Chemical Equilibration at the Hagedorn Temperature

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Chemical Equilibration at the Hagedorn Temperature

• Jaki Noronha-Hostler
• Collaborators C. Greiner and I. Shovkovy

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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

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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
Cant explain apparent equilibrium
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Production of anti-baryons

• production
• production

• annihilation rate

chemical equilibration time

• Rapp and Shuryak, PRL 86, 2980 (2001)
• Greiner and Leupold, J. Phys. G 27, L95 (2001)

detailed balance
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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 t1-3 fm/c.
• Greiner, Koch-Steinheimer, Liu, Shovkovy, and
  Stoecker

Huovinen and Kapusta
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Hagedorn Resonances

• In the 1960s Hagedorn found a fit for an
  exponentially growing mass spectrum
• Provides extra degrees of freedom near the
  critical temperature to push hadrons into
  equilibrium

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Master Equations for the decay

• master equation

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Parameters

• Hagedorn States (mesonic, non-strange) M2-7 GeV
• Branching Ratios
• Gaussian distribution
• Decay Widths

Hammer 72
Future microcanonical model
Ranges from Gi250-1090 MeV
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Estimates of Equilibration times HS np

• Case 1 Pions are held in equilibrium
• Case 2 Hagedorn States are held in equilibrium

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Estimates of Equilibration times HS np

• 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)
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Estimates of Equilibration times HS np

• 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

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Baryon anti-Baryon decay widths
(Fuming Liu)
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Estimates of Equilibration times

• Case 1 Pions are held in equilibrium

Reminder HS appear only near Tc!
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Estimates of Equilibration times

• Case 2 Hagedorn States are held in equilibrium
• Case 3 Pions and Hagedorn States are held in
  equilibrium

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Estimates of Equilibration times

• Case 4 All are out of equilibrium

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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