Diffusion and Two Particle Correlations Sean Gavin Wayne

Diffusion and Two Particle Correlations Sean Gavin Wayne State University

Charge fluctuations from QGP hadronization Does diffusion hide them? I. why diffusion? II. causal diffusion III. how diffusion modifies correlations and fluctuations IV. results a. rapidity fluctuations b. angular correlations (in progress) Mohamed Abdel-Aziz & S. G. Phys. Rev. C 70 (2004) 034905

Charge Fluctuation Puzzle quark-gluon degrees of freedom seen at RHIC expect: hadronization changes net-charge fluctuations • phase transition Rajagopal, Stephanov & Shuryak; Mishustin; Bower & Gavin; Antoniou et al. , Wilk et al. • hadronization Jeon & Koch; Asakawa et al. ; Bialas ― Jeon & Koch (N )qgp 2 hadron gas values problem: STAR, PHENIX, NA 49, CERES: not seen! ask: how does the hadronic medium hide hadronization?

How to Reduce Net-Charge Fluctuations Flow - advection • can’t reduce charge fluctuations • can increase them Diffusion • smooths distribution • reduces fluctuations charge conserved diffusion is only mechanism

Causal Diffusion "classic" diffusion dynamics: x random walk x 2 t infinite propagation speed v = x/ t as t 0 causal diffusion equation • Grad moment method – Muronga; Koide • propagation speed v = D/ d • diffusion time d • classic regime: d 0, v Grad; Israel & Stewart -v v

Diffusion Current diffusion: particle flow from high to low density classic: • • problem: current responds instantly to gradients particles “know” the surrounding density beforehand causal: • relaxation time d time lag • approximate

Causal vs. Classic Diffusion Bjorken flow plus causal diffusion – d. N dy Abdel-Aziz & S. G. V/ V V = 2 D/ 0 classic rapidity width 1. 5 • D ~ 2 fm • d ~ 6 fm 1. 0 Sasaki et al. • hadrons form 0 ~ 5 – 10 fm Find: width spreads more slowly for causal diffusion 0 d = 0. 5 / 0

Diffusion and Correlations spatial correlation function for single charge species diffusion equation for r(x 1, x 2) Van Kampen, Stochastic Processes in Physics and Chemistry, (Elsevier, 1997); Gardiner, Handbook of Stochastic Methods, (Springer, 2002) fluctuations equilibrate by diffusing through volume • global equilibrium – diffusion drives r equilibrium • Poisson fluctuations

Diffusion on Net-Charge Correlations charge species a, b , annihilation/creation reaction-diffusion eq’ns for rab net charge correlation function diffusion equation reaction terms cancel due to charge conservation

Dynamic Fluctuations from Correlations Pruneau, Voloshin & S. G. correlation function pair distribution : correlations fluctuations dynamic fluctuations = variance – thermal contribution net charge fluctuations for , species

Dynamic Net-Charge Fluctuations correlation function net charge fluctuations Nch = N+ N and Ntot = N++N diffusion drives q in global equilibrium dynamic fluctuations ≈ for N+ ≈ N

Fluctuations correlation function gaussian near midrapidity • relative rapidity r 1 2 • weak dependence on a 1 2 two-body diffusion equation grows one body width, V fluctuations, rapidity window : fluctuations

Can Diffusion Obliterate Fluctuations? Jeon–Koch estimate • QGP N Abdel-Aziz, S. G initial value at hadronization • STAR N 1. 5 • Can hadronic diffusion dissipate the difference? , • Not likely: lifetime of HG from resonances ~ 5 to 10 fm D = 2 fm, d fm, 9 fm J-K estimate wrong? Bialas; C. Nonaka, B. Muller, S. A. Bass, M. Asakawa Maybe the whole picture is wrong: s. QGP? bs. QGP?

Angular Correlations Abdel-Aziz, S. G correlation function with radial expansion vr • diffusion radial velocity • boosts particles into an opening angle r (fm) azimuthal separation diffusion r , r find: broadening with time importance of diffusion (rad)

Summary: Diffusion Alters Charge Correlations I. Diffusion may explain part of the fluctuation puzzle a. Rapidity fluctuations b. Probe contribution – azimuthal correlations II. Causal Diffusion – relativistic transport is interesting Muronga; Moore & Teaney; Koide; Sasaki at al. III. Probe: Correlations and Fluctuations

Classic Diffusion in Rapidty diffusion broadens rapidity density diffusion + Bjorken flow, n random walk in rapidity y vs. proper time V = 2 D/ 0 V diffusion coefficient D hadron formation at 0 / 0