The ridge and the cone as hydro evolution of perturbations

(Cathie BNL workshop, Feb,2009)(Cathie BNL workshop, Feb,2009)

Edward ShuryakEdward ShuryakStony BrookStony Brook

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?

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)

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

The jets we trigger on are biased to be near the nuclear surface:

thus their phi is thus their phi is correlated with the correlated with the flowflow

Forward-backward Forward-backward jets deposite jets deposite several extra several extra particles into the particles into the fireballfireball

Those gets carried Those gets carried by the flow and by the flow and seen as a ridge, in a seen as a ridge, in a wide rapidity rangewide rapidity range

STAR found that the``ridge” exists even without any hard trigger

(Phobos further observed that ridge extends at least till |y|=4)

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

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 evolutionTiming of 3 main ``eras” = variable speed of sound – is the key element

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/cAnd thus large angular sizeBut the actual solution to the problem reveals creation of smaller-brighter second waves which we may see

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

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

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

Nucl-th/01012042

Realistic geometry made the geometric limit even lower!

<= !

matter produced at RHIC goes matter produced at RHIC goes through 3 basic stages -- through 3 basic stages --

QGP,M,H QGP,M,H -- with similar duration -- with similar duration but quite but quite different internal different internal

structurestructure.. there is no reason why there is no reason why

quenching is the same: say it quenching is the same: say it may be enhanced near Tc may be enhanced near Tc

“Onionization” (slicing matter into shells/bins of the same entropy density then adjusting quenching to reproduce the RAA(b) and predicting v2)

Glauber matter Glauber matter distribution, as abovedistribution, as above

Hard jets by binary Hard jets by binary scaling, as abovescaling, as above

Calculated vCalculated v22 for each for each shell (b=5,7,10 fm)shell (b=5,7,10 fm)

The maximum The maximum vv22maxmax(b)(b) is is

the absolute geometric the absolute geometric limitlimit

It happens to be at RHIC It happens to be at RHIC at the near-Tc matter - at the near-Tc matter - known as the M (mixed known as the M (mixed or magnetic) phase or magnetic) phase

How new geom.limit v2max(b)

compares to the data?

<= the only <= the only really relevent data really relevent data at high pt areat high pt are magenta starsmagenta stars and and red starred star

(there are also PHENIX higher (there are also PHENIX higher stat. data we cannot show)stat. data we cannot show)

All those are below the All those are below the absolute geometric limitabsolute geometric limit

vv22maxmax(b) (b)

(closed blue diamonds) (closed blue diamonds) Central points should be Central points should be

dominated by QGP while dominated by QGP while peripheral by M and thus are peripheral by M and thus are closer to closer to vv22

maxmax(b) (b)

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: Conclusion: quenching is stronger quenching is stronger near Tc near Tc as compared to QGP, as compared to QGP, in in spite of lower entropy densityspite of lower entropy density

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

Why is signal from Mach cone so weak in simulations yet seems to be observed?The same story The same story

as for all hydro as for all hydro perturbations => perturbations =>

Naively expands Naively expands with a speed of with a speed of sound and makes sound and makes large (weak) conelarge (weak) cone

But actually, due But actually, due to variable speed to variable speed of sound and of sound and expansion expansion

Two waves, the Two waves, the second much second much brighterbrighter

Why may jet quenching be so large near Tc?There are lattice data There are lattice data

indicating that near indicating that near Tc the plasma is Tc the plasma is made of monopolesmade of monopoles

MMmonomono(Tc) = 300 (Tc) = 300 MeV , less than MeV , less than MMq,gq,g=800 MeV or so: =800 MeV or so: larger recoil energylarger recoil energy

Also B circle Also B circle around moving around moving charge, unlike E charge, unlike E =>=>

Coil-like magnetic Coil-like magnetic current around E current around E field is createdfield is created

(dual Faraday)(dual Faraday)

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 directly observable consequence of the QCD phase transition

Summary on quenchingNew geometric limit vNew geometric limit v22

maxmax(b) is (finally) (b) is (finally) aboveabove the data the data (at p(at ptt>6GeV)>6GeV)

Fits to vFits to v22(b) data suggest (b) data suggest stronger near-Tcstronger near-Tc (M (M phase) phase) quenching quenching

If conical flow originates in the mixed-phase =>If conical flow originates in the mixed-phase =>large large Mach angleMach angle

Perhaps Perhaps brighter second cone brighter second cone explains why conical explains why conical signal is not as weak as in simulationssignal is not as weak as in simulations

It may be the first evidence for M=magnetic plasmaIt may be the first evidence for M=magnetic plasma

reserve

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)

electric/magnetic couplings (e/g) must run in the opposite directions!

Old good Dirac condition (in QED-type units e2= s)

at the e=g “equilibrium line”s(el)= s(mag) =1(the best liquid there?)

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?

s(electric) s(magnetic)=1

``Magnetic scenario” for sQGP: Liao,ES hep-ph/0611131

s(el)

s(mag)

Near Tc the plasma is made of monopoles

Is 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 later and explode like overheated magnet

E

B

those have mass about 300 MeV which is much less than quarks/gluons