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

Abstract In this paper, we study the thermalization of gluons and N f 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 ↔ 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 = f 0 θ ( 1 − p Q s ) with Q s the saturation momentum and f 0 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 f 0 . In fact, we observe, depending on the value of f 0 , three different patterns: (a) thermalization without BEC for f 0 ≤ f 0 t , (b) thermalization with transient BEC for f 0 t f 0 ≤ f 0 c , and (c) thermalization with BEC for f 0 c f 0 . The values of f 0 t and f 0 c depend on N f . When f 0 ≳ 1 > f 0 c , the onset of BEC occurs at a finite time t c ∼ 1 ( α s f 0 ) 2 1 Q s . We also find that quark production slows down the thermalization process: the equilibration time for N f = 3 is typically about 5 to 6 times longer than that for N f = 0 at the same Q s and f 0 .