Oscillations of the quark-gluon plasma

from oscillations to fast thermalization

dedicated to Professor Andrzej Białas on the occasion of His 70-th birthday

or

Wojciech Florkowski

1. Development of the color-flux-tube model by Białas and Czyż

development by Białas and Czyż in the series of papers published in the 1980s

color-flux-tube model: Casher, Neuberger, Nussinov, PR D20 (1979) 179

- A. Białas and W. Czyż, Boost-invariant Boltzmann-Vlasov equations for relativistic quark-antiquark plasma, Phys. Rev. D30 (1984) 2371

- A. Białas and W. Czyż, Chromoelectric flux tubes and the transverse momentum distribution in high-energy nucleus-nucleus collisions, Phys. Rev. D31 (1985) 198

- A. Białas and W. Czyż, Oscillations of relativistic, boost-invariant quark-antiquark plama, Z. Phys. C28 (1985) 255

- A. Białas and W. Czyż, Conversion of color field into q anti-q matter in the central region of high-energy heavy-ion collisions, Nucl. Phys. B267 (1986) 242

- A. Białas and W. Czyż, Production and collective motion of q anti-q plasma in heavy-ion collisions, Acta Phys. Pol. B17 (1986) 635

- and more others ...

- chromoelectric fields stronger than in „elementary” e+ e- annihilations Biro, Nielsen, Knoll, Nucl. Phys. B245 (1984) 449 (increased multiplicity, increased production of strange particles)

- oscillations of the quark-antiquark plasma

- fast (t0<1 fm/c) production of dense matter

k number of color charges q which span the initial field, g coupling constant

A. Białas, W. Czyż, A. Dyrek, and WF, Oscillations of quark-gluon plasma generated in strong color fields, Nucl. Phys. B296 (1988) 611

time dependence of the chromoelectric field (LHS) and the energy density of quarks and gluons (RHS) for various values of the parameter k

time dependence of the average transverse (LHS) and longitudinal (RHS) momentum of quarks and gluons for various values of the parameter k

[8 gluon fields are separated into 2 „neutral fields” (chromoelectric field E3 , E8) and 6 „charged gluons” (treated as particles together with quarks)]

A. Dyrek and WF, Production of heavy quarks in strong chromoelectric fields, Nuovo Cim. A102 (1989) 1013

the ratio of strange quarks to up and down quarks

dduu

ssR

1

quantitatively similar results to those obtained by P. Koch, B. Muller, and J. Rafelski, Phys. Rep. 142 (1986) 167

2. Early-thermalization in relativistic heavy-ioncollisions

A. Białas, Fluctuations of string tension and transverse-mass distribution Phys. Lett. B31 (1999) 301

gaussian fluctuations of the string tension can account for the „thermal” distribution of transverse mass of particles created in decay of a color string

1) the data collected at RHIC suggest that matter is well thermalized and exhibits collective behavior (bound states above TC, Shuryak; plasma instabilities, Mrówczyński; Hawking-Unruh effect, Kharzeev)

2) already in more elementary collisions we observe thermal features, Boltzmann distributions in transverse momentum, Hagedorn, 1960s

22

2

exp ,exp~ pmmT

m

pd

dN

the measured transverse-momentum spectra have thermal (exponential) shape, Hagedorn, 1960s

string models of hadronic collisions use the Schwinger formula

2

2

2

Schwinger exp~

m

pd

dN

Białas: appropriate averaging over κ may produce an exponential function

2

,exp~exp2

2

2

TT

mmPd

fluctuations may appear due to stochastic nature of the QCD vacuum (H.G. Dosch, Yu. A. Simonov)

my personal follow-up of this idea, WF, Schwinger tunneling and thermal character of hadron spectra, Acta Phys. Pol. B35 (2004) 799

quark spectra in the color-flux tube model are exponential due to the dynamic oscillations of the chromoelectric field E

T

m

tE

mtPdt exp~

)(exp

2

2'

oscillations in varying chromoelectric fields may explain the origin ofthe thermal spectra in heavy-ions but this effect is not capable of describing thermal features observed in elementary processes

it is conceivable, however, that the effect of the stochastic vacuumplays an additional role in heavy-ion collisions leading to even morepronounced thermalization effects

Instead of Conclusions ...

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