Hagedorn states and

Thermalization

DM2010, High Density Nuclear Matter, Stellenbosch, South Africa

(courtesyL. Ferroni)

Hadronization at the phase boundary…?

Hadronization – molecular dynamical simulation

C. Traxler et al., PRC59 1620 (1999)

… Hagedorn spectrum

Hadron Resonance Gas with Hagedorn States and comparison to lattice QCD close to

• Hagedorn spectrum:

• RBC collaboration:

J. Noronha-Hostler, J. Noronha, CG arXiv:0909.2908

The order and shape of QGP phase transitionI.Zakout, CG and J. Schaffner-Bielich, NPA 781 (2007) 150,

PRC78:034916 and arXiv: 1002.3119

)4(~),( ][)2( Bvmemcvm BHTm

density of states:4

1

)( B

Crossover transition in bag-like models

L. Ferroni and V. Koch, PRC79 (2009) 034905

][)(~)( BHTm

emcm density of states:

Strangeness production at SpS energies

J. Geiss

Production of Antihyperons:QGP signature…?

P. Koch, B. Müller, J. Rafelski

Production of Anti-Baryons

R.Rapp and E. Shuryak, Phys.Rev.Lett.86 (2001) 2980

C.Greiner and S.Leupold, J.Phys. G27 (2001) L95

Multimesonic channels

But

But:

SPS

Chemical Freeze-out and of QCD

Hadronic resonance gas

vs. lattice:

(P. Braun-Munzinger, J. Stachel, C. Wetterich, Phys.Lett.B596:61-69 (2004))

Chemical equilibration of baryon / anti-baryons:

Multimesonic channels:

Possible solution by Hagedorn states

C. Greiner, P. Koch, F. Liu, I. Shovkovy, H. Stöcker

J.Phys.G31 (2005)

Estimate for baryon/antibaryon production

(Micro)canonical decay of Hagedorn States(Fuming Liu)

Rate EquationsJ. Noronha-Hostler, CG, I. Shovkovy, PRL 100:252301, 2008; and arXiv:0909.2908

Decay Widths

Linear fit (PDG)

Baryon anti-baryon decay ((micro)canonical)

the average proton number is

Analogously for Kaons, Lambdas and Omegas (!)

for

Time Scale Estimate

Assuming and

where and

Rising Populations

• pions and HS held at equilibrium:

kaons

protons

Expanding fireball

Varying parameters has only small effect!

protons

Varying parameters has only small effect!

kaons

Lambdas

Omegas

M. Beitel

The strange sector of baryons/antibaryons

Importance of baryonic HS ?

Summary Potential Hagedorn States close to critical temperature:

can explain fast chemical equilibration by HS regeneration roughly:

roughly:

smaller shear viscosity of QCD matter at

Future: embedding into UrQMD

J. Noronha-Hostler, M. Beitel, CG,

I.Shovkovy arXiv:0909.2908, PRC in press

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many thanks, Jean

Particle Ratios as a Probe of the QCD Critical Temperature

J. Noronha-Hostler, H. Ahmad, J. Noronha, CG, arXiv:0906.3960

Hagedorn States provide a unique method to compare lattice results for Tc using thermal fits

Hagedorn states provide a lower chi^2 than thermal fits without Hagedorn states

Transport Coefficients of Hadronic Matter near

J. Noronha-Hostler, J. Noronha, CG, PRL103:172302 (2009)

While both η (due to the small MFP of HS) and s increase with increasing T, the entropy increases quicker close to Tc, which decreases η/s.

of a hadron gas including HS matches well with the lattice at

HRG

HS

39

Baryonfusion

Quark annihilation

Recombination

Three-particle interactions through parton rearrangement

Elliptic flow excitation function

UrQMD+ Recombination, Baryonfusion, Quark annihilation[H.Petersen et al. , arXiv:0805.0567v1 (2008)] [G.Gräf, diploma thesis, Frankfurt (2009)]

Lambda multiplicity

Same mechanism previously implemented in QGSM[Bleibel , Burau et al. , arXiv: nucl-th/0610021 (2007)][Bleibel , Burau et al. , arXiv: 0711.3366 (2008)]

- preliminary -

C.Greiner, AIP Conf. Proc. 644:337 (2003)

production at RHIC

I. Shovkovy, J. Kapusta (2003)

Thermal rates within chiral SU(3) description

Chemical population ofbaryons / anti-baryons:

P. Huovinen, J. Kapusta (2004)

Insufficient by a factor of 3 to 4

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