Distribution of nuclear matter and radiation in the fragmentation region

We study the fragmentation (far forward/backward) region of heavy-ion collisions by considering an at-rest nucleus which is struck by a relativistic sheet of colored glass. By means of a simple classical model, we calculate the subsequent evolution of baryons and the associated radiation. We confirm that the struck nucleus undergoes a compression and that the dynamics of the early times of the collision are best described by two separate fluids as the produced radiation's velocity distribution is very different to the velocity distribution of the matter in the struck nucleus.

Figure 1

Longitudinal kinematics of the process in (1+1)D, a string of stationary quarks that are struck by a relativistic ($v=1$) sheet of colored glass, causing the quarks to move off with varying momenta.

Figure 2

Distribution of matter and radiation (without formation time) when the shockwave has (a) traversed part of the stationary matter distribution and (b) moved beyond the initial matter distribution. Both figures use $N=$ 600 matter particles, $\frac{p_0}{m}=10$, and $F=$ 30.

Figure 3

$\frac{dN}{dz}$ as a function of time for (a) the matter distribution and (b) the radiation (with formation time) distribution. The red curves connect points on the (continuous set in $t$) $(z,t)$ curves that have ${}^z/_t=0.85$. The faint vertical lines are at $z$ values that correspond to $\frac{z}{t}=0.85$ for each $t$ curve. $R=14$ fm/c, $N=600$, $F=30$, $Q_s=1$ GeV.

Figure 4

The radiation profile at various $\tau$ without formation time (solid curves) and with formation time (dashed curves), described by appropriately transformed Eq. (3.11). Progressively lighter curves are at later times. $R=14$ fm/c, $N=600$, $F=30$.

Figure 5

The late-time distribution of the (a) number density and (b) transverse energy density for the matter, using $R=14$ fm, $N=600$ matter particles, and $\frac{p_0}{m}=10$.

Figure 6

The average $v$ and $y$ for the matter [solid blue curves, given by Eqs. (4.4) and (4.5)] and radiation (warm colored curves, see Appendix C2) particles at different proper times as a function of space-time rapidity. Here again $\frac{p_0}{m}=10$, and $F=$ 30. The solid warm colors are the radiation without formation time while the dashed lines include a formation time of ${\tau }_f^{-1}=Q_s=1$ GeV.

Figure 7

Comoving density profile of nuclear matter as the color-glass shockwave traverses the nucleus. The dotted line shows the initial density of matter before the sheet strikes the target nucleus.

Figure 8

The number density (left column) and the average momentum rapidity (right column) for the matter (solid blue curves), the radiation without formation time (solid orange curves), and the radiation with formation time (dashed orange curves), as a function of the space-time rapidity, for proper time progressing from top to bottom. The radiation curves in the left-hand column have been scaled down by multiplying by ${30}^{-1}$.

Figure 9

(a) The baryon chemical potential and (b) the temperature, as a function of the space-time rapidity for an ideal gas of quarks, antiquarks, and gluons, at various proper times.

Figure 10

(a), (b) Two gluons radiated from a quark at the origin, with velocities $v_1$ and $v_2$. (c) Two gluons radiated from a quark at position $(z_i,{}^{z_i}/_{vb})$.

Figure 11

Gluons radiated from different nuclei with different velocities arrive at the same point in $(z,t)$ and their velocities are to be averaged.

Figure 12

The start of the collision in three different frames. Boosting from the rest frame of one nucleus, to the center-of-mass frame, and on to the rest frame of the other nucleus.

Figure 13

The space-time trajectories of the left (dark) and right (light) edges of nuclei $A$ (green) and $B$ (red) in the rest frame of (a) nucleus $B$ and (b) the center of mass. Superimposed (blue) is the line of constant proper time corresponding to the end of the collision.