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Energy and Number Density Created at RHIC

Energy and Number Density Created at RHIC. What’s in the PHENIX White Paper, and a little bit more. Paul Stankus, ORNL PHENIX Focus, Apr 11 06. Energy Density, Take 1. Just divide energy by volume, in some frame. 2R/ g ~ .13 fm. 2R ~ 14 fm. Boosted Frame

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Energy and Number Density Created at RHIC

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  1. Energy and Number Density Created at RHIC What’s in the PHENIX White Paper, and a little bit more Paul Stankus, ORNLPHENIX Focus, Apr 11 06

  2. Energy Density, Take 1 Just divide energy by volume, in some frame. 2R/g ~ .13 fm 2R ~ 14 fm • Boosted Frame • = E/V = gM/(V0/g) = e0g2 gRHIC = 106 • e ~ 1570 GeV/fm3 (!!) Rest Frame e = E/V = M/V0 e ~ 0.14 GeV/fm3 = e0

  3. Energy Density, Take 2 Examine a box with total momentum zero. e = ? e=2g2e0~ 3150 GeV/fm3 e = 0 Very high, but very short-lived!

  4. Energy Density, Take 3 Count up energy in produced particles/matter. Define produced as everything at velocities/rapidities intermediate between those of the original incoming nuclei. Two extremes: All particles Bjorken All fluid Landau

  5. The Bjorken Picture: Pure Particles • Key ideas: • Thin radiator • Classical trajectories • Finite formation time

  6. Particles in a thin box with random velocities Release them suddenly, and let them follow classical trajectories without interactions Strong position-momentum correlations!

  7. J.D. Bjorken, Phys. Rev. D 27 (1983) 140“Highly relativistic nucleus-nucleus collisions: The central rapidity region” Key idea: Use the space-momentum correlation to translate between spatial density dN/dz and momentum density dN/dpZ The diagram is appropriate for any frame near mid-rapidity, not just the A+A CMS frame specifically. Thin radiator

  8. Useful relations for particles in different Lorentz frames x x’ z z’ pT = pX= ppZ = 0 y = 0 E=√m2+pT2mT pT = pX mT =√m2+pT2pZ = mT sinh(y) E = √m2+p2 = mT cosh(y) bZ= pZ/E = sinh(y)/cosh(y) y =tanh-1(bZ) y  bZforbZ<<1

  9. Exercise: Count particles in the green box at some time t, add up their energies, and divide by the volume. R Particles in the box iff 0<bZ<dZ/t (limit of infinitely thin source) dZ Valid for material at any rapidity and for any shape in dET(t)/dy! A plateau in dET(t)/dy is not required.

  10. How low can t go? Two basic limits: eBjorken For many years this eBjorken formula was used with a nominal tForm=1.0 fm/c with no real justification, even when it manifestly violated the crossing time limit for validity! 2R/g = 5.3 fm/c for AGS Au+Au, 1.6 fm/c for SPS Pb+Pb.

  11. Better formation time estimates Generic quantum mechanics: a particle can’t be considered formed in a frame faster than hbar/E Translation: tForm 1/mT ~ 1/<mT> PHENIX Data: (dET/dh)/(dNch/dh) ~ 0.85 GeV Assuming 2/3 of particles are charged, this implies tForm ~ 0.35 fm/c

  12. Some assumptions we’ve used • Transverse energy density dET/dy only goes down with time. • The number density of particles does not go down with time (entropy conservation). • We can estimate, or at least bound, thermalization time from other evidence. An unanswered question:What are the initially produced particles? (Bj: “quanta”)

  13. Identifying the intial “quanta” Multiplicities in Au+Au at RHIC were lower than initial pQCD predictions. Indicates need for “regularization”. Good candidate is CGC. CGC identifies intial quanta as high-ish pT gluons (~1 GeV), which is consistent with our particle picture.

  14. The Landau Picture: Pure Fluid • Key ideas: • Complete, instant thermalization • Fluid evolves according to ideal relativistic fluid dynamics (1+1) • Very simple √s dependences for multiplicity and dN/dy (Gaussian)

  15. Multiplicities Widths Courtesy of P. Steinberg; see nucl-ex/0405022

  16. Basic Thermodynamics Hot Sudden expansion, fluid fills empty space without loss of energy. dE = 0 PdV > 0 thereforedS > 0 Hot Hot Gradual expansion (equilibrium maintained), fluid loses energy through PdV work. dE = -PdV thereforedS = 0 Hot Isentropic Adiabatic Cool

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