Modified Kolmogorov wave turbulence in QCD matched onto “Bottom-up” thermalization

Abstract

We investigate modification of Kolmogorov wave turbulence in QCD calculating gluon spectra as functions of time in the presence of a low energy source which feeds in energy density in the infrared region at a time-dependent rate. Then considering the picture of saturation constraints as has been constructed in the “bottom-up” thermalization approach we revisit that picture for RHIC center-mass energy, W = 130 GeV , and also extend it to LHC center-mass energy, W = 5500 GeV , thus for two cases having an opportunity to calculate the equilibration time, τ eq | therm , of the gluon system produced in a central heavy ion collision at mid-rapidity region. Thereby, at RHIC and LHC energies we can match the equilibration time, obtained from the late stage gluon spectrum of the modified Kolmogorov wave turbulence, onto that of the “bottom-up” thermalization and other evolutional approaches as well. In addition, from the revised “bottom-up” approach we find the gluon liberation coefficient to be on the average, ε ≃ 0.81 – 1.06 at RHIC and ε ≃ 0.50 – 0.56 at LHC. We also present other phenomenological estimates of τ therm which, at QCD realistic couplings, yield 0.45 – 0.65 fm ⩽ τ therm ⩽ 0.97 – 2.72 fm at RHIC and 0.31 – 0.40 fm ⩽ τ therm ⩽ 0.86 – 2.04 fm at LHC. We show that the second upper-bounds of τ therm in both cases are due to the late stage gluon spectrum of the original Kolmogorov wave turbulence in QCD, previously deduced with a low energy source which feeds in energy density at a constant rate. On the other hand, the lower-bounds and first upper-bounds of τ therm are due to the late stage gluon spectrum of the modified QCD wave turbulence, deduced here at the specific time-dependent rate. In the latter case, at certain conditions, taking also into account both very small and realistic couplings we give estimates: 0.65 fm ⩽ τ therm ⩽ 1.29 fm at RHIC and 0.52 fm ⩽ τ therm ⩽ 1.16 fm at LHC, as well as at realistic couplings we find 0.53 < τ therm < 0.7 fm at RHIC and 0.41 < τ therm < 0.65 fm at LHC.