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Constraints induced by Finite Plasma Formation Time on some Physics Observables at RHIC

Outline:

•Demonstrate where long formation time comes from

•Show its influence on experimental observables

•View on non-photonic electrons result and J/ puzzle

•Are there some theoretical proves?

•What should we do next?

•Conclusions

Vlad Pantuev, SUNY at Stony Brook

See V.P. hep-ph/0506095, hep-ph/0509207 and

www.phenix.bnl.gov/WWW/publish/pantuev/Formation_Time_BNL.ppt

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“pQCD-based calculations … reproduce much of the published data on high pT hadron production in nuclear collisions.

Nevertheless, it is important to ask to what extent the data require this description to be the correct one.”

P.Jacobs and M. van Leeuwen, QM2005 proceedings, nucl-ex/0511013

Let us forget about paradigm of “standard” models with jet quenching…

Let’s look at experimental data and “see what we see”…

Use common sense…

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0 RAA for 200 GeV Au Au Collisions

Min. bias

0-10% 10-20%

20-30% 30-40%

40-50%

RAA appears flat all the way to pT~20 GeV/c

New region for PHENIX

PHENIX Preliminary

Nuclear modification factor

RAA = YieldAA/<N binary> : Yield pp

The Story, which is known for 5 years…

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Where formation time comes from?

New quality data:

Raa for 5-6 GeV/c pions vs.in reaction plane, PHENIX QM2005, preliminary

Ncoll for 50-55% cent in x-y plane. WS, Glauber This is a key point. No absorption!

X

OK

stopped

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We construct a simple model:

•Monte Carlo simulation of A+A based of Glauber approach

•Woods-Saxon density distribution

•Restrict to high pt >4 GeV/c pions, where Raa does not depend on pt

•Assume, all pions are produced by parton/jet fragmentation

•Number of partons/jets is proportional to Ncoll

•Ignore longitudinal expansion (actually, I don’t care)

•Jets, moving at some direction and produced not deeper than distance L will leave unmodified

•Jets, produced in the core region deeper than L will be absorbed completely

•This is pure corona jet production, but we have to find corona thickness L from experiment. L could be larger than a Woods-Saxon type skin

•L should be on the order of the size of in-plane interaction zone at 50-55% centrality, about 2-3 fm

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Look in-plane, =0

Look out-plane, =/2

Cutoff L=2.3 fm/c is adjusted for in-plane 50-55% centrality Raa=0.9

Raa() is inclusive measurement and in a particular event you always look at some angle.

x-y projections of Ncoll centers for 40-45% centrality from Glauber model with Woods-Saxon density distribution.

L

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Can calculate Raa as a ratio of seen number of collisions after the cut, Ncoll, to the average total number of binary collisions, <Nbinary > , for particular centrality class

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Black boxes -Results of my estimation with L=2.3 fm

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0 , points with error bars – exp. data. Syst. errors are not shown

Data are for high pt pi0s, PHENIX, blue cicles – 4.59 GeV/c, green squares – 5-7 GeV/c

No flow!

This actually was prediction! Before QM2005

Can calculate elipticity parameter v2 as jet surviving probability in and out of plane

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Additional tests

•Smooth cut edge -> Very little change.

•Consider the thickness of material integrated over the path as a cut-off -> centrality dependence becomes very strong, can’t describe the data

•Consider the constant density Ncoll envelope as a cut-off edge -> centrality dependence becomes very strong, can’t describe the data

•Assume, Npart , not Ncoll, is a critical value -> centrality dependence becomes weaker, v2 < 5%

•Use nucleus in the hard sphere model -> v2 becomes large, about 20%

For Au+Au at 62.4 GeV data we get L=3.5 fm

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What could be the physical interpretation of the geometrical cutoff L=2.3 fm ?

Our guess is that it is, actually, formation time of strongly interacting plasma,

T=L/c = 2.3 fm/c,

or, at least, the time when strong parton energy loss starts.

We don’t want to exclude QGP formation at early stages, but in takes time to become sQGP, strongly interacting quark-gluon plasma .

Very elegant explanation: Jets, particles have time, about 2-3 fm/c, to escape from interaction region. After that time a highly dense matter is formed and this matter absorbs jets.

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We will list constraints induced by finite plasma formation time on some physical observables at RHIC:

1. Raa for high pt particles is determined purely by such a “corona” production, not by parton partial energy loss, or in other words,

2. All pions (all light hadrons) above 5 GeV/c are produced from corona

3. Azimuthal dependence of Raa in reaction plain explained

4. Automatically explains flatness of Raa at high momenta

5. T=2.3 fm/c was adjusted for Raa in-plane for 50-55% centrality, but describes all Raa for Au+Au and Cu+Cu

6. There is no flow contribution to v2 at high pt, it is purely geometry effect, v2 can reach 11-12%.

7. Explains v2 at low-to-high pt dependence (see backup). Hydro works!

8. So-called, PHOBOS Npart scaling is completely described (just do not show here)

9. No/weak dependence of properties of near-side jets on centrality. All jets are produced from corona region

10.Di jets. Iaa is described. Details are next

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Trigger, near side jet

Be careful! I assume away side particle with high momentum too

We observe pure tangential di-jet production with very little of back “jet bending” or widening!

Away side jet

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STAR away side jet

I_aa for A+A is ratio of:

Yield of associate particles per trigger

To

Similar Yield in p + p

P.S. Iaa does not contain Nbinary, in contrast to Raa

Curve - results of our calculation for Au+Au with away side jet width sigma=0.35 radians

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Width of the back jet depends on associate particle momentum range, so, let’s calculate I_aa for different away side jet width…

Assume Gaussian shape of away jet. Numbers next to the curves is width in radians

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STAR Phys. Rev. Lett. 90, (2003), Disappearance of away side jet

PHENIX 2005

Trigger= 2.5-4 GeV/c

Assoc. = 1 – 2 GeV/c

Trigger= 4 - 6 GeV/c

Assoc. = 2 – 4 GeV/c

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11. All di-jets at high pt are from corona region. Good estimate of Iaa is a prove

12. There is no “punch-through” or re-appearance at high pt di-jets. 20-25% are there

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STAR: Emergence of dijets with increasing pT(assoc) (???)

correlations (not background subtracted)

8 < pT(trig) < 15 GeV/cpT(assoc) > 2 GeV/cpT(assoc) > 3 GeV/cpT(assoc) > 4 GeV/cpT(assoc) > 5 GeV/cpT(assoc) > 6 GeV/cpT(assoc) > 7 GeV/cpT(assoc) > 8 GeV/c

Watch the width of near and away side jets. No change!

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13. Away-side jet, been produced from corona, should not change its shape for associate particle above 4 GeV/c.

At pt < 4 GeV/c we see medium response to the absorbed jets. Shock wave, Cherenkov cone? … and Baryons!

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Open charm and J/ production

14. Absorption in the core is very strong, we may expect also strong c-quark suppression

15. c-quark corona production must lead to anisotropy or v2, similar to light hadrons at high pt.

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PHENIX QM2005 preliminary result, statistical errors only

The effect sits really on geometrical limit. It means not “just” absorption but very strong absorption/energy loss.

Measured v2 is close to corona expectation. Most of models are in trouble

T= 2.3 fm/c

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Theory:Greco, Ko, Rapp: PLB 595 (2004) 202

Do we need charm flow? Probably, not…

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RAA vs Npart comparison to cold nuclear effects

● Prediction is from pQCD calculations, including 3mb nuclear

absorption and shadowing ● Seems to underestimate the suppression● Note: abs somewhat too high wrt d+Au data

Forward rapidity Mid rapidity

Now J/psi. QM2005

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RAA vs Npart Comparison to theoretical predictions

• Models which reproduce NA50 data, with J/ suppression only.

• No regeneration mechanism.

J/ suppression is over-estimated

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2. No absorption in corona, some absorption in plasma, i.e. Kostyuk &Co, BUT recalculated as

Raa=R_geom + (1-R_geom)*Theor

Dotted line.

1. No absorption in corona, very strong absorption in plasma: solid red line as geometrical limit.

PHENIX prelim. data in muon and central arms. Stat. errors only

…not so much left for re-generation. Rapidity distribution will be as in p-p…

I consider just 4 scenarios:

3. Normal nuclear absorption (overestimated) in corona and strong absorption in plasma: dashed line, and

Raa=R_geom * R_vogt

4. Some absorption in corona and strong absorption in plasma

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… but I will not put “a bullet” that I can explain J/ production by formation time only (just one parameter T, time!) …

Nevertheless, if corona plays a significant role in J/ production, I would expect v2 value up to 11-12%

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Do we have theoretical justifications for such a picture with long formation time and much stronger than expected jet suppression?

From M. Thoma QM2005 talk, hep-ph/0509154:

plasma coupling parameter Epot/Tkin , << 1 for gas, >> 1 crystal. At RHIC more like = 1.5 – 6 - 10, liquid. Strongly coupled plasmas show enhanced cross section -> large collisional energy loss or jet quenching

S.-J. Sin & I. Zahed, Phys.Lett. B608(2005)265: “… the quark-gluon liquid is very opaque. High energy jets at RHIC would not make it beyond 1/3 fm”

S. Peigne, P.-B. Gossiaux, T. Gousset, hep-ph/0509185. “Retardation effect for collisional energy loss of hard partons produced in a QGP”. They found E retardation time ~ 5 fm/c !

E. Shuryak goes even beyond “liquid” sQGP, introducing polymeric chains: J. Lia & E. Shuryak, hep-ph/0508035

“Bottom-up” thermalization gives 2-3 fm/c and correct tendency with energy

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What to do next?

Most of knowledge rely now on experimental data. sQGP demonstrates too unpredictable properties :(

Need of more analysis techniques to extract information from the data

There is nothing “interesting” in high pt “tails”: pions > 4 GeV/c, baryons >5 GeV/c, but they are extremely useful for trigger purposes

Plasma information sits at low momentum, search there

Baryon production could be the key to sQGP properties. Two, three-particle correlations with baryons is the right way

Subtraction of contribution from corona region (from spectra, from v2, from correlations…) at each centrality class will help to “crystallize” sQGP properties

We should stop load students with obsolete projects

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For conclusions:

• Experimental data lead to inevitable conclusion to the existence of a 2-3 fm/c formation time of Strongly interacting QGP at 200 GeV

• Parton absorption in sQGP is VERY strong (no energy loss?)

• All conventional models with partial parton energy loss do not work. Too many experimental facts do not fit into standard models and are ignored or half explained! (*, **)

• We don’t have yet a solid theoretical justification of such a long time

• The existence of formation time is a direct sign that sQGP is actually formed at RHIC

• Formation time gets longer at lower energy: 2.3 fm/c at 200 GeV, 3.5 fm/c at 62 GeV.

• At even lower energy, formation time is so long that sQGP can’t be formed at all because of fast longitudinal expansion

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Chicken on the way to the BS-QGP side of the road.

Picture From Berndt Muller, QM2005 Summary Talk

“Don’t be chicken, learn to fly, be an eagle. High above there is no fear, and one can see what people do in other fields.”E. Shuryak, in Proceedings of QM2005, hep-ph/0510123

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Back up

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How to explain rising and falling down v_2 with momentum?

100%

0%pt

core+hydro+exp corona,

power law

Relative contribution

At low momentum hydro scenario produces most of particles and v2 increases with momentum. At high pt, particles are produced from corona with smaller v2.

Corona contribution “dilutes” hydro/thermo v2 at high pt

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Visualization of free streaming jets in Au+Au(just for fun)

Take Glauber MC with W-S density distribution.Use N-N collision vertex x-y positions as production points for all jets.

Let jets free streaming in random angle between 0 and 2. Mathematically it is just x(T)=x_0 + T*cos(), y(T)=y_0 + T*sin(),

T - is time in fm/c.

No interactions, cascading or jet fragmentation.Choose semi-central events 40-45% as the most interesting .

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Original x-y Ncoll distribution at time zero

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Now, let jets move…

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… and move…

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Look at the shallow structure in the center and two left-right peaks…

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Question to experts: could these two separate “coral” islands to the left and to the right be seen by HBT? Different from the whole event sizes ?

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The central shallow is filled by jets still moving from periphery to the center direction. It becomes empty (from jets) after ~10 fm/c

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Be careful with fast conclusions: the central area will be filled by soft and secondary particles, which I do not consider here…

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Now, draw event at the moment when, as I estimate in hep-ph/0506095, at T=2.3 fm/c, the sQGP is actually formed. All jets within W-S radii envelope after this time should be completely absorbed. (The central grey area in the right figure should actually be black, reproducing total absorption.)

Doing the similar cuts for other centralities, I found exactly the same R_aa numbers as in preprint, where I used just two directions in and out of plane.

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Green line is for Raa extracted with free expansion method

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Hadron-triggered fragmentation functions

• Away-side D(zT) suppressed, but shape unchanged

~0.54

~0.25

Scalingfactors

8 < pT(trig) < 15 GeV/c

QM2005, STAR data

Look at this jump, which corresponds to about 3 GeV/c !

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A+A collisions have few stages. I want to emphasize the significance of Plasma Formation Time . It’s about 2-3 fm/c

Collision itself

Plasma formation

“plasma”Mixed phase

Hadron gas

2-3 fm/c! This was ignored!