Wojciech Broniowski Jan Kochanowski U., Kielce and Inst. of … · 2014. 10. 18. ·...

52
Hydrodynamics in small and medium systems Wojciech Broniowski Jan Kochanowski U., Kielce and Inst. of Nucl. Phys. PAN, Cracow Hydrodynamics of Strongly Coupled Fluids, ECT*, 11-16 May 2014 1. p-Pb (research with P. Bożek) 2. α-clustered nucleus-A (research with E. Ruiz Arriola and M. Rybczyński) WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 1 / 51

Transcript of Wojciech Broniowski Jan Kochanowski U., Kielce and Inst. of … · 2014. 10. 18. ·...

Page 1: Wojciech Broniowski Jan Kochanowski U., Kielce and Inst. of … · 2014. 10. 18. · Hydrodynamicsinsmallandmediumsystems Wojciech Broniowski Jan Kochanowski U., Kielce and Inst.

Hydrodynamics in small and medium systems

Wojciech Broniowski

Jan Kochanowski U., Kielce and Inst. of Nucl. Phys. PAN, Cracow

Hydrodynamics of Strongly Coupled Fluids, ECT*, 11-16 May 2014

1. p-Pb (research with P. Bożek)2. α-clustered nucleus-A (research with E. Ruiz Arriola and M. Rybczyński)

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 1 / 51

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Collectivity in small and medium systems

Main questions:What is the nature of the initial state and correlations therein?What are the limits/conditions on applicability of hydrodynamics?

What is the ground state of light nuclei?

Other analyses of collectivity in small systems:

Romatschke, Luzum, arXiv:0901.4588, Prasad et al., arXiv:0910.4844,Bozek, arXiv:0911.2393, Werner et al., arXiv:1010.0400,Deng, Xu, Greiner, arXiv:1112.0470, Yan et al., arXiv: 0912.3342,Bozek, arXiv:1112.0912 Shuryak, Zahed, arXiv:1301.4470,Bzdak et al.,arXiv:1304.3403, Qin, Müller, arXiv:1306.3439,Werner et al., arXiv:1307.4379

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 2 / 51

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Method

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 3 / 51

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Flow develops

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 4 / 51

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3-stage approach

Our three-phase approach (“Standard Model of heavy-ion collisions”):

initial → hydro → statistical hadronization

(successful in description of A+A collisions)

Initial phase - Glauber model GLISSANDOHydrodynamics - 3+1 D viscous event-by-eventStatistical hadronization - THERMINATOR

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 5 / 51

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Hydrodynamics [Bożek 2011]

3+1 D viscous Israel-Stewart event-by-event hydrodynamics (viscouscorrections essential due to large gradients)

τinit = 0.6 fm/c, η/s = 0.08 (shear), ζ/s = 0.04 (bulk)Gaussian smearing of the sources, r = 0.4 fm – physical effectaverage initial temperature in the center of the fireball adjusted to fit themultiplicityrealistic equation of state (lattice + hadron gas [based on Chojnacki,Florkowski 2007])

freezeout at Tf = 150 MeV

lattice spacing of 0.15 fm (thousands of CPU hours for onereaction)

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 6 / 51

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Highlights of p-Pb

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 7 / 51

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Size in p-Pb vs Pb-Pb

fixed Npart = 19

p+Pb compact

p+Pb standard

Pb+Pb

0.0 0.5 1.0 1.5 2.0 2.50

1

2

3

4

5

6

7

<r2>

12 @fmD

dist

ribu

tion

smaller size in p-Pb → larger entropy density → more rapid expansionstandard - source positioned at the center of the nucleonscompact - source at the CM of the colliding pair

[see also Bzdak, Schenke, Tribedy, Venugopalan, arXiv:1304.3403]All in all, initial conditions in most central p-Pb not very far from those inperipheral Pb-Pb

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 8 / 51

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Typical evolution in p-Pb

standard compact

pPb 5020GeV Npart=19

-4 -2 0 2 4

1

2

3

4

5

x HyL @fmD

Τ@f

mcD

pPb 5020GeV Npart=19

-4 -2 0 2 4

1

2

3

4

5

x HyL @fmD

Τ@f

mcD

isotherms at freeze-out Tf = 150 MeV for two sections in the transverse plane

evolution lasts about 4 fm/c - shorter but more rapid than in A+A

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Ridge in p-Pb, ATLAS

φ∆0

2

4

η∆

)η∆,φ∆C

( 1

1.1

-4 -2

0

2

4

(a)

φ∆0

2

4

η∆)η∆,φ∆

C( 1

1.04

-4 -2

0

2

4

(b)

ATLAS =5.02 TeVNNsp+Pb -1bµ 1 ≈ L ∫ <4 GeV

a,b

T0.5<p<20 GeVPb

TEΣ >80 GeVPbTEΣ

φ ∆-1 0 1 2 3 4 5η ∆

-5-4-3-2-1012345

)φ ∆, η ∆C

(

0.980.99

11.011.021.031.04

<4 GeVT

c=0-3.4%, 0.5<p

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Projection on 2 ≤ |∆η| ≤ 5, ATLAS

Y (∆φ) =

∫B(∆φ)d(∆φ)

NC(∆φ) − bZYAM

The near-side ridge from our model:

φ∆0 0.5 1 1.5 2 2.5 3

)φ∆Y

(

0

0.1

0.2

0.3

0.4

0.5

0.6

< 4.0 GeVT

0.5 < p

c=0-3.4%

red - standard, blue - compact

[CGC: Dusling, Venugopalan, arXiv:1210.3890, 1211.3701, 1302.7018]

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v2, v3 vs CMS

0 50 100 150 200 250 300 3500

0.02

0.04

0.06

0.08

0.1

0.12p-Pb 5.02TeVCMS

|>2η∆ |22v

<20 sub.track

|>2, Nη∆ |22v

|>2 3+1D Hydroη∆ |22v

trackN

2v

0 50 100 150 200 250 300 3500

0.01

0.02

0.03

0.04p-Pb 5.02TeVCMS

|>2η∆ |23v

<20 sub.track

|>2, Nη∆ |23v

|>2 3+1D Hydroη∆ |23v

trackN

3v

v3 somewhat too large for lower-multiplicity collisions→ limit of validity of the model

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LHC: v2 vs ATLAS

20 40 60 80 100 1200

0.02

0.04

0.06

0.08

0.1

0.12 p-Pb 5.02TeV ATLAS22v42v2PC2v

hydro Glauber22v hydro Glauber+NB22v hydro Glauber+NB42v

GeV⟩ EΣ ⟨

2v

(NB – additional fluctuations of the strength of the sources, adjusted in such away that the experimental multiplicity distribution is reproduced)

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 13 / 51

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v2, v3 vs pT

0 1 2 3 40

0.05

0.1

0.15

0.2<150track N≤ CMS 1202nv

<20 sub.)track

CMS (N2nv 3+1D Hydro2nv

p-Pb 5.02TeVnv

[GeV/c]T

p

2v

3v

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Identified 〈pT 〉[Bożek, WB, Torrieri, PRL 111 (2013) 172303]

20 40

0

0.5

1

1.5 >

[G

eV]

< p

a) 3+1D Hydro

p-Pb 5.02 TeV

ALICE Data (preliminary)

ηdN/d

20 40

0

0.5

1

1.5 b) HIJING

-π+π

-K+K

pp

ηdN/d

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Identified v2 and v3

0 0.5 1 1.5 20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18 p-Pb 5.02TeV ALICE Data 0-20%

πKp

2v

[GeV/c]T

p

0 0.5 1 1.5 20

0.05

0.1p-Pb 5.02TeV 0-20%

πKp

3+1D Hydro3v

[GeV/c]T

p

Resonance decays affect the mass ordering in v3

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α clusters

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Some history

David Brink: After Gamow’s theory of α-decay it was natural to investigatea model in which nuclei are composed of α-particles. Gamow developed arather detailed theory of properties in his book "Constitution of Nuclei"published in 1931 before the discovery of the neutron in 1932. He supposedthat 4n-nuclei like 8Be, 12C, 16O ... were composed of α-particles

Gen

erat

ed b

y C

amS

cann

er fr

om in

tsig

.com

Generated by CamScanner from intsig.com

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Shell model (and its problems)

Eugene Wigner, Maria Goeppert-Mayer, Hans Jensen, Nobel in 1963

Michael P. Carpenter: However, in the 1960s, excited states in nuclei thatcomprise equal numbers of protons and neutrons, (e.g., 12C and 16O) wereidentified that could not be described by the shell model, and it wassuggested by Ikeda and others that these states could be associated withconfigurations composed of α particles

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Present theory status

9Be 12C[M. Freer: WPCF13, H. Fynbo+Freer: Physics 4 (2011) 94]

ground

Hoyle 0+

other excited, 2+ . . .

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16O

Ab initio calculations of 16O with chiral NN force (Juelich 2014)→ strong α clusterization

ground state excited

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Computational techniques

(massive effort)

Funaki et al.: certain states in self-conjugated nuclei ... can be described asproduct states of α particles, all in the lowest 0S state. We define a stateof condensed α particles in nuclei as a bosonic product state in goodapproximation, in which all bosons occupy the lowest quantum state of thecorresponding bosonic mean-field potential (αBEC)

Another approach: Fermionic Molecular Dynamics (FMD)

Quantum Variational Monte Carlo (with 2- and 3-body forces) for A=2-12[R. Wiringa et al., http://www.phy.anl.gov/theory/research/density/]

All approaches to light nuclei give clusters

Goal (not yet accurately reached):reproduce ground-state energy, excitation spectrum, EM form factor, ...

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 22 / 51

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Merge the two ideas: α’s and flow

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 23 / 51

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From α clusters to flow in relativistic collisions

[WB, Ruiz Arriola, PRL 112 (2014) 112501]

α clusters → asymmetry of shape → asymmetry of initial fireball →→ hydro or transport → collective harmonic flow

Generated by CamScanner from intsig.com

nuclear triangular geometry → fireball triangular geometry → triangular flow

What are the signatures, chances of detection?

Related idea: triton/3He–Au at RHIC in 2015 [Sickles (PHENIX) 2013]The case of light nuclei is more promising, as it leads to abundant fireballs

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 24 / 51

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12C-208Pb – single event

why ultrarelativistic?reaction time is much shorter than time scales of the structure→ a frozen “snapshot” of the nuclear configuration

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

5

(Nw > 70 - flat-on orientation)

Imprints of the three α clusters clearly visible

[simulations with GLISSANDO 2]WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 25 / 51

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... more events

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

5

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 26 / 51

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... more events

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

5

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 27 / 51

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... more events

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

5

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 28 / 51

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... more events

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

5

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 29 / 51

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... more events

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

5

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 30 / 51

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... more events

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

5

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 31 / 51

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... more events

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

5

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 32 / 51

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... more events

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

5

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 33 / 51

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The meaning of intrinsic

Ground state of 12C is a 0+ state (rotationally symmetric wave function).The meaning of deformation concerns multiparticle correlations betweenthe nucleons

Superposition over orientations:

|Ψ0+(x1, . . . , xN )〉 =1

∫dΩΨintr(x1, . . . , xN ; Ω)

The intrinsic density of sources of rank n is defined as the average overevents, where the distributions in each event have aligned principal axes:f intrn (~x) = 〈f(R(−Φn)~x)〉. Brackets indicate averaging over events andR(−Φn) is the inverse rotation by the principal-axis angle in each event

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 34 / 51

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Back to 12C – intrinsic density

Intrinsic distributions in 12C: three α’s in a triangular arrangement

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

x [fm]

-4 -3 -2 -1 0 1 2 3 4y

[fm]

-4

-3

-2

-1

0

1

2

3

4

0

0.01

0.02

0.03

0.04

0.05

0.06

clustered unclustered

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 35 / 51

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Constraints on 12C from EM form factor

0 1 2 3 40.000

0.005

0.010

0.015

r @fmD

ΡHrL

@fm-

3D

0.0 0.5 1.0 1.5 2.0 2.5 3.010-5

10-4

0.001

0.01

0.1

1

q @fm-1D

Fem2HqL

Electric charge density (dashed line) and the corresponding distribution ofthe centers of protons (solid line) in 12C for the data plotted against theradius, for the BEC calculation – agrees with the experimental data for thecharge form factor

Central depletion naturally explained with the hole between the clusters

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 36 / 51

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12C from Wiringa’s MC

0 1 2 3 4 50.00

0.02

0.04

0.06

0.08

0.10

0.12

r (fm)

ρ(r)

(fm

-3)

12C(0+) - AV18+UX

ρp rms p = 2.35

Distribution of the centers of protons = neutrons in 12C

smaller central depletion

GLISSANDO implements these clustered distributions→ carry out detailed simulations

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 37 / 51

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12C from Wiringa’s MC

0 1 2 3 4 50.00

0.02

0.04

0.06

0.08

0.10

0.12

r (fm)

ρ(r)

(fm

-3)

12C(0+) - AV18+UX

ρp rms p = 2.35

Distribution of the centers of protons = neutrons in 12C

smaller central depletion

GLISSANDO implements these clustered distributions→ carry out detailed simulations

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 37 / 51

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12C–208Pb collision

Intrinsic distributions in the transverse plane of the fireball (here withNw > 70 – large multiplicity enforcing the flat-on collision)

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

x [fm]

-4 -3 -2 -1 0 1 2 3 4y

[fm]

-4

-3

-2

-1

0

1

2

3

4

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

clustered unclustered

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 38 / 51

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Geometry of nucleus → geometry of fireball

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

x [fm]

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

y [fm

]

-4

-3

-2

-1

0

1

2

3

4

intrinsic density of 12C → geometry of the fireball

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 39 / 51

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Eccentricity parameters

Eccentricity parameters εn (Fourier analysis)

εneinΦn =

∑j ρ

nj einφj∑

j ρnj

describe the shape of each event (j labels the sources in the event,n=rank, Φn is the principal axis angle)

Two components:

internal (from existent mean deformation of the fireball)from fluctuations

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 40 / 51

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Digression: d-A by Bożek

The deuteron has an intrinsic dumbbell shape with very large deformation:rms ' 2 fm

Initial entropy density in a d-Pb collision with Npart = 24 [Bożek 2012]

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

x @fmD

y@f

mD

(GeV/c)T

±hp0.5 1.0 1.5 2.0 2.5 3.0 3.5

2v

0.00

0.05

0.10

0.15

0.20

0.25

0.30 [0.48,0.7]∈|η∆PHENIX, 200 GeV, d+Au, 0-5%, | [2,5]∈|η∆ATLAS, 5.02 TeV, p+Pb, 0-2%, | [0.48,0.7]∈|η∆PHENIX, 200 GeV, d+Au, 0-5%, |

[2,5]∈|η∆ATLAS, 5.02 TeV, p+Pb, 0-2%, |

Bozek, priv. comm.,Bzdak, et al. 1304.3403, priv comm:

= 20part

/s = 0.08, IP-Glasma, Nη = 20

part/s = 0.08, MC-Glauber, Nη

=200 GeVNNshydro., d+Au

Resulting large elliptic flow confirmed with the later RHIC analysisWB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 41 / 51

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Geometry vs multiplicity correlations in 12C-Pb

Specific feature of the 12C collisions:

Generated by CamScanner from intsig.com

The cluster plane parallel or perpendicular to the transverse plane:

higher multiplicity lower multiplicityhigher triangularity lower triangularitylower ellipticity higher ellipticity

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 42 / 51

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Ellipticity and triangularity vs multiplicity

wN

40 45 50 55 60 65 70 75 80

0.2

0.25

0.3

0.35

0.4

0.45

0.5

wN

40 45 50 55 60 65 70 75 80

0.2

0.25

0.3

0.35

0.4

0.45

0.5

>2∈)/<2

∈(σ>3∈))/<

3∈(σ>2∈<>3∈<

clustered unclusteredClusters:When Nw then 〈ε3〉 and 〈ε2〉

and 〈σ(ε3)/ε3〉 , 〈σ(ε2)/ε2〉 tending to√

4/π − 1 ∼ 0.52

No clusters:similar behavior for n = 2 and n = 3

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 43 / 51

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Shape-flow transmutation

The eccentricity parameters are transformed (in all models based oncollective dynamics) into asymmetry of the transverse-momentum flowIt has been found that

〈vn〉 grows with 〈εn〉

→ for 12C collisions v3 should grow with multiplicity even stronger than ε3

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 44 / 51

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Triangularity vs ellipticity

2∈

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

3∈

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2∈

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

3∈

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

1

2

3

4

5

6

7

clustered unclustered

Clusters:Anticorrelation of ε2 and ε3

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 45 / 51

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Dependence on the collision energy

wN

40 45 50 55 60 65 70 75 80

0.2

0.25

0.3

0.35

0.4

0.45

0.5>3∈))/<

3∈(σ>2∈<>3∈<

=32mb, a=0.145inelNNσ

wN

45 50 55 60 65 70 75 80 85

0.2

0.25

0.3

0.35

0.4

0.45

0.5>3∈))/<

3∈(σ>2∈<>3∈<

=42mb, a=0.145inelNNσ

wN

60 70 80 90 100 110

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

>3∈))/<3

∈(σ>2∈<>3∈<

=73mb, a=0.12inelNNσ

32mb (SPS) 42mb (RHIC) 72mb (LHC)

Qualitative conclusions hold from SPS to the LHC

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 46 / 51

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Other systems

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 47 / 51

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Other systems (Wiringa’s distributions)

wN

10 15 20 25 30 35 40 45 50 550.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7 7Be-Pb, SPS>2∈<>3∈<>4∈<

wN

10 15 20 25 30 35 40 45 50 550.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7 9Be-Pb, SPS>2∈<>3∈<>4∈<

wN

45 50 55 60 65 70 75 80 850.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4 C-Au, RHIC>2∈<>3∈<>4∈<

wN

45 50 55 60 65 70 75 80 850.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4 O-Pb, tet., SPS>2∈<>3∈<>4∈<

wN

45 50 55 60 65 70 75 80 850.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4 O-Pb, sq., SPS>2∈<>3∈<>4∈<

[work with Maciej Rybczyński]

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 48 / 51

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Conclusions

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 49 / 51

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Is there collectivity in p-Pb?

Collective dynamics is compatible with the high-multiplicity soft LHC datafor p-Pb

Large v2 and v3 coefficients measured in p-Pb reasonably reproduced,including the pT dependenceModel 2D correlations exhibit the two ridges, in particular thenear-side ridgeMass ordering in 〈pT 〉 and flow coefficients reproduced

Numerous effects should still be incorporated (jets, core-corona, ...)– more important for the lower-multiplicity events

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 50 / 51

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α clusters

Clustered geometry of the ground state → harmonic flow

Best signatures of 12C-208Pb collisionsIncrease of triangularity with multiplicity for the highest multiplicityeventsDecrease of scaled variance of triangularity with multiplicity for thehighest multiplicity eventsAnticorrelation of ellipticity and triangularity

Extensions (in progress)Other systems, more detailed modeling involving e-by-e hydro

Possible future data (NA61, RHIC?) in conjunction with a detailedknowledge of the dynamics of the evolution of the fireball would allow toplace constrains on the α-cluster structure of the colliding nuclei.Conversely, the knowledge of the clustered nuclear distributions may helpto verify the fireball evolution models

WB (UJK, IFJ PAN) hydro for light and medium ECT* 2014 51 / 51