Rapidity profile of the initial energy density in heavy-ion collisions

The rapidity dependence of the initial energy density in heavy-ion collisions is calculated from a threedimensional McLerran-Venugopalan model introduced by Lam and Mahlon. This model is infrared safe since global color neutrality is enforced. In this framework, the nuclei have nonzero thickness in the longitudinal direction. This leads to Bjorken-x-dependent unintegrated gluon distribution functions, which in turn result in a rapidity-dependent initial energy density after the collision. These unintegrated distribution functions are substituted in the initial energy density expression, which has been derived for the boost-invariant case. We argue that using three-dimensional (x-dependent) unintegrated distribution functions together with the boost-invariant energy formula is consistent given that the overlap of the two nuclei lasts less than the natural time scale for the evolution of the fields (1/Qs) after the collision. The initial energy density and its rapidity dependence are important initial conditions for the quark gluon plasma and its hydrodynamic evolution.