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, $\left(\mathrm{dE}/L^2\right)/d\eta$, is equal to $f\left(g^2\mu L\right)(g^2\mu {)}^3/g^2$, where ${\mu }^2$ is proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, a nonperturbative computation of $f\left(g^2\mu L\right)$ shows that it varies 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 $g^2\mu L$. This includes the range relevant for collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Extrapolating to SU(3), we estimate $dE/d\eta$ for Au-Au collisions in the central region at RHIC and LHC.