The ridge and the cone as hydro evolution of perturbations

1. The ridge and the cone as hydro evolution of perturbations (Cathie BNL workshop, Feb,2009) Edward Shuryak Stony Brook

2. Outlook: • 3 ways to deposit extra matter into the fireball • The fate of the perturbation • When does jet quenching take place? • Why the Mach cone angle is so large? Which cone do we see? • Conclusions • Why large quenching near Tc?

3. Three main observations from jet correlations may be explained by: • ``Shoulder” on the away side => ``conical flow” (H.Stoecker,J.Casalderrey+ES, 2005) • ``Hard ridge” => forward-backward bremmstrahlung cones kicked out by hydro radial flow (Shuryak 0706.3531, PRC76) • ``Soft ridge” => initial stage fluctuation of the color changes (Dumitru,Gelis,McLerran,Venugopalan, 0804.3858, Gavin et al 0806.4718)

4. Note that 4 (not 2) jets are always produced, we just don’t think about forward-backward ones (which have wide rapidity distribution) • The main idea (Voloshin): jet particles can be carried out by hydro • Jet quenching creates correlation between the triggered jet direction and flow, producing ridge

5. The jets we trigger on are biased to be near the nuclear surface: • thus their phi is correlated with the flow • Forward-backward jets deposite several extra particles into the fireball • Those gets carried by the flow and seen as a ridge, in a wide rapidity range

6. STAR found that the``ridge” exists even without any hard trigger (Phobos further observed that ridge extends at least till |y|=4)

7. Ridge is attributed to initial-state color charge fluctuation, leading to longitudinal fields,(Both E and B)

8. three ways to deposit extra matter (entropy): Jet quenching (2 transverse jets) Forward-backward jets due to hard collision Initial state color fluctuations What happens next is quite nontrivial , but we should be able to reproduce it via hydro evolution Timing of 3 main ``eras” = variable speed of sound – is the key element

9. Naively, ``spots” should excite a wave and get expanded to a spherical (or conical, or cylindrical) wave Like in the case of stone thrown into the pond, nothing is left at the original position: so how can they be observed? Its size =>the sound horizon => is comparable to fireball size 6-8 fm/c And thus large angular size But the actual solution to the problem reveals creation of smaller-brighter second waves which we may see

10. Perturbation evolution on top of a (Big-Bang-like) expansion 3 eras – QGP,mixed and hadronic have about equal timing except in QGP, expansion is Hubble-like considered by J.Casalderrey+ES,hep-ph/0511263 The first two terms are just sound propagation,Others come from the time dependence of the scale factor R and of the time-dependent speed of sound The third term leads to amplification if 3cs^2-1<0, which is the case except in QGP

11. Results for two spots, one at the fireball center (r=0), another at the rim (r=6 fm) In the QGP phase, just a sound wave is formed, and it moves out leaving nothing at the center In the mixed phase propagation is stalled but splitting into 2 waves occurs

12. Note that intensity has extra r^2, So at the rim (where hydro effects leading to ``ridge” are the largest) The second inner circle is not the same as outer one, but in fact the factor 5 brighter than the outer one

13. Nucl-th/01012042

15. Realistic geometry made the geometric limit even lower! <= !

16. matter produced at RHIC goes through 3 basic stages -- QGP,M,H -- with similar duration but quite different internal structure. there is no reason why quenching is the same: say it may be enhanced near Tc

17. “Onionization” (slicing matter into shells/bins of the same entropy density then adjusting quenching to reproduce the RAA(b) and predicting v2) • Glauber matter distribution, as above • Hard jets by binary scaling, as above • Calculated v2 for each shell (b=5,7,10 fm) • The maximum v2max(b) is the absolute geometric limit • It happens to be at RHIC at the near-Tc matter - known as the M (mixed or magnetic) phase

18. How new geom.limit v2max(b) compares to the data? <= the only really relevent data at high pt aremagenta stars and red star (there are also PHENIX higher stat. data we cannot show) • All those are below the absolute geometric limitv2max(b) (closed blue diamonds) • Central points should be dominated by QGP while peripheral by M and thus are closer to v2max(b)

19. a realistic model “weighted onion”):two different quenching in QGP and M phases, zero in H =quenching(QGP)/quenching(M)fitted to STAR data at pt>6 GeV suggests  Conclusion: quenching is stronger near Tc as compared to QGP, in spite of lower entropy density

20. Why is the``Mach cone” angle so large? The angle does not depend on centrality and pt: universal, good <cs>=.3 Cos(<cs>)=1.26 if quenching happens instantly (all three eras included) But if the main quenching is near Tc => <cs>=.2 or so and the value becomes consistent !!! Cos(<cs>)=1.36

21. Why is signal from Mach cone so weak in simulations yet seems to be observed? The same story as for all hydro perturbations => Naively expands with a speed of sound and makes large (weak) cone But actually, due to variable speed of sound and expansion Two waves, the second much brighter

22. Why may jet quenching be so large near Tc? There are lattice data indicating that near Tc the plasma is made of monopoles Mmono(Tc) = 300 MeV , less than Mq,g=800 MeV or so: larger recoil energy Also B circle around moving charge, unlike E => Coil-like magnetic current around E field is created (dual Faraday)

23. Summary on the ridge • ``spots” (at wide range of rapidity) can be induced either by hard collisions or initial fluctuations • Their subsequent evolution is studied by hydro, on top of expanding fireball • Mixed phase => small cs => wave splitting => brighter second wave • If so, we seem to obtain a directlyobservable consequence of the QCD phase transition

24. Summary on quenching New geometric limit v2max(b) is (finally) above the data (at pt>6GeV) • Fits to v2(b) data suggest stronger near-Tc (M phase) quenching • If conical flow originates in the mixed-phase =>large Mach angle • Perhaps brighter second cone explains why conical signal is not as weak as in simulations • It may be the first evidence for M=magnetic plasma

25. reserve

26. Magnetic objects and their dynamics: classics • Dirac explained how magnetic charges may coexists with quantum mechanics (1934) • ‘t Hooft and Polyakov discovered monopoles in Non-Abelian gauge theories (1974) • ‘t Hooft and Mandelstamm suggested “dual superconductor” mechanism for confinement (1982) • Seiberg and Witten shown how it works, in the N=2 Super -Yang-Mills theory (1994)

27. ``Magnetic scenario” for sQGP: Liao,ES hep-ph/0611131 electric/magnetic couplings (e/g) must run in the opposite directions! s(electric) s(magnetic)=1 Old good Dirac condition (in QED-type units e2= s) s(el) at the e=g “equilibrium line” s(el)=s(mag)=1 (the best liquid there?) s(mag) monopoles gets dominant before deconfinement, as they are much lighter/denser than gluons/quarks =>s(mag) smaller thans(el) how small can s(mag)be?

28. Near Tc the plasma is made of monopolesIs the “neck” a metastable flux tube? Dual Faraday law: rapidly created electric flux through C cause B (rotating tangent to C) which accelerates monopoles into rotating magnetic current --coil -- which mechanically contains the electric flux but gets dissipated laterand explode like overheated magnet B E those have mass about 300 MeV which is much less than quarks/gluons