/psi due to 3. neglecting normal suppression and shadowing effect at RHIC

17. Tsinghua University WeiHai July 23 2012 Numerical Results and Analysics 26% ! reduced threshold of J/psi makes regeneration more easily + mean field force mean field force kicks J/psi to low P_t region affects regeneration only

18. Tsinghua University WeiHai July 23 2012 Numerical Results and Analysics Due to experimental data including B-decay and shadowing effect; calculations here contains these factors too, which are absent in calculations at RHIC energies. describing exprimental data well at low pt region! ( Black lines are provided by Kai Zhou)

19. Tsinghua University WeiHai July 23 2012 Numerical Results and Analysics effective region of mean field on J/psi production is around pt=0.5GeV, which is smaller than averaged pt at RHIC and LHC: 2~3GeV So, even the mean field effect affects J/psi pt-spectra significantly, it changes total yield slightly.

20. Tsinghua University WeiHai July 23 2012 Numerical Results and Analysics 1. Global yield of J/psi is slightly enhanced by the mean field effect.

21. Tsinghua University WeiHai July 23 2012 Numerical Results and Analysics 1. total J/psi production are less affected by the mean field effect. the averaged pt square are suppressed.

22. Tsinghua University WeiHai July 23 2012 Summary 1. We developed a pertubative expansion to study the mean field effect on J/psi production. 2. Though the mean field changes global yield of J/psi slightly, it changes J/psi pt-spectrum significantly. 3. Initial J/psi production, which happens before the formation of QGP is not affected by the mean field effect; but regeneration which happens in the evolution of QGP, is largely enhancement at low transverse momentum.

23. Tsinghua University WeiHai July 23 2012 Thank you for your attention !

24. Tsinghua University WeiHai July 23 2012 Numerical Results and Analysics Deviation exists between calculation and data at low pt, because shadowing effect, which will reduce regeneration, is not considered in this calculation.

25. Tsinghua University WeiHai July 23 2012 BUCKUP

26. Tsinghua University WeiHai July 23 2012