Evolution of pressures and correlations in the Glasma produced in high energy nuclear collisions

We consider the SU(2) Glasma with gaussian fluctuations and study its evolution by means of classical Yang-Mills equations solved numerically on a lattice. Neglecting in this first study the longitudinal expansion we follow the evolution of the pressures of the system and compute the effect of the fluctuations in the early stage up to $t\approx 2$ fm/c, that is the time range in which the Glasma is relevant for high energy collisions. We measure the ratio of the longitudinal over the transverse pressure, $P_L/P_T$, and we find that unless the fluctuations carry a substantial amount of the energy density at the initial time, they do not change significantly the evolution of $P_L/P_T$ in the early stage, and that the system remains quite anisotropic. We also measure the longitudinal fields correlators both in the transverse plane and along the longitudinal direction: while at initial time fields appear to be anticorrelated in the transverse plane, this anticorrelation disappears in the very early stage and the correlation length in the transverse plane increases; on the other hand, we find that the longitudinal correlator decreases for a small longitudinal separation while being approximately constant for larger separation, which we interpret as a partial loss of longitudinal correlation induced by the dynamics.
Comment: 14 pages, 10 figures. To appear on Phys. Rev. D. In V2 the discussion about isotropization has been resized, while a broad discussion about the gauge invariant correlators along the longitudinal direction and the breaking of the Glasma color strings has been added. In V3 a mistake about the definition of the parallel transporter has been corrected