From Color Fields to Quark Gluon Plasma

1. From Color Fields to Quark Gluon Plasma Rainer Fries University of Minnesota in Collaboration with J. I. Kapusta, Y. Li (Minnesota); S. A. Bass, B. Müller (Duke) Quark Matter 2005 Budapest, Hungary August 5, 2005

2. Introduction • The mysterious first fm/c • Many good ideas are around • Color strings, color ropes • Hard scatterings, minijets (parton cascades) • Color glass condensate Initial stage < 1 fm/c Equilibration, hydrodynamics From Color Fields to Quark Gluon Plasma

3. Introduction • The mysterious first fm/c • Many good ideas are around • Color strings, color ropes • Hard scatterings, minijets (parton cascades) • Color glass condensate • How to get reliable predictions at  0? • Realistic initial conditions for hydrodynamics • How much energy (in the soft sector) is deposited between the nuclei, and where is it? PCM ? Hydro cl QCD From Color Fields to Quark Gluon Plasma

4. Outline of the Model • pQCD description of hard parton scattering (for Q > Q0) • (Event-by-event) simulation by a Parton Cascade Model • Hydro evolution of the plasma from initial conditions • , p, v, (nB) to be determined as functions of , x at  = 0 • Equilibrated plasma from decay of color fields Tf • Energy momentum conservation  constrain Tpl through Tf • Approximate Tf through classical gluon field F • Calculate F as near field (small  expansion) of charge distributions in the collision • Primordial color fluctuations in the nuclei • Color ionization through hard processes From Color Fields to Quark Gluon Plasma

5. Outline of the Model • pQCD description of hard parton scattering (for Q > Q0) • Hydro evolution of the plasma from initial conditions • Equilibrated plasma from decay of color fields Tf • Approximate Tf through classical gluon field F • Calculate F as near field (small  expansion) of charge distributions in the collision Hydro Minijets Color Charges J Class. Gluon Field F Field Tensor Tf Plasma Tensor Tpl From Color Fields to Quark Gluon Plasma

6. - - - + + + ’2 ’2 ’1 ’1 2 1 1 1 1 2 2 2 Color Charges and Currents • Charges propagating along the light cone, Lorentz contracted to very thin sheets ( currents J) • Local charge fluctuations appear frozen (fluc >> 0) • Charge transfer by hard processes is instantaneous (hard << 0) • Solve classical EOM for gluon field I II III Charge fluctuations ~ McLerran-Venugopalan model (boost invariant) Charge fluctuations + charge transfer @ t=0 (boost invariant) Charge fluctuations + charge transfer with jets (not boost invariant) From Color Fields to Quark Gluon Plasma

7. Transverse Structure • Solve expansion around  = 0, simple transverse structure • Effective transverse size 1/ of charges,  ~ Q0 • During time , a charge feels only those charges with transverse distance < c • Discretize charge distribution, using grid of size a ~ 1/ • Associate effective classical charge with ensemble of partons in each bin • Factorize SU(3) and x dependence • Solve EOM for two such charges colliding in opposite bins a Bin in nucleus 2 Bin in nucleus 1 Tube with field From Color Fields to Quark Gluon Plasma

8. The Gluon Field • Boost invariant case II: • Ansatz in the forward light cone • Boundary conditions at  = 0 Using the notation of Kovner, McLerran & Weigert; axial gauge Field of single nucleus Transfer charge Additional term: bremsstrahlung from charge transfer (hard process) =0 =0 From Color Fields to Quark Gluon Plasma

9. The Gluon Field II • Solved EOM up to order 3 • Small time behavior of the field: • Higher orders in g: • Fixed relation between direct and bremsstrahlung gluons • Superposition of the fields F in neighboring tubes • Reasonable estimate of the gluon field for 0 < 1/Q0 • Calculate energy momentum tensor Tf: ~ From Color Fields to Quark Gluon Plasma

10. Back to Charges • Classical color vector T corresponding to n partons • Corresponds to random walk in SU(3) space (Jeon & Venugopalan) • Probability distribution • Tf linear combination of color singlets dk2 • Expectation values for ni color charges • E.g. (Number of effective color degrees of freedom) From Color Fields to Quark Gluon Plasma

11. Space-Time Picture • Coarse graining/averaging over transverse bins at  = 0 • Minimize dependence on shape of charge distribution in one bin • Remaining structures of size ~ a • Force acting on the light cone charges • Assume realistic trajectory of charges (Kapusta & Mishustin) • Deceleration of the nuclei • Obtain positions * and rapidities y* of the baryons at  = 0 • Finally: decay into plasma at  = 0 From Color Fields to Quark Gluon Plasma

12. Coupling to the Plasma Phase • General structure of Tf (boost invariant case) • Use energy-momentum conservation to match to plasma phase • Instantaneous matching From Color Fields to Quark Gluon Plasma

13. The Plasma Phase • Matching gives 4 equations for 5 variables • Complete with equation of state • E.g. for p = /3: Bjorken: y = , but cut off at * From Color Fields to Quark Gluon Plasma

14. Preview • The field exhibits flow B 0 • from gradient of charges in transverse direction From Color Fields to Quark Gluon Plasma

15. More to Come • This can lead to radial flow in the early plasma phase… • … and to elliptic flow b = 8 fm From Color Fields to Quark Gluon Plasma

16. Summary • Model for the initial state of high energy nuclear collisions • Based on hard processes  soft gluon fields • Classical gluon field from direct production and bremsstrahlung • Expansion for small times  • Deceleration of charges • Matching to plasma using energy & momentum conservation • Outlook: • Apply hydro! • Realistic, non-boost invariant implementation of hard processes • Interface with PCM • Further connection with PCM: jets in strong color fields? From Color Fields to Quark Gluon Plasma