anisotropic flow at the lhc as measured by...

INTERNATIONAL SCHOOL OF NUCLEAR PHYSICS34th Course: PROBING THE EXTREMES OF MATTER

WITH HEAVY IONSERICE–SICILY: 16 – 24 SEPTEMBER 2012

Sponsored by the: • Deutsche Forschungsgemeinschaft • European Physical Society • Italian Ministry of University and Research • Sicilian Regional Government

PURPOSE OF THE COURSE

The program concentrates on the following topics: The QCD phase diagram;Hydrodynamic evolution of the fireball; Transport properties of strong-interactionmatter; RHIC low-energy scan; Results from ALICE; Initial conditions at LHC energies;Quarkonia production at the highest beam energies; Electromagnetic signals; Fluctuationsand criticality; Particle interferometry in pp and AA collisions; Heavy-ion collisionsat high baryon densities.

APPLICATIONS

Persons wishing to attend the Course should register online at: http://www.physik.tu-darmstadt.de/erice/ – http://www.uni-tuebingen.de/erice/or apply in writing to:

• Professor Dr Amand FAESSLERUniversität TuebingenAuf der Morgenstelle 14 – D-72076 TUEBINGEN, GermanyTel +49.7071.2976370 – Fax +49.7071.295388e-mail: [email protected]

• Professor Dr Jochen WAMBACHInstüt Kernphysik Technische Universitaet DarmstadtSchlossgartenstrasse 9 – D-64289 DARMSTADT, Germanye-mail: [email protected]

They should specify:

i) date and place of birth together with present nationality;ii) degree and other academic qualifications;iii) present position and place of work;iv) postal and e-mail address.

Further information on the School and application forms for fellowships canbe found at the same web address.

POETIC TOUCH

According to legend, Erice, son of Venus and Neptune, founded a smalltown on top of a mountain (750 metres above sea level) more than three thousandyears ago. The founder of modern history — i.e. the recording of events in amethodic and chronological sequence as they really happened without referenceto mythical causes — the great Thucydides (~500 B.C.), writing about eventsconnected with the conquest of Troy (1183 B.C.) said: «After the fall of Troy someTrojans on their escape from the Achaei arrived in Sicily by boat and as they settlednear the border with the Sicanians all together they were named Elymi: their townswere Segesta and Erice.» This inspired Virgil to describe the arrival of the Trojanroyal family in Erice and the burial of Anchises, by his son Aeneas, on the coastbelow Erice. Homer (~1000 B.C.), Theocritus (~300 B.C.), Polybius (~200 B.C.),Virgil (~50 B.C.), Horace (~20 B.C.), and others have celebrated this magnificentspot in Sicily in their poems. During seven centuries (XIII-XIX) the town of Ericewas under the leadership of a local oligarchy, whose wisdom assured a long periodof cultural development and economic prosperity which in turn gave rise to themany churches, monasteries and private palaces which you see today.

In Erice you can admire the Castle of Venus, the Cyclopean Walls (~800B.C.) and the Gothic Cathedral (~1300 A.D.). Erice is at present a mixture ofancient and medieval architecture. Other masterpieces of ancient civilization areto be found in the neighbourhood: at Motya (Phoenician), Segesta (Elymian), andSelinunte (Greek). On the Aegadian Islands — theatre of the decisive naval battleof the first Punic War (264-241 B.C.) — suggestive neolithic and paleolithic vestigesare still visible: the grottoes of Favignana, the carvings and murals of Levanzo.

Splendid beaches are to be found at San Vito Lo Capo, Scopello, andCornino, and a wild and rocky coast around Monte Cofano: all at less than onehour’s drive from Erice.

More information about the «Ettore Majorana» Foundation and Centrefor Scientific Culture can be found on the WWW at the following address:

http://www.ccsem.infn.it

PLEASE NOTEParticipants must arrive on September 16, not later than 7 pm.

A. FAESSLER – J. WAMBACHDIRECTORS OF THE SCHOOL

A. ZICHICHIEMFCSC PRESIDENT AND DIRECTOR OF THE CENTRE

TOPICS AND LECTURERS

Color Glass Condensate and the implications for the LHC• J. ALBACETE, CEA/Saclay, Gif-sur-Yvette, FR

New results from ALICE I• P. BRAUN-MUNZINGER, GSI, Damstadt, DE

Penetrating probes for heavy-ion collisions• T. HEMMICK, SUNY, Stony Brook, NY, US

Hydrodynamic description of ultrarelativistic heavy-ion collisions• T. HIRANO, University of Tokyo, JP

Gluon saturation, geometric scaling and color glass condensatesin heavy-ion collisions• K. ITAKURA, KEK, Tsukuba, JP

Recent results from PHENIX• B. JACAK, Stony Brook, NY, US

Dileptons and photons in heavy-ion collisions• R. RAPP, College Station, Texas AM University, TX, US

Sound propagation in the quark-gluon plasma• E. SHURYAK, SUNY, Stony Brook, NY, US

The planned NICA facility in Dubna• A. SORIN, Joint Institute for Nuclear Research, Dubna, RU

Collective flow at the LHC• R. SNELLINGS, Utrecht University, NL

New results from ALICE II• J. STACHEL, University of Heidelberg, DE

Recent results from the HADES experiment• J. STROTH, University of Frankfurt, DE

The equation of state in weak coupling• A. VUORINEN, University of Bielefeld, DE

Quarkonia production in heavy-ion collisions• P. ZHUANG, Tsinghua University, Beijing, CH

«ETTORE MAJORANA» FOUNDATION AND CENTRE FOR SCIENTIFIC CULTURETO PAY A PERMANENT TRIBUTE TO GALILEO GALILEI, FOUNDER OF MODERN SCIENCE

AND TO ENRICO FERMI, THE “ITALIAN NAVIGATOR”, FATHER OF THE WEAK FORCES

Anisotropic Flow at the LHC as measured by ALICE

1

Raimond Snellings

1) Elliptic Flow

2) What do we learn from various particle species?

3) Higher harmonics

4) What’s next?

2

Content

3

In a Heavy Ion Collision

x, b

yz

an anisotropic system is created

px

x

y

py

x (fm)-5 0 5 -5 0 5 -5 0 5 -5 0 5

2 fm/c 4 fm/c 6 fm/c 8 fm/cTime

b

z

-5 0 5

-5

0

5b = 7 fm

0 fm/c

x

y

px

py

Tim

e

Tim

e

• the system in coordinate space configuration is anisotropic (for a non-central collision almond shape). However, initial momentum distribution isotropic (spherically symmetric)

• interactions among constituents generate a pressure gradient which transforms the initial coordinate space anisotropy into the observed momentum space anisotropy → anisotropic flow

• self-quenching → sensitive to early stage

� =⇥y2 � x2⇤⇥y2 + x2⇤

v2 = �cos 2�⇥

Elliptic Flow

4

STA

R P

hys.

Rev

. Let

t. 86

, 402

–407

(200

1)

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1v2

nch /n max

Elliptic flow is large

Ideal hydro gets the magnitude for more central collisions

5

Flow at RHIC

RHIC Scientists Serve Up “Perfect” LiquidNew state of matter more remarkable than predicted -- raising many new questionsApril 18, 2005

6

7

The Perfect Liquid?

(GeV)NNs1 10 210 310 410

2v

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

STARPHOBOSPHENIXNA49CERESE877EOSE895FOPI

?

What to expect at the LHC: still the perfect liquid or approaching a viscous ideal gas?

8

The Perfect Liquid?

(GeV)NNs

1 10 210 310 410

2v

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

ALICESTARPHOBOSPHENIXNA49CERESE877EOSE895FOPI

CERN, November 26, 2010:‘the much hotter plasma produced at the LHC behaves as a very low viscosity liquid (a perfect fluid)..’

K. A

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LICE

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ratio

n) P

RL 1

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2523

02 (2

010)

Physics 3, 105 (2010)

RHIC, the higher energy jets available at the LHC wouldtravel further through the plasma before completelydissipating their energy, but the ATLAS measurementsshowed that the stopping distance for a jet is compa-rable to the radius of lead nuclei used in the collisions.(The deposited energy/momentum goes into a shock orsound wave [7, 8], which still has to propagate for sometime, until the final freeze-out, when it turns into theobserved hadrons.) One theory that could explain thissurprising result is a strong coupling theory called theAdS/CFT correspondence, a spin-off from string theorythat relates the strong-coupling limit of quarks and glu-ons to a theory of gravity in a higher dimension. In theAdS/CFT picture, the equilibration of the quark-gluonplasma is connected to the production of a black hole,and jet quenching can be mapped to falling into thisblack hole (for reviews, see, e.g., Refs. [9, 10]). Predic-tions based on this theory suggest that the stopping dis-tance of a jet varies as E1/3⇥ /T

4/3 [6], which means thatat the LHC, a jet with E⇥ = 100 GeV stops at the samedistance as a 35 GeV jet at RHIC—similar to what AT-LAS observed. Collectively, these results from ALICEand ATLAS are providing new evidence that the quark-gluon plasma produced at the LHC is still strongly cou-

pled. After just three weeks of the LHC run with heavyions, we are witnessing a very exciting start of this newera.

References

[1] K. Aamodt et al. (ALICE Collaboration), Phys. Rev. Lett. 105,252302 (2010).

[2] G. Aad et al. (ATLAS Collaboration), Phys. Rev. Lett. 105, 252303(2010).

[3] K. Aamodt et al. (ALICE Collaboration), Phys. Rev. Lett. 105,252301 (2001).

[4] D. Teaney, J. Lauret, and E. V. Shuryak, Phys. Rev. Lett. 86, 4783(2001).

[5] G. Policastro, D. T. Son, and A. O. Starinets, J. High Energy Phys.0209, 043 (2002).

[6] P. M. Chesler, K. Jensen, A. Karch, and L. G. Yaffe, Phys. Rev. D79, 125015 (2009).

[7] H. Stöcker, Nucl. Phys. A 750, 121 (2005).[8] J. Casalderrey-Solana, E. V. Shuryak, and D. Teaney, J. Phys. Conf.

Ser. 27, 22 (2005); Nucl. Phys. A 774, 577 (2006).[9] I. R. Klebanov and J. M. Maldacena, Phys. Today 62, No. 1, 28

(2009).[10] E. Shuryak, Prog. Part. Nucl. Phys. 62, 48 (2009).

About the Author

Edward ShuryakEdward Shuryak received his Ph.D. in 1970 at Budker Institute of Nuclear Physics, Novosi-birsk, Russia, where he later became a professor, before moving to the physics departmentat Stony Brook University in 1990. He has held visiting positions at CERN, BrookhavenNational Laboratory, and several other institutions. He is a Fellow of the American Phys-ical Society and has served on the Editorial Board of Physical Review C. In 2008 he wasrecognized as an Outstanding Referee by the American Physical Society. His research in-terests include the theoretical description of the quark-gluon plasma and high-energy ioncollisions. In the late 1970s he introduced the term “quark-gluon plasma.”

DOI: 10.1103/Physics.3.105URL: http://link.aps.org/doi/10.1103/Physics.3.105

c� 2010 American Physical Society

Physics 3, 105 (2010)

Viewpoint

A “Little Bang” arrives at the LHC

Edward ShuryakDepartment of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USAPublished December 13, 2010

The first experiments to study the quark-gluon plasma at the LHC reveal that even at the hottest temperaturesever produced at a particle accelerator, this extreme state of matter remains the best example of an ideal liquid.

Subject Areas: Particles and Fields

A Viewpoint on:Elliptic Flow of Charged Particles in Pb-Pb Collisions at

⇧sNN = 2.76 TeV

K. Aamodt et al. (ALICE Collaboration)Phys. Rev. Lett. 105, 252302 (2010) – Published December 13, 2010

Observation of a Centrality-Dependent Dijet Asymmetry in Lead-Lead Collisions at⇧

sNN = 2.76 TeV with theATLAS Detector at the LHCG. Aad et al. (ATLAS Collaboration)Phys. Rev. Lett. 105, 252303 (2010) – Published December 13, 2010

In November, the Large Hadron Collider (LHC) atCERN began its first heavy-ion run, producing lead-leadcollisions with the highest center of mass energy everachieved. Now, a pair of papers appearing in PhysicalReview Letters, from the ALICE [1] and ATLAS [2] exper-iments at the LHC, presents a first glimpse of what newinformation these high-energy collisions will offer aboutthe quark-gluon plasma—the state of matter believed tohave filled the universe at the time of the Big Bang. TheALICE results strongly indicate that the quark-gluonplasma remains a nearly ideal liquid, as seen earlier atthe Relativistic Heavy Ion Collider (RHIC), even at sig-nificantly higher energies. Complementing this work,the ATLAS team has shown that even very high energyjets of particles emitted from the collision lose a largefraction of their energy into the quark-gluon plasma(and are sometimes completely dissipated), a sign thatthe quarks and gluons are strongly interacting with thehotter plasma.

The quark-gluon plasma (QGP) is the extreme stateof matter that occurs above a critical temperature Tc ⇥170 MeV (2 trillion degrees Kelvin). Unlike the world welive in, where quarks and gluons are not free, but boundinto nucleons, the QGP can be viewed as a plasma con-sisting of quarks and gluons that interact via Coulom-bic forces. (The “color” charge of quarks and gluonsdetermines the strength of the strong force in the sameway that electric charge determines the strength of theelectromagnetic force.) Laboratory collider experimentsseek to understand the strength of these forces and theireffect on the properties of the QGP.

Prior to experiments in 2000 at Brookhaven NationalLaboratory’s RHIC facility, the main question was how

best to study the thermodynamics and kinetics of thequark-gluon plasma. In particular, knowing the meanfree path of particles in the plasma was important be-cause it determined whether the QGP behaved as a liq-uid or a gas. The RHIC experiments essentially an-swered these questions by observing the explosion (the“Little Bang”) created in the collision of high-energygold ions. The experiments showed that the resultingplasma could be excellently described by a hydrody-namic picture of a nearly ideal liquid, in which particleshad a mean free path that was effectively zero.

The detectors at RHIC and the LHC capture the dy-namics of the explosion by measuring the symmetry ofthe subsequent flow of particles: the radial flow (⇥0),the elliptic flow (⇥2), the triangular flow (⇥3), and so on.(These are actually the Fourier components of the flow,projected onto the harmonics ⇤cos(n�)⌅, where � is theangle that wraps around the line of collision). The com-ponents depend on the impact parameter (that is, how“head on” the colliding nuclei are), the particle types,and their transverse momenta.

At RHIC, measuring how these flow componentsvary with different experimental conditions providedinformation about matter in a temperature range be-tween 0.5Tc and 2Tc. The LHC has a higher collisionenergy than RHIC and is therefore expected to producehotter matter. Showing that this is indeed the case, acompanion paper from ALICE provides the first mea-surement of the density of charged particles producedin the collisions [3]. ALICE determined the number ofcharged particles, or “multiplicity” of a collision, as afunction of the “pseudorapidity”—a measure of the an-gle of particle trajectories with respect to the line of col-

DOI: 10.1103/Physics.3.105URL: http://link.aps.org/doi/10.1103/Physics.3.105

c� 2010 American Physical Society

1) not in line with expectations from pure ideal hydro (measured v2 increased too much)

2) not in line with simple triangular scaling

3) in line with expectations from models incorporating viscous corrections (viscous hydro, parton cascades, hybrid models) 9

First LHC v2 measurement

(GeV)NNs

1 10 210 310 410

2v

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

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ALICESTARPHOBOSPHENIXNA49CERESE877EOSE895FOPI

K. A

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LICE

Col

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ratio

n)

PRL

105,

252

302

(201

0)

beam-yη

-12 -10 -8 -6 -4 -2 0

2v

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.090-40%: event average

> 0T

p

{EP}2PHOBOS v

PRL 94, 122303 Pb-Pb 2.76 TeV{2}

2ALICE v

Au-Au 200 GeV

Au-Au 130 GeV

Au-Au 62.4 GeV

Au-Au 19.6 GeV

ALI−PREL−27811

10

v2 as function of pt

Elliptic flow as function of transverse momentum does not change much from RHIC to LHC energies, can we understand that?

K. A

amod

t et a

l. (A

LICE

Col

labo

ratio

n)

PRL

105,

252

302

(201

0)

)c (GeV/t

p0 1 2 3 4 5

{4}

2v

0.05

0.1

0.15

0.2

0.25

10-20%20-30%30-40%10-20% (STAR)20-30% (STAR)30-40% (STAR)

11

v2 as function of pt

(GeV/c)t

p0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

2v

0

0.05

0.1

0.15

0.2

0.25 = 2.76 TeV, Heinz&ShenNNsHydro prediction for Pb-Pb events at /s=0.2CGC initial conditions,

Kp

centrality 20%-40%

RHIC hydroLHC hydro

Hyd

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hen,

Hei

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nen

& S

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3226

Charged particle flow sums contributions of different mass particles which do individually change significantly as function of beam energy according to hydroThis prediction we can test

Mass dependence of v2(pt)

12

)c (GeV/T

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0.25|>1}η∆{SP, |2v

π

p

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|>2}η∆{EP, |2v

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pp+

= 2.76 TeV 10-20%NNsPb-Pb arXiv:1205.5761

ALI−PREL−30717

)c (GeV/T

p

0 1 2 3 4 5 6

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0

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0.1

0.15

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= 2.76 TeV 40-50%NNsPb-Pb arXiv:1205.5761

ALI−PREL−30721

centrality dependence clearly shows the effect of increasing radial flow

13

(GeV/c)t

p0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

2v

0

0.05

0.1

0.15

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0.25 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at (PHENIX data: Au-Au@200 GeV)

(PHENIX)-K-

(PHENIX)p|>1}{2, |

2, v±

|>1}{2, |2

, v±K|>1}{2, |

2, vp

centrality 20%-40%

RHIC hydroLHC hydro(CGC initial conditions)

/s=0.2)(

Hydro: Shen, Heinz, Huovinen & Song, arXiv:1105.3226

viscous hydro does capture energy dependence but fails quantitatively for the protons in more central collisions (both for RHIC and the LHC!)


14

viscosity (η/s)QGP = 24π =0.16 if MC-KLN initial conditions are used. So far the data yield no evidence for a changeof (η/s)QGP between RHIC and LHC that would reflect the different temperature ranges probed. Overall, the QGPliquid created in heavy-ion collisions at the LHC appears to be as strongly coupled as at RHIC energies.

0

0.1

0.2

0.3

0.4

0.5

0.6

v 2/ε

Pb+Pb @ 2.76 A TeV

5%-10%

pionskaonsprotonsVISHNU

0 1 2

Pb+Pb @ 2.76 A TeV

10%-20%


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6Pb+Pb @ 2.76 A TeV

20%-30%


0 1 2pT (GeV)0

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0.2

0.3

0.4

0.5

0.6

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30%-40%


0 1 2pT (GeV)

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40%-50%


0 1 2pT (GeV)

Pb+Pb @ 2.76 A TeV

50%-60%


FIGURE 5. (Color online) Same preliminary data from ALICE [20, 21] as in Fig. 4, but now compared with VISHNUcalculations with (η/s)QGP =0.2, using the same MC-KLN initial conditions as in Fig. 3. Shown is the eccentricity-scaled ellipticflow, i.e. v2{2}/εx{2} for the experimental data and 〈v2〉/〈εx〉 for the theoretical curves.

Acknowledgments: This work was supported by the U.S. Department of Energy under grants No. DE-AC02-05CH11231, DE-SC0004286 and (within the framework of the JET Collaboration) No. DE-SC0004104. Extensivecomputing resources provided by the Ohio Supercomputing Center are gratefully acknowledged.

REFERENCES

1. U. Heinz, Preprint arXiv:nucl-th/0512051.2. T. Hirano, U. Heinz, D. Kharzeev, R. Lacey and Y. Nara, J. Phys. G 34, S879 (2007).3. T. Hirano, U. Heinz, D. Kharzeev, R. Lacey and Y. Nara, Phys. Lett. B636, 299 (2006).4. S. A. Bass et al., Prog. Part. Nucl. Phys. 41, 255 (1998).5. H. Song, S. A. Bass and U. Heinz, Phys. Rev. C 83, 024912 (2011).6. H. Song and U. Heinz, Phys. Lett. B658, 279-283 (2008); Phys. Rev. C 77, 064901 (2008); and Phys. Rev. C 78, 024902

(2008).7. H. Song, S. A. Bass, U. Heinz, T. Hirano and C. Shen, Phys. Rev. Lett. 106, 192301 (2011).8. J.-Y. Ollitrault, A. M. Poskanzer and S. A. Voloshin Phys. Rev. C 80, 014904 (2009).9. C. Shen, S. A. Bass, T. Hirano, P. Huovinen, Z. Qiu, H. Song, U. Heinz, in Quark Matter 2011, J. Phys. G, in press (Preprint

arXiv:1106.6350 [nucl-th]).10. Z. Qiu and U. Heinz, these proceedings (Preprint arXiv:1108.1714 [nucl-th]).11. K. Aamodt et al. [ALICE Collaboration], Phys. Rev. Lett. 107, 032301 (2011).12. A. Adare et al. [PHENIX Collaboration], Preprint arXiv:1105.3928 [nucl-ex].13. Z. Qiu and U. Heinz, Phys. Rev. C 84, 024911 (2011).14. H. Song, S. A. Bass, U. Heinz, T. Hirano and C. Shen, Phys. Rev. C 83, 054910 (2011).15. C. Shen, U. Heinz, P. Huovinen and H. Song, Preprint arXiv:1105.3226 [nucl-th].16. H. Song, S. A. Bass and U. Heinz, Phys. Rev. C 83, 054912 (2011).17. K. Aamodt et al. [ALICE Collaboration], Phys. Rev. Lett. 105, 252302 (2010).18. M. Floris et al. [ALICE Collaboration], in Quark Matter 2011, J. Phys. G, in press (Preprint arXiv:1108.3257 [hep-ex]).19. T. Hirano and K. Tsuda, Phys. Rev. C 66, 054905 (2002); P. F. Kolb and R. Rapp, ibid. 67, 044903 (2003); P. Huovinen, Eur.

Phys. J. A37, 121 (2008).20. R. Snellings et al. [ALICE Collaboration], in Quark Matter 2011, J. Phys. G, in press (Preprint arXiv:1106.6284 [nucl-ex]).21. M. Krzewicki et al. [ALICE Collaboration], in Quark Matter 2011, J. Phys. G, in press (Preprint arXiv:1107.0080 [nucl-ex]).

U. Heinz, C. Shen, and H. Song arXiv:1108.5323

Hybrid calculations (VISHNU) fix the more central collisionsIs there a strong contribution from the hadronic phase?


15

)c (GeV/T

p

0 0.5 1 1.5 2 2.5 3 3.5

2v

0

0.05

0.1

0.15

0.2|>1}η∆{SP, |2v

π

K

p

s0K

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/s=0.2)ηVISH2+1 (CGC, π

Kp

Λφ

AIP Conf. Proc. 1441, 766PRC84 044903

= 2.76 TeV 10-20%NNsPb-Pb

ALI−PREL−28470


)c (GeV/T

p

0.5 1 1.5 2 2.5 3 3.5 4

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0

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0.15

0.2

0.25

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Ω

/s=0.2)ηVISH2+1 (CGC, π

Kp

ΞΩ

AIP Conf. Proc. 1441, 766PRC84 044903


ALI−DER−32328

The phi meson is also not described by pure viscous hydro The multi-strange baryons are closer to viscous hydroIs this in line with expectations from an hadronic contribution?

Scaling?

16

)c (GeV/T

p

0 1 2 3 4 5 6

2v

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

|>1}η∆{SP, |2v

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φ

|>2}η∆{EP, |2v

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pp+arXiv:1205.5761


ALI−PREL−28480

)c (GeV/q

)/n0 - mT(m

0 0.5 1 1.5 2 2.5 3

q/n

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0

0.02

0.04

0.06

0.08

0.1

|>1}η∆{SP, |2v

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pp+arXiv:1205.5761


ALI−PREL−28484

)c (GeV/T

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0 1 2 3 4 5 6

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0

0.05

0.1

0.15

0.2

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|>1}η∆{SP, |2v

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|>2}η∆{EP, |2v

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pp+


arXiv:1205.5761

ALI−PREL−28462

The phi meson follows at low-pt the mass scaling while at intermediate pt follows the pions as would be expected in a reco pictureNo KET scaling observed

Scaling?

17

(GeV/c)q)/n0-mt(m0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

q/n 2v

0

0.05

0.1

0.15 = 2.76 TeV, Heinz&ShenNNsHydro prediction for Pb-Pb events at centrality 40%-50%

hydro

K hydro

p hydro

hydro LHC(CGC initial conditions)

/s=0.2)(

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nz, H

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& S

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arX

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3226

Viscous hydro and many (most?) models do not show a universal scaling versus KET In a simple blast-wave model how well the scaling works depends on the magnitude of the transverse flow

Scaling?

18

)c (GeV/q

)/n0 - mT(m

0 0.5 1 1.5 2 2.5 3

q/n

2v

0

0.02

0.04

0.06

0.08

0.1

|>1}η∆{SP, |2v

π

p

K {SP}2v

φ

|>2}η∆{EP, |2v

π

pp+arXiv:1205.5761


ALI−PREL−28484

)c (GeV/q

)/n0 - mT(m

0 0.5 1 1.5 2 2.5 3

)q

/nπ 2

)/(v

q/n

2(v

0

0.2

0.4

0.6

0.8

1

1.2

1.4

|>1}η∆{SP, |2v

π

p

K

s0

K

Λ

{SP}2v

φ

|>2}η∆{EP, |2v

π

pp+

= 2.76 TeV 10-20%NN

sPb-Pb

ALI−DER−42469

At low pt the mass ordering of the breaking of the KET scaling in the data is in agreement with that in viscous hydro

Anisotropic Flow

19

x, b

yz

S. Voloshin and Y. Zhang (1996)

harmonics vn quantify anisotropic flow

Azimuthal distributions of particles measured with respect to the reaction plane (spanned by impact parameter vector and beam axis) are not isotropic.

vn is not an observable

20

• since the common symmetry planes cannot be measured event-by-event, we measure quantities which do not depend on it’s orientation: multi-particle azimuthal correlations

• assuming that only correlations with the symmetry plane are present - not a very good assumption (jets, resonances, etc)!

hhein(�1��2)ii = hhein(�1� n�(�2� n))ii= hhein(�1� n)ihe�in(�2� n)ii= hv2ni

hvni = hhein(�1� n)ii

v2 fluctuations

21

• If v2 fluctuates

• If

• -> fluctuations in the initial conditions change our various observables related to v2

M. Miller and RS, arXiv:nucl-ex/0312008

eccentricity

-1

-0.5

0

0.5

1 (a)

Impact parameter (b)0 2 4 6 8 10 12 14 16 18 20

eccentricity

0

0.2

0.4

0.6

0.8 >∈<1/2>2∈<1/4>4∈<1/6>6∈<

(b)

eccentricity fluctuations and its possible effect on v2 measurements:M. Miller and RS, arXiv:nucl-ex/0312008 (2003)participant eccentricityPHOBOS QM2005: Nucl. Phys. A774: 523 (2006)

v2 � �

hv2i 6=ph(v2)2i

Flow Fluctuations

22

when (2-particle) nonflow is corrected for or negligible!

in limit of “small” (not necessarily Gaussian) fluctuations

in limit of only (Gaussian) fluctuations

vn{4} = 0

vn{2} =2��v̄n

v2n{2} = v̄2n + �2vv2n{4} = v̄2n � �2v

v2n{2}+ v2n{4} = 2v̄2nv2n{2}� v2n{4} = 2�2v

xx’

y’ΨPP

ΨRP

y

23

v2 versus centrality in ALICE

centrality percentile0 10 20 30 40 50 60 70 80

2v

0

0.05

0.1

= 2.76 TeVNNsALICE Preliminary, Pb-Pb events at

(charged hadrons)2v > 0)ηΔ ({2}2v > 1)ηΔ ({2}2v

{4}2v{6}2v{8}2v

Clear separation between v2{2} and higher order cumulantsHigher order cumulant v2 estimates are consistent within

uncertainties

v2 fluctuations

24

�vnvn

⇥✓v2n{2}� v2n{4}v2n{2}+ v2n{4}

◆ 12

For more central collisions the data is between MC Glauber and MC-KLN CGC

centrality percentile0 5 10 15 20 25 30 35 40 45 50

21)/2

)2

{4}

2 -

v2

{2}

2((v

0.02

0.04

0.06

= 2.76 TeVNNsALICE Preliminary, Pb-Pb events at

ALICE


21 ))2{4

}2

+ v

2{2

}2

)/(v

2{4

}2

- v

2{2

}2

f(v) =

((v

0.2

0.4

0.6

0.8

1 = 2.76 TeVNNsALICE Preliminary, Pb-Pb events at

)2

ALICE f(v

)2MC-KLN f(

)2MC Glauber f(

>2/2/

v2 fluctuations

25


42 2

+ v

22 2v

/

42 2

- v

22 2v

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 = 2.76 TeVNNsPb-Pb > 0Tp

| < 2η |≤0

| < 4η |≤2

ALI−PREL−28061

Modeling the initial state of HIC

b

R

ri

dNgluons

d� d2b

��=0

⇥ Q2s (⇤

s,b) �⇤

s0.3 Npart

• In the CGC, multiplicities rise proportional to the (local) saturation scale

• Color electric-magnetig fields after the collision are purely longitudinal: Flux Tube picture

François Gelis

CGC

Why small-x gluons matter

Color Glass Condensate

Factorization

Stages of AA collisions

Leading Order

Leading Logs

Glasma fields

Initial color fields

Link to the Lund model

Rapidity correlations

Matching to hydro

Glasma stress tensor

Glasma instabilities

Summary

20

Glasma flux tubes

• The initial chromo-!E and !B fields form longitudinal“flux tubes” extending between the projectiles:

• Correlation length in the transverse plane: ∆r⊥ ∼ Q−1s

• Correlation length in rapidity: ∆η ∼ α−1s

• The flux tubes fill up the entire volume

Correlation length in the transverse plane:

Correlation length in rapidity

�r� � 1/Qs(x)�⇥ � 1/�s

Flux tubes

François Gelis

CGC

Why small-x gluons matter

Color Glass Condensate

Factorization

Stages of AA collisions

Leading Order

Leading Logs

Glasma fields

Initial color fields

Link to the Lund model

Rapidity correlations

Matching to hydro

Glasma stress tensor

Glasma instabilities

Summary

19

Initial classical fields, Glasma

Lappi, McLerran (2006)

• Immediately after the collision, the chromo-!E and !B fieldsare purely longitudinal and boost invariant :

0 0.5 1 1.5 2

g2µ!

0

0.2

0.4

0.6

0.8

[(g2µ)4/g2]

Bz

2

Ez

2

BT

2

ET

2

• Glasma = intermediate stage between the CGC and the

quark-gluon plasma

Introduction

Bookkeeping

Classical fields

!Diagrammatic expansion

!Retarded propagators

!Classical fields

!Gluon spectrum at LO

!Glasma

!Generating functional

Factorization

Summary

CERN

François Gelis – 2007 Lecture III / IV – Hadronic collisions at the LHC and QCD at high density, Les Houches, March-April 2008 - p. 31

Initial Glasma fields

Lappi, McLerran (2006) (Semantics : Glasma ≡ Glas[s - plas]ma)

" Before the collision, the chromo-!E and !B fields are localizedin two sheets transverse to the beam axis

" Immediately after the collision, the chromo-!E and !B fieldshave become longitudinal :

Ez = ig[

Ai1,Ai2

]

, Bz = ig"ij[

Ai1,Aj2

]

0 0.5 1 1.5 2

g2µ!

0

0.2

0.4

0.6

0.8

[(g2µ)4/g2]

Bz

2

Ez

2

BT

2

ET

2

16

Javier Albacete

The v2 fluctuations are very similar as function of η and pt

(GeV/c)T

p0 1 2 3 4 5 6 7 8

1/2

)]2

{4}

2+

v2

{EP

}2

)/(v

2{4

}2

-v2

{EP

}2

[(v

0

0.5

10-5%

5-10%

10-20%

20-30%

30-40%

40-50%

= 2.76 TeVNN

sALICE Pb-Pb

ALI−PUB−16212

ALICE: arXiv:1205.5761

26

Initial conditions and vn

6 4 2 0 2 4 66

4

2

0

2

4

6

y(fm)

x(fm)

G. Qin, H. Petersen, S. Bass, and B. Muller

initial spatial geometry not a smooth almond (for which all odd harmonics are zero due to reflection symmetry)

may give rise to higher odd harmonics versus their planes of symmetry

x, b

y z

2⇡

N

dN

d�= 1 +

1X

n=1

2vn cosn(�� n)2⇡

N

dN

d�= 1 +

1X

n=2,4,6,...

2vn cosn(�� R)

27

Shear Viscosityτ=0.4 fm/c

-10 -5 0 5 10

x [fm]

-10

-5

0

5

10

y [fm

]

0

100

200

300

400

500

600

ε [fm

-4]

τ=6.0 fm/c, ideal

-10 -5 0 5 10

x [fm]

-10

-5

0

5

10

y [fm

]

0

2

4

6

8

10

12

ε [fm

-4]

τ=6.0 fm/c, η/s=0.16

-10 -5 0 5 10

x [fm]

-10

-5

0

5

10

y [fm

]

0

2

4

6

8

10

12

ε [fm

-4]

Music, Sangyong Jeon

initial conditions ideal hydro η/s=0 viscous hydro η/s=0.16

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.5 1 1.5 2 2.5 3

v 3

η/s=0.08

η/s=0.16

pionskaons

protons

p (GeV/c)tHydro: Alver, Gombeaud, Luzum & Ollitrault, Phys. Rev. C82 (2010)

Larger η/s clearly smoothes the distributions and suppresses the higher harmonics (e.g. v3)

28

the vn’s

ALICE Collaboration, arXiv:1105.3865 PRL 107 (2011) 032301

The v3 with respect to the reaction plane determined in the ZDC and with the v2 participant plane is consistent with zero as expected if v3 is due to fluctuations of the initial eccentricity

The v3{2} is about two times larger than v3{4} which is also consistent with expectations based on initial eccentricity fluctuations centrality percentile

0 10 20 30 40 50 60 70 800

0.05

0.1

ALICE > 1}ηΔ{2, 2v > 1}ηΔ{2, 3v > 1}ηΔ{2, 4v

{4}3vRPΨ3/

v2

2Ψ3/ v×100

Alver, Gombeaud, Luzum & Ollitrault, Phys. Rev. C82 034813 (2010)/s=0.08η Glauber 3v

/s=0.16η CGC 3v

We observe significant v3 and v4 which compared to v2 has a different centrality dependence (strong constrain for η/s)

v3

29


3v

0.005

0.01

0.015

0.02

0.025

PRL 107, 032301 (2011){4}3

v

{6}3

v

c < 5 GeV/T

p≤| < 0.8 0.2 η|

= 2.76 TeVNN

sPb-Pb

ALI−PREL−29357

We observe as for v2 that v3{4} and v3{6} agree within errors and the difference of about a factor 2 between v3{2} and v3{4} and v3{6} matches that observed in Glauber calculations (indication of the number of sources?)

We can now even measure the pt dependence of v3 using higher order cumulants

)c (GeV/T

p0 1 2 3 4 5

{4}

nv

0.05

0.1

0.15

0.2

0.25

0.3

{4}2

v

10-20%

20-30%

30-40%

{4}3

v

: PRL105, 252302 (2010){4}2

v

| < 0.8η|

= 2.76 TeVNN

sPb-Pb

ALI−PREL−32788

Correlations between vn

30

centrality percentile0 10 20 30 40 50 60 70

5-p

art

icle

cum

ula

nt

-0.3

-0.2

-0.1

0

0.1

0.2

-610×

(PRL 107 (2011) 032301)〉)5

ϕ-24

ϕ-23

ϕ-22

ϕ+31

ϕcos(3〈

〉)3

ϕ-2

ϕ-1

ϕcos(2〈〉)2

ϕ-21

ϕcos(2〈-2〉)5

ϕ-4

ϕ-3

ϕ-22

ϕ+21

ϕcos(2〈

〉)3

ϕ-2

ϕ-21

ϕcos(3〈〉)2

ϕ-21

ϕcos(2〈-2〉)5

ϕ-4

ϕ-23

ϕ-22

ϕ+21

ϕcos(3〈

c < 5 GeV/T

p≤| < 0.8 0.2 η| = 2.76 TeVNN

sPb-Pb

ALI−PREL−29328

hcos(3�1 + 3�2 � 2�3 � 2�4 � 2�5)i = v23v32 cos[6( 3 � 2)]hcos(2�1 + 2�2 � 2�3 � �4 � �5)i � 2hcos(2�1 � �2 � �3)ihcos(2�1 � 2�2)i = �v32v21 cos[2( 2 � 1)]

hcos(3�1 + 2�2 � 2�3 � 2�4 � �5)i � 2hcos(3�1 � 2�2 � �3)ihcos(2�1 � 2�2)i = �v3v32v1 cos[3 3 � 2 2 � 1)]

The 5 particle cumulants allow us to cleanly measure if there is a correlations between the various planes

Conclusions• Elliptic flow measurements provided strong constraints on the bulk properties of hot

and dense matter produced at RHIC and LHC energies and have led to the new paradigm of the QGP as the so called perfect liquid

• At the LHC we observe even stronger flow than at RHIC which is expected for almost perfect fluid behavior

• viscous hydro calculations fail to describe proton v2 while hybrid models do a much better job

• does this hadronic contribution also explain the v2 of the phi meson and multi-strange baryons?

• At the LHC KET scaling is broken (but was it ever a well founded scaling?)• v2 fluctuations are in qualitative agreement with expectations from Glauber models

and rather independent of η and pt

• The measurements of v3 and higher vn’s at RHIC and at the LHC indicate that these flow coefficients behave as expected from a created system which has a small η/s

• The fluctuations can be used to do “event shape engineering” which provides new ways to compare to models

31

multi-particles

32

centrality percentile0 10 20 30 40 50 60 70

5-p

art

icle

cum

ula

nt

-0.3

-0.2

-0.1

0

0.1

0.2

-610×

(PRL 107 (2011) 032301)〉)5

ϕ-24

ϕ-23

ϕ-22

ϕ+31

ϕcos(3〈

〉)3

ϕ-2

ϕ-1

ϕcos(2〈〉)2

ϕ-21

ϕcos(2〈-2〉)5

ϕ-4

ϕ-3

ϕ-22

ϕ+21

ϕcos(2〈

〉)3

ϕ-2

ϕ-21

ϕcos(3〈〉)2

ϕ-21

ϕcos(2〈-2〉)5

ϕ-4

ϕ-23

ϕ-22

ϕ+21

ϕcos(3〈

c < 5 GeV/T

p≤| < 0.8 0.2 η| = 2.76 TeVNN

sPb-Pb

ALI−PREL−29328

)c (GeV/(a)T

p0 1 2 3 4 5

〉)c

ϕ+

2b

ϕ-3

aϕ

cos(

〈-

-50

-40

-30

-20

-10

0

-610×

0-5%

5-10%

10-20%

20-30%

30-40%

40-50%

= 2.76 TeVNN

sPb-Pb c < 5 GeV/(b,c)

T p≤| < 0.8 0.2 η|

ALI−PREL−29333

v2 and v3

33

η

-4 -3 -2 -1 0 1 2 3 4 5

nv

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09 = 2.76 TeV 30-40%NNsPb-Pb

> 0T

p

ALICE AMPT

{2}2v w. String melting

{4}2v-1 = 3.2 fmµ = 0.33, sα

{2}3v-2Lund: a = 0.5, b = 0.9 GeV

ALI−PREL−28053

η

-4 -3 -2 -1 0 1 2 3 4 5

2v

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09 = 2.76 TeVNNsPb-Pb > 0

Tp

Centrality classes: event average

2.5-15%

15-25%

25-50%

{2}2

ALICE v arXiv:1204.1409{EP}2

CMS v

ALI−PREL−27803

Event shape engineering

34

(GeV/c)T

p0 2 4 6 8 10 12 14 16 18 20

sele

cti

on

)2

(No

q{E

P}

2(S

E)/

v{E

P}

2 v

0

0.5

1

1.5

2

(VZERO-A)2

5% high q

(VZERO-A)2

10% low q

= 2.76 TeVNNsPb-Pb

|

Flow Fluctuations

• for σv

anisotropic flow at the lhc as measured by...

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