Initial Gluon Multiplicity in Heavy-Ion Collisions

Abstract

The initial gluon multiplicity per unit area per unit rapidity, $\mathrm{dN}/{L}^{2}/d\ensuremath{\eta}$, in high energy nuclear collisions, is equal to ${f}_{N}({g}^{2}\ensuremath{\mu}L)({g}^{2}\ensuremath{\mu}{)}^{2}/{g}^{2}$, with ${\ensuremath{\mu}}^{2}$ proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, we compute ${f}_{N}({g}^{2}\ensuremath{\mu}L)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.14\ifmmode\pm\else\textpm\fi{}0.01$ for a wide range in ${g}^{2}\ensuremath{\mu}L$. Extrapolating to SU(3), we predict $\mathrm{dN}/{L}^{2}/d\ensuremath{\eta}$ for values of ${g}^{2}\ensuremath{\mu}L$ relevant to the Relativistic Heavy Ion Collider and the Large Hadron Collider. We compute the initial gluon transverse momentum distribution, $\mathrm{dN}/{L}^{2}/{d}^{2}{k}_{\ensuremath{\perp}}$, and show it to be well behaved at low ${k}_{\ensuremath{\perp}}$.