The Transverse Energy as a Barometer of a Saturated Plasma

The evolution of the gluon plasma produced with saturation initial conditions is calculated via Boltzmann transport theory for nuclear collisions at high energy. The saturation scale increases with A and √ s, and thus we find that the perturbative rescattering rate decreases relative to the initial longitudinal expansion rate of the plasma. The effective longitudinal pressure remains significantly below the lattice QCD pressure until the plasma cools to near the confinement scale. Therefore, the transverse energy per unit of rapidity and its dependence on beam energy provides a sensitive test of gluon saturation models: the fractional transverse energy loss due to final state interactions is smaller and exhibits a weaker energy dependence than if ideal (nondissipative) hydrodynamics applied throughout the evolution. In collisions of heavy ions at high energy a large number of gluons is liberated from the nuclear wave functions. The " plasma " is produced from copious minijet gluons at central rapidity, y ≃ 0, with transverse momentum p T > p 0. For large p 0 , the produced gluon plasma is dilute. As p 0 decreases, however, the density of gluons increases rapidly due to the increase of G(x, p 2 T) as x ≈ 2p T / √ s decreases. It has been conjectured [1,2] that below some transverse momentum scale p 0 ≤ p sat the phase-space density of produced gluons may saturate since gg → g recombination could limit further growth of the structure functions. Phenomenologically, this condition may arise when gluons (per unit rapidity and transverse area) become closely packed and fill the available nuclear interaction transverse area. The saturation scale p sat can thus be estimated from dN (p sat)/dy = p 2 sat R 2 A /β, where β ∼ 1. For β = 1 the solution reported in EKRT [3] was p sat ≈ 0.208A p sat and √ s are in units of GeV, and C 1 ≡ dE T /dy/p sat dN/dy ≈ 1.34A −0.007 √ s 0.021. Our focus is to investigate whether the final observed dE f T /dy can be used to test the predicted A and √ s dependence of the initial dE i T /dy. Different gluon saturation models based on classical Yang-Mills equations [2,4] suggest that the factor β may vary parametrically as β(p sat) = 4πα(p sat)N c /c(N 2 c − 1), where c ∼ 1 is a nonperturbative …