Initial Conditions from Color Glass Condensate



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Nuclei at very high energy, characterized by a saturation scale, can be described by an e?ective theory of Quantum ChromoDynamics (QCD) called Color Glass Condensates. The earliest phase of the collision of two nuclei is modeled as the collision of two sheets of color glass. The classical ?eld resulting from the collision then decays and equilibrates to a plasma of quarks and gluons. Using a recursive solution of the Yang-Mills equations, we calculate analytic expressions for the gluon ?eld created in ultra-relativistic heavy ion collisions at small times ?. We have worked out explicit solutions for the ?elds and the energy momentum tensor up to 4^th order in an expansion in ? . We generalize the existing calculations to go beyond the limit of large homogenous nuclei. This allows us to calculate radial and elliptic ?ow of gluon ?elds. The resulting transverse and longitudinal structure of the Poynting vector ?eld has a rich phenomenology. Besides the well known radial and elliptic ?ow in transverse direction, classical quantum chromodynamics predicts a rapidity-odd transverse ?ow that tilts the ?reball for non-central collisions, and it implies a characteristic ?ow pattern for collisions of non-symmetric systems A + B. The rapidity-odd transverse ?ow translates into a directed particle ?ow v_1 which has been observed at RHIC and LHC. The global ?ow ?elds in heavy ion collisions could be a powerful check for the validity of classical Yang-Mill dynamics in high energy collisions. We also propose a procedure to calculate the energy momentum tensor of gluon ?elds on an event-by-event basis. The matching of the initial ?eld energy momentum tensor to viscous hydrodynamic initial conditions is discussed and some preliminary results of a subsequent hydrodynamic evolution are shown. Our results can provide event-by-event initial conditions for hydrodynamic simulations of nuclear collisions that include initial flow and initial shear stress.