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

In very high energy nuclear collisions, the initial energy of produced gluons per unit area per unit rapidity, $dE/L^2/d\eta$, is equal to $f(g^2\mu L) (g^2\mu)^3/g^2$, where $\mu^2$ 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 $f(g^2\mu L)$. It decreases rapidly for small $g^2\mu L$ 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 $g^2\mu L$, 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.