1. Chemical Equilibration at the Hagedorn Temperature Jaki Noronha-Hostler Collaborators: C. Greiner and I. Shovkovy

2. Outline Motivation: understanding chemical freeze-out in heavy ion collisions –Hagedorn Resonances Master Equations for the decay –Parameters Estimates of Equilibration times –Baryon anti-baryon decay widths Conclusions and Outlook

3. Motivation Standard hadron gas: Kapusta and Shovkovy, Phys. Rev. C 68, 014901-1 (2003) Greiner and Leupold, J. Phys. G 27, L95 (2001) Huovinen and Kapusta, Phys. Rev. C 69, 014901 (2004) Some suggest long time scales imply that the hadrons are “born in equilibrium” –Heinz,Stock, Becattini… - chemical eq. time Can’t explain apparent equilibrium

4. Production of anti-baryons production detailed balance annihilation rate annihilation rate chemical equilibration time Rapp and Shuryak, PRL 86, 2980 (2001) Greiner and Leupold, J. Phys. G 27, L95 (2001)

5. Baryon anti-baryon production lower by a factor of 3-4 Can be produced through where HS are mesonic Hagedorn resonances with time scales of  =1-3 fm/c. –Greiner, Koch-Steinheimer, Liu, Shovkovy, and Stoecker Motivation Huovinen and Kapusta

6. Hagedorn Resonances In the 1960’s Hagedorn found a fit for an exponentially growing mass spectrum Provides extra degrees of freedom near the critical temperature to “push” hadrons into equilibrium

7. Master Equations for the decay master equation master equation

8. Parameters Hagedorn States (mesonic, non-strange) M=2-7 GeV Branching Ratios –Gaussian distribution: Decay Widths Hammer ‘72 Future: microcanonical model Ranges from  i =250-1090 MeV

9. Estimates of Equilibration times: HS $ nπ Case 1: Pions are held in equilibrium Case 2: Hagedorn States are held in equilibrium

10. Estimates of Equilibration times: HS $ nπ Case 3: Both are out of equilibrium –Quasi-equilibrium- when the right hand side goes to zero before full equilibrium is reached. = 0 (Quasi-equilibrium)

11. Estimates of Equilibration times: HS $ nπ Quasi-equlibrium is reached on the time scales of Case 1 and Case 2 Because resonances decay into many pions a small deviation of the pions from equilibrium makes it more difficult for the resonances to reach equilibrium

12. Baryon anti-Baryon decay widths (Fuming Liu)

13. Estimates of Equilibration times: Case 1: Pions are held in equilibrium Reminder: HS appear only near T c!

14. Estimates of Equilibration times: Case 2: Hagedorn States are held in equilibrium Case 3: Pions and Hagedorn States are held in equilibrium

15. Estimates of Equilibration times: Case 4: All are out of equilibrium

16. Conclusions and Outlook Our preliminary results and time scale estimates indicate that baryon anti-baryon pairs can be born out of equilibrium. Fully understand time scales when all particles are out of equilibrium Include a Bjorken expansion to observe the fireball cooling over time (already done) Improve branching ratios by using a microcanonical model Include non-zero strangeness… in the baryon anti-baryon part