Abstract
Using a recursive solution of the Yang-Mills equation, we calculate analytic expressions for the gluon fields created in ultra-relativistic heavy ion collisions at small times τ. We have worked out explicit solutions for the fields and the energy momentum tensor up to 4th order in an expansion in τ. We generalize the McLerran-Venugopalan model to allow for a systematic treatment of averaged charge densities μ2 that vary as a function of transverse coordinates. This allows us to calculate radial, elliptic and directed flow of gluon fields. Our results can serve as initial conditions for hydrodynamic simulations of nuclear collisions that include initial flow.
Highlights
Nuclear collisions at high energies at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) can create and probe novel forms of QCD matter
A thermalized Quark Gluon Plasma (QGP) is created in nuclear collisions at RHIC and LHC after a time of about 1 fm/c
The natural limit of a nucleus at very high energy is characterized by a saturated gluon density in which the gluon field can be described by a quasi-classical field [3, 4]
Summary
Nuclear collisions at high energies at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) can create and probe novel forms of QCD matter. Large uncertainties in the hydrodynamic evolution come from the incomplete understanding of the initial conditions, i.e. the evolution of the nuclear collision prior to 1 fm/c. This is where another new phase of QCD, Color Glass Condensates (CGC) plays an important part. Sources have large Bjorken-x while the small-x gluons are treated through the classical field F μν. They are related by the Yang-Mills equation [Dμ, F μν ] = Jν. The energy momentum tensor of the gluon field after the collision can be calculated. One can check that this energy momentum tensor is boost invariant owing to the original boost-invariant setup of the colliding nuclei
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