The initial gluon multiplicity in heavy ion collisions

TL;DR

The initial gluon multiplicity per unit area per unit rapidity, dN/L2/d eta, in high energy nuclear collisions, is equal to f(N)(g( 2)mu L) (g(2)mu)(2)/ g(2), with mu(2).

Abstract

The initial gluon multiplicity per unit area per unit rapidity, dN/L^2/dη, in high energy nuclear collisions, is equal to f_N (g^2μL) (g^2μ)^2/g^2, with μ^2 proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, we compute f_N (g^2μL)=0.14\pm 0.01 for a wide range in g^2μL. Extrapolating to SU(3), we predict dN/L^2/dηfor values of g^2μL in the range relevant to the Relativistic Heavy Ion Collider and the Large Hadron Collider. We compute the initial gluon transverse momentum distribution, dN/L^2/d^2 k_\perp, and show it to be well behaved at low k_\perp.

Figures (3)

• Figure 1: a: $n(k_\perp)\equiv dN/L^2/d^2 k_\perp$ as a function of the gluon momentum $k$ for $g^2\mu L=35.35$ and the values 0.138 (squares), 0.276 (plusses), and 0.552 (diamonds) of $g^2\mu a$. The gluon momentum $k$ is in units of $g^2\mu$. The solid line is a fit of the lattice analog of the perturbative expression Eq. (\ref{['LPT']}) to the high-momentum part of the $g^2\mu a=0.138$ data. b: $n(k_\perp)$ at soft momenta at $g^2\mu a=0.29$ for the values 148.5 (plusses) and 297 (diamonds) of $g^2\mu L$.
• Figure 2: The function $f_N$, defined in Eq. (\ref{['BJN']}) as a function of $g^2\mu L$, obtained by the relaxation method (plusses) and by the Coulomb gauge fixing (diamonds). The values of $g^2\mu a$ are 0.276 for $g^2\mu L=35.35$ and $g^2\mu L=70.8$; 0.29 for $g^2\mu L=148.5$ and $g^2\mu L=297$; and 0.414 for $g^2\mu L=212$.
• Figure 3: Gluon dispersion relation $\omega(k_\perp)$ obtained from Eq. (\ref{['nfree']}), for the values 70.8 (diamonds), 148.5 (plusses), and 297 (squares), with the values of $g^2\mu a$ as in Figure \ref{['nvsmul']}.