Chemical Equilibration at the Hagedorn Temperature

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 - chemical eq. time • 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… Can’t explain apparent equilibrium

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

5. Motivation • 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 t=1-3 fm/c. • Greiner, Koch-Steinheimer, Liu, Shovkovy, and Stoecker 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

8. Parameters • Hagedorn States (mesonic, non-strange) M=2-7 GeV • Branching Ratios • Gaussian distribution: • Decay Widths Hammer ‘72 Future: microcanonical model Ranges from Gi=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 Tc!

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