Quark production, Bose–Einstein condensates and thermalization of the quark–gluon plasma

In this paper, we study the thermalization of gluons and NfNf flavors of massless quarks and antiquarks in a spatially homogeneous system. First, two coupled transport equations for gluons and quarks (and antiquarks) are derived within the diffusion approximation of the Boltzmann equation, with only 2↔22↔2 processes included in the collision term. Then, these transport equations are solved numerically in order to study the thermalization of the quark–gluon plasma. At initial time, we assume that only gluons are present and we choose the gluon distribution of a form inspired by the color glass picture, namely f=f0θ(1−pQs) with QsQs the saturation momentum and f0f0 a constant. The subsequent evolution of the system may, or may not, lead to the formation of a (transient) Bose condensate (BEC) of gluons, depending on the value of f0f0. In fact, we observe, depending on the value of f0f0, three different patterns: (a) thermalization without BEC for f0≤f0tf0≤f0t, (b) thermalization with transient BEC for f0tf0cf0≳1>f0c, the onset of BEC occurs at a finite time tc∼1(αsf0)21Qs. We also find that quark production slows down the thermalization process: the equilibration time for Nf=3Nf=3 is typically about 5 to 6 times longer than that for Nf=0Nf=0 at the same QsQs and f0f0.