1. Glasma, minijets, strings  long range  correlations  Venugopalan Ask: how does viscous flow modify these correlations? Viscosity, Flow and the Ridge Sean Gavin Wayne State University I. Soft ridge (no jet tag)  L. Ray’s talk II. Transverse flow fluctuations in viscous hydro III. Effect on transverse momentum correlations IV. Rapidity + Azimuthal Correlation Data V. Transverse flow and the hard ridge? SG, Abdel-Aziz, PRL 97, 162302 (2006) SG, G. Moschelli, in progress Pruneau, Voloshin, SG, NPA 802, (2008) 107

2. hard ridge: high p t particle interacting with softer matter

3. soft ridge: correlations of the matter

4. Momentum Correlation Landscape p t fluctuations STAR p t fluctuations STAR, J.Phys. G32 (2006) L37 soft ridge: soft ridge: near side peak ridge similar to ridge with jet tag but at ordinary p t scales -- no jet tag jet-like correlations from radial flow our aim:untagged correlations our aim: hydro modification of untagged correlations Pruneau, Voloshin, S.G

5. Centrality Dependence Trends STAR, J.Phys. G32 (2006) L37 near side peak pseudorapidity width   azimuthal width   centrality dependence: path length   rapidity broadening: viscous diffusion   s ~  SG + Abdel-Aziz, PRL 97, 162302 (2006) claim: claim: azimuthal narrowing due to viscous diffusion + transverse and elliptic flow

6. Transverse Flow  p t Fluctuations neighboring fluid elements flow past one another  viscous friction small variations in radial flow in each event shear viscosity drives velocity toward the average damping of radial flow fluctuations  viscosity

7. Evolution of Fluctuations diffusion equation diffusion equation for momentum current kinematic viscosity shear viscosity  entropy density s, temperature T r z momentum current momentum current for small fluctuations momentum conservation u u(z,t) ≈ v r  v r  shear stress

8. Hydrodynamic Momentum Correlations momentum flux density correlation function deterministic diffusion equation for   deterministic diffusion equation for  r g  r g  r g,eq fluctuations diffuse through volume, driving r g  r g,eq width in relative rapidity grows from initial value   fluctuating momentum current particles jump between fluid cells  Langevin noise

9. observable: Transverse Momentum Covariance propose: propose: measure C(  ) to extract width  2 of  r g measures momentum-density correlation function C depends on rapidity interval  C()C() 

10.  s ~ 0.08 ~ 1/4  Current Data? STAR measures rapidity width of p t fluctuations most peripheral  * ~ 0.45 find width  * increases in central collisions central  * ~ 0.75 freezeout  f,p ~ 1 fm,  f,c ~ 20 fm  ~ 0.09 fm at T c ~ 170 MeV  J.Phys. G32 (2006) L37 naively identify naively identify  * with 

11. 0.08 <  s < 0.3 Current Data? STAR measures rapidity width of p t fluctuations most peripheral  * ~ 0.45 find width  * increases in central collisions central  * ~ 0.75 J.Phys. G32 (2006) L37 naively identify naively identify  * with  (strictly, ) but but maybe  n  2  * STAR, PRC 66, 044904 (2006) uncertainty range  *    2  * 

12. Shear Viscosity Measurements consensus: viscosity is extremely small light quark v 2 only a bound -- ideal hydro works each observable -- different theoretical uncertainties

13. Part of a Correlation Landscape: Soft Ridge STAR near side peak S.G. + G. Moschelli in progress Theory untriggered correlations: no jet tag ridge near side peak: similar to ridge with jet tag but at ordinary p t scales

14. Flow  Azimuthal Correlations mean flow depends on position blast wave opening angle for each fluid element depends on r correlations: momentum distribution: gaussian spatial r(x 1, x 2 ) :  t -- width in  t -- width in

15. Measured Flow Constrains Correlations diffusion + flow for correlations constraints: constraints: flow velocity, radius from measured v 2,  p t  vs. centrality radial plus elliptic flow: radial plus elliptic flow: “eccentric” blast wave n part STAR 200 GeV Au+AuPHENIX 200 GeV Au+Au Heinz et al.

16. Rapidity and Azimuthal Trends rapidity width: viscous broadening,  s ~  azimuthal width: flow dominates viscosity effect tiny for identified particles   for identified particles K/  = 1.1  0.3 p/  = 1.6  0.5 assume: initial widths centrality independent Glasma?  Venugopalan’s talk Dumitru et al., arXiv:0804.3858 STAR data, J.Phys. G32 (2006) L37  

17. Hard Ridge: Transverse Flow? C. Pruneau, S. Voloshin + S.G., NPA 802, (2008) 107; see also: C.Y. Wong, PRC 76, 054908 (2007) any effect of transverse flow on jets  ridge-like structure PYTHIA + transverse boost jet tag particle 3 < pt < 20 GeV associates 0.2 < pt < 1 GeV flow-like effects for jets? Cronin (pA, dA, leptons) radial color fields Fries, Kapusta + Li further clues from 3 particle correlations

18. Summary: hydro and the ridge? viscous hydro explains centrality dependence of soft ridge rapidity broadening  viscous diffusion very small  s  near side peak from transverse flow centrality dependence of soft ridge  viscous diffusion + flow hard ridge from boosted jets generic feature of radially boosted source? source of long range correlations for soft ridge? initial conditions for hydro minijets, glasma, string fragmentation?  Trainor; Venugopalan

19. Compare Near to Away-Side near away near p t conserved per event p t conserved per event Borghini et al. away side feature independent of away side feature independent of r(x 1, x 2 ) compare near and away side integrated C for each feature other observables to come C [GeV 2 ]

20. Fluctuation Observable where subtract variance of pt per particle

21. sQGP + Hadronic Corona  Forbidden Zone? viscosity in collisions -- Hirano & Gyulassy supersymmetric Yang-Mills:  s   pQCD and hadron gas:  s ~ 1 Broadening from viscosity rapidity width from H&G Bjorken  large hadronic viscosity increases width Does data suggest viscosity initially below quantum bound? STAR

22. Azimuthal Correlations from Flow transverse flow: transverse flow: narrows angular correlations no flow         v rel elliptic flow: v 2 contribution STAR subtracted viscous diffusion: increases spatial widths  t and  t     t    t   - 1/2 momentum conservation:  sin  ; subtracted Borghini, et al

23. Elliptic and Transverse Flow flow observables: flow observables: fix  x,  y, and R vs. centrality n part STAR 200 GeV Au+AuPHENIX 200 GeV Au+Au transverse plus elliptic flow: transverse plus elliptic flow: “eccentric” blast wave blast wave: elliptic flow transverse flow

24. Blast Wave Azimuthal Correlations STAR 200 GeV Au+Au data azimuthal trend :  t  system size  t constant roughly: gaussian spatial r(x 1, x 2 ) :  t -- width in  t -- width in

25. we want: Uncertainty Range STAR measures: density correlation function    density correlation function  r n  r n  r n,eq may differ from  r g maybe  n  2  * STAR, PRC 66, 044904 (2006) uncertainty range  *    2  *  0.08   s  0.3 momentum density correlations density correlations

26. covariance Covariance  Momentum Flux unrestricted sum: correlation function: C =0 in equilibrium 

27. viscous diffusion viscous diffusion drives fluctuation g t    V  = 2 /  0 /0/0 VV random walk in rapidity random walk in rapidity y vs. proper time  kinematic viscosity  Ts formation at  0 Viscosity Broadens Rapidity Distribution  rapidity broadening increase