Inflation of Fireballs, the Gluon Wind and the Homogeneity of the HBT Radii at RHIC

Abstract

We solve analytically the ellipsoidally expanding fireball hydrodynamics with source terms in the momentum and the energy equations, using the non-relativistic approximation. We find that energy transport from high pt jets of gluons to the medium leads to a transient, exponential inflation of the fireballs created in high energy heavy ion collisions. In this transient, inflatory period, the slopes of the single particle spectra increase, while the HBT radius parameters decrease exponentially with time. This effect is shown to be similar to the development of the homogeneity of our Universe due to an inflatory period. Independently of the initial conditions, and the exact value of the freeze-out time and temperature, the meausurables (single particle spectra, the correlation functions, the slope parameters, elliptic flow, HBT radii and cross terms) become time independent during the late, non-inflatory stages of the expansion, and they satisfy new kind of scaling laws. If the expansion starts with a transient inflation caused by the gluon wind, it leads naturally to large transverse flows and the simultaneous equality and scaling behaviour of the HBT radius parameters, R_{side} \approx R_{out} \approx R_{long} \approx t_f \sqrt{T_f/m}. With certain relativistic corrections, the scaling limit is \tau_f \sqrt{T_f/m_t}, where m_t is the mean transverse mass of the pair.