Initial Energy Density of Gluons Produced in Very-High-Energy Nuclear Collisions

Abstract

In very-high-energy nuclear collisions, the initial energy of produced gluons per unit area per unit rapidity, $(\mathrm{dE}/{L}^{2})/d\ensuremath{\eta}$, is equal to $f({g}^{2}\ensuremath{\mu}L)({g}^{2}\ensuremath{\mu}{)}^{3}/{g}^{2}$, where ${\ensuremath{\mu}}^{2}$ is proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, a nonperturbative computation of $f({g}^{2}\ensuremath{\mu}L)$ shows that it varies rapidly for small ${g}^{2}\ensuremath{\mu}L$ but varies only by $\ensuremath{\sim}25%$, from $0.208\ifmmode\pm\else\textpm\fi{}0.004$ to $0.257\ifmmode\pm\else\textpm\fi{}0.005$, for a wide range $35.36$-- $296.98$ in ${g}^{2}\ensuremath{\mu}L$. 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 $dE/d\ensuremath{\eta}$ for Au-Au collisions in the central region at RHIC and LHC.