Nonequilibrium quark production in the expanding QCD plasma

We perform real-time lattice simulations of nonequilibrium quark production in the longitudinally expanding QCD plasma. Starting from a highly occupied gluonic state with vacuum quark sector, we extract the time evolution of quark and gluon number densities per unit transverse area and rapidity. The total quark number shows after an initial rapid increase an almost linear growth with time. Remarkably, this growth rate appears to be consistent with a simple kinetic theory estimate involving only two-to-two scattering processes in small-angle approximation. This extends previous findings about the role of two-to-two scatterings for purely gluonic dynamics in accordance with the early stages of the bottom-up thermalization scenario.

Figure 1

A schematic plot of the lattice momentum (29) as a function of the integer $k$. We call the modes in $-k_{\max }\le k\le k_{\max }$ physical modes, which are denoted by black filled circles, while the modes denoted by open circles correspond to doublers. The continuum dispersion is shown by a gray solid line.

Figure 2

Time evolution of the gluon transverse momentum distribution evaluated at $p_z=0$ for different times $Q_s\tau$.

Figure 3

Time evolution of the quark number density. The inset shows the early-time behavior. The lattice result is compared to the kinetic theory estimate based on $2\leftrightarrow 2$ scatterings.

Figure 4

Time evolution of the quark distribution function at earlier times $Q_s\tau \le 110$. Left: The transverse momentum distribution at $p_z=0$. Right: The longitudinal momentum distribution at $p_{\perp }=0$.

Figure 5

The second moment of the quark transverse momentum distribution at earlier times $Q_s\tau \le 110$ (left) and at later times $Q_s\tau \ge 110$ (right). (Here we used a smaller transverse lattice spacing $Q_s{a}_{\perp }=0.417$ in order to have better resolution in the high momentum region.)

Figure 6

Time evolution of the quark distribution function at later times $Q_s\tau \ge 110$. Left: The transverse momentum distribution at $p_z=0$. Right: The longitudinal momentum distribution at $p_{\perp }=0$.

Figure 7

Time evolution of the Debye mass scale. Three different transverse system sizes are compared. The smallest nonzero transverse momenta are indicated by gray horizontal lines for each system size. The expected temporal power law ${\tau }^{-1/2}$ is also indicated by a gray dashed line. These results are obtained by pure Yang-Mills simulations with the lattice parameters $Q_s{a}_{\perp }=0.625$, $N_{\eta }=256$, and $a_{\eta }=1.95\times {10}^{-3}$.

Figure 8

Time evolution of the number densities of gluons and quarks. The gluon number is multiplied by $g^2={10}^{-4}$. The kinetic theory estimates are indicated by gray dashed lines.

Figure 9

Quark number density for $n_0=10$. The kinetic estimate (46) well fits the lattice result. Without the Pauli blocking term, the production rate is overestimated.

Figure 10

Quark transverse momentum distribution for different quark masses at the time $Q_s\tau =250$.

Figure 11

Time evolution of the quark number density for different quark masses.

Figure 12

The integrated transverse spectrum for different quark masses at $Q_s\tau =110$ as a function of the transverse momentum (left) and of the transverse mass (right).

Figure 13

The integrated transverse spectrum for different quark masses at $Q_s\tau =250$ as a function of the transverse momentum (left) and of the transverse mass (right).

Figure 14

Quark distribution functions at $Q_s\tau =200$ for $g^2{N}_f=0.5$ as compared to $g^2{N}_f={10}^{-4}$. Left: Transverse momentum dependence at $p_z=0$. Right: Longitudinal momentum dependence at $p_{\perp }=0$.

Figure 15

Quark number density per flavor for $g^2{N}_f=0.5$ as compared to $g^2{N}_f={10}^{-4}$.

Figure 16

Comparison of the gluon number density and the quark number density for $g^2{N}_f=0.5$. Both of the number densities are multiplied by $g^2={10}^{-4}$. The kinetic theory estimates based on Eq. (46) are indicated by gray dashed lines.

Figure 17

Comparison of the three methods for the transverse distribution function at $Q_s\tau =250$.

Figure 18

Comparison of the three methods for the longitudinal distribution function at $Q_s\tau =150$ and $Q_s\tau =250$.

Figure 19

Comparison of the transverse distributions for physical modes and doubler modes computed by three methods.

Figure 20

Comparison of the longitudinal distributions for physical modes and doubler modes computed by three methods.

Figure 21

Transverse momentum distributions at $Q_s\tau =200$. Three different transverse lattice parameters are compared.

Figure 22

Longitudinal momentum distributions at $Q_s\tau =200$. Three different longitudinal lattice parameters are compared.

Figure 23

Time evolution of the quark number density for different lattice parameters. Left: Dependence on transverse lattice parameters. Right: Dependence on the longitudinal lattice parameters.