The initial energy density of gluons produced in very high energy nuclear collisions

TL;DR

This work estimates dE/deta for Au-Au collisions in the central region at RHIC and LHC byrapolating to SU(3), which shows that it varies rapidly for small g(2)&mgr;L but varies only by approximately 25%, for a wide range 35.36- 296.98 in g( 2) &mgr:L.

Abstract

In very high energy nuclear collisions, the initial energy of produced gluons per unit area per unit rapidity, $dE/L^2/dη$, is equal to $f(g^2μL) (g^2μ)^3/g^2$, where $μ^2$ is proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, we perform a non--perturbative numerical computation of the function $f(g^2μL)$. It decreases rapidly for small $g^2μL$ but varies only by $\sim 25$%, from $0.208\pm 0.004$ to $0.257\pm 0.005$, for a wide range 35.36--296.98 in $g^2μL$, including the range relevant for collisions at RHIC and LHC. Extrapolating to SU(3), we estimate the initial energy per unit rapidity for Au-Au collisions in the central region at RHIC and LHC.

Figures (3)

• Figure 1: $\varepsilon\tau/(g^2\mu)^3$ as a function of $g^2\mu\tau$ for $g^2\mu L = 5.66$ (diamonds), $35.36$ (pluses) and $296.98$ (squares). Both axes are in dimensionless units. Note that $\varepsilon\tau =0$ at $\tau=0$ for all $g^2\mu L$. The lines are exponential fits $\alpha + \beta\,e^{-\gamma\tau}$ including all points beyond the peak.
• Figure 2: $\varepsilon\tau/(g^2\mu)^3$ as a function of $g^2\mu a$. The points in the upper plot correspond to $g^2\mu L = 5.66$ (diamonds), $8.84$ (pluses), $17.68$ (squares), and $35.36$ (x's). The lower plot has $g^2\mu L = 70.7$ (diamonds), $106.06$ (pluses), $148.49$ (squares), $212.13$ (triangles) and $296.98$ (x's). Lines in the lower plot are fits of form $a-b\cdot x$. The $g^2\mu a$ ranges are different in the two halves. The points in the upper half are typically closer to the continuum limit.
• Figure 3: $\varepsilon\tau/(g^2\mu)^3$ extrapolated to the continuum limit: $f$ as a function of $g^2\mu L$. The error bars are smaller than the plotting symbols.