Large baryon densities achievable in high-energy heavy-ion collisions outside the central rapidity region

Nuclei are nearly transparent to each other when they collide at high energy, but the collisions do produce high-energy density matter in the central rapidity region where most experimental measurements are made. What happens to the receding nuclear fireballs? We calculate the energy loss of the nuclei using the color glass condensate model. We then use a simple space-time picture of the collision to calculate the baryon and energy densities of the receding fireballs. For central collisions of large nuclei at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider we find baryon densities more than ten times that of normal nuclear matter. These results provide initial conditions for subsequent hydrodynamic evolution and could test the equation of state at very high baryon densities.

Figure 1

Time evolution of the energy density for different values of the ultraviolet cutoff scale $Q$ given the hydrodynamic initial energy density ${\varepsilon }_{\mathrm{hydro}}({\tau }_0=0.6\mathrm{fm}/c)=30.0{\mathrm{GeV}/\mathrm{fm}}^3$.

Figure 2

The dependence of $F_{\mathcal{A}}\left(\tau \right)$ and $F_{\mathcal{B}}\left(\tau \right)$ on proper time for $Q=4.0\mathrm{GeV}$.

Figure 3

Rapidity of the central core of a gold projectile nucleus in the center-of-momentum frame for $\sqrt{s_{NN}}=200\mathrm{GeV}$ as a function of proper time. The result is insensitive to the choice of $Q$ in the physically relevant range.

Figure 4

Excitation energy per baryon in the central core of a gold projectile nucleus in the center-of-momentum frame for $\sqrt{s_{NN}}=200\mathrm{GeV}$ as a function of proper time. The result is mildly sensitive to the choice of $Q$ in the physically relevant range.

Figure 5

Momentum space rapidity $y_{\mathrm{P}}$ and coordinate space pseudorapidity ${\eta }_{\mathrm{P}}$ as functions of proper time for the central core of a gold projectile nucleus in the center-of-momentum frame for $\sqrt{s_{NN}}=200\mathrm{GeV}$. The ultraviolet cutoff is $Q=4.0\mathrm{GeV}$. The condition $y_{\mathrm{P}}<{\eta }_{\mathrm{P}}$ is maintained in the physically relevant proper time range.

Figure 6

Net-baryon rapidity distribution at $\tau =0.6\mathrm{fm}/c$ in the center-of-momentum frame after the collision for Au+Au at $\sqrt{s_{NN}}=200\mathrm{GeV}$. The initial beam rapidities are $y_0=\pm 5.36$.

Figure 7

The energy and baryon densities at $\tau =0.6\mathrm{fm}/c$ as functions of the transverse distance for central collisions of Au nuclei at $\sqrt{s_{NN}}=200\mathrm{GeV}$.

Figure 8

Contour plot of the proper baryon density for central collisions of Au nuclei at $\sqrt{s_{NN}}=200\mathrm{GeV}$. The numbers are in units of baryons per ${\mathrm{fm}}^3$. The horizontal axis measures the distance along the beam direction in the local rest frame. Care must be taken when interpreting this plot since the rapidity of the matter and therefore the frame of reference depend on $r_{\perp }$.

Figure 9

Schematic picture of the tube for the central core of a nucleus in its local rest frame.

Figure 10

Contour plot of the proper baryon density for central collisions of gold nuclei at $\sqrt{s_{NN}}=200\mathrm{GeV}$. The numbers are in units of baryons per ${\mathrm{fm}}^3$. The horizontal axis is the space-time pseudorapidity in the center-of-momentum frame.

Figure 11

The temperature and baryon chemical potential in the fragmentation region as a function of momentum space rapidity at $\tau =0.6\mathrm{fm}/c$. Values are calculated for $z^{\prime }=0$ as defined in Eq. (17). Only matter with energy densities larger than $1.0{\mathrm{GeV}/\mathrm{fm}}^3$ have been displayed.

Figure 12

Ratio of baryon chemical potential to temperature as a function of momentum space rapidity at $\tau =0.6\mathrm{fm}/c$.

Figure 13

The initial temperatures and baryon chemical potentials in the fragmentation regions at $\tau =0.6\mathrm{fm}/c$ with energy density larger than $1.0{\mathrm{GeV}/\mathrm{fm}}^3$. Values are calculated for $z^{\prime }=0$ as defined in Eq. (17).

Figure 14

Phase trajectories of adiabatic expansion at three different rapidities and entropy per baryon ratios.

Figure 15

Entropy per baryon as a function of the momentum space rapidity. A rapidity scan may help locate the critical point.

Figure 16

Baryon density achievable in the central core as a function of $r_{\perp }$ for three different collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$.

Figure 17

Energy density achievable in the central core as a function of $r_{\perp }$ for three different collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$.

Figure 18

Baryon chemical potential achievable in the central core as a function of $r_{\perp }$ for three different collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. Only regions with energy density larger than $1.0{\mathrm{GeV}/\mathrm{fm}}^3$ have been displayed.

Figure 19

Temperature achievable in the central core as a function of $r_{\perp }$ for three different collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. Only regions with energy density larger than $1.0{\mathrm{GeV}/\mathrm{fm}}^3$ have been displayed.

Figure 20

Contour plot of the proper baryon density for central collisions of Cu nuclei at $\sqrt{s_{NN}}=200\mathrm{GeV}$. The numbers are in units of baryons per ${\mathrm{fm}}^3$. The horizontal axis is the space-time pseudorapidity in the center-of-momentum frame.

Figure 21

Contour plot of the proper baryon density for central tip-tip collisions of U nuclei at $\sqrt{s_{NN}}=200\mathrm{GeV}$. The numbers are in units of baryons per ${\mathrm{fm}}^3$. The horizontal axis is the space-time pseudorapidity in the center-of-momentum frame.

Figure 22

Net baryon rapidity distribution in Cu+Au central collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. The initial beam rapidities are $\pm 5.36$. Peripheral regions of the Au nucleus do not participate in the collision.

Figure 23

Contour plot of the proper baryon density for central collisions of gold nuclei at $\sqrt{s_{NN}}=62.4\mathrm{GeV}$. The numbers are in units of baryons per ${\mathrm{fm}}^3$. The horizontal axis is the space-time pseudorapidity in the center-of-momentum frame.

Figure 24

Contour plot of the proper baryon density for central collisions of lead nuclei at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The numbers are in units of baryons per ${\mathrm{fm}}^3$. The horizontal axis is the space-time pseudorapidity in the center-of-momentum frame.

Figure 25

Adiabatic phase trajectories for the central cores of the fireball in Au+Au collisions at $\sqrt{s_{NN}}=62.4$ and 200 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ and 5.02 TeV.

Figure 26

Schematic picture of the transverse overlap region for noncentral collisions of two nuclei.

Figure 27

Contour plot of the proper baryon density for the gold projectile fireball in the transverse plane for the slice $z^{\prime }=0$. The collision is Au+Au at $\sqrt{s_{NN}}=200\mathrm{GeV}$ with impact parameter $b=0\mathrm{fm}$. The numbers are in units of baryons per ${\mathrm{fm}}^3$. The position $x=0,y=0$ corresponds to the center of the fireball.

Figure 28

Contour plot of the proper baryon density for the gold projectile fireball in the transverse plane for the slice $z^{\prime }=0$. The collision is Au+Au at $\sqrt{s_{NN}}=200\mathrm{GeV}$ with impact parameter $b=2.3\mathrm{fm}$. The numbers are in units of baryons per ${\mathrm{fm}}^3$. The highest density occurs at $x=0,y=-b$.

Figure 29

Contour plot of the proper baryon density for Au+Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ with impact parameter $b=7\mathrm{fm}$ in the $x\text{−}\eta$ plane for $y=0$. The numbers are in units of baryons per ${\mathrm{fm}}^3$.