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

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

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

Method

Flow develops

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

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)

Highlights of p-Pb

Size in p-Pb vs Pb-Pb

fixed Npart = 19

p+Pb compact

p+Pb standard

0.0 0.5 1.0 1.5 2.0 2.50

12 @fmD

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

Typical evolution in p-Pb

standard compact

pPb 5020GeV Npart=19

-4 -2 0 2 4

x HyL @fmD

pPb 5020GeV Npart=19

-4 -2 0 2 4

x HyL @fmD

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

Ridge in p-Pb, ATLAS

φ∆0

)η∆,φ∆C

φ∆0

η∆)η∆,φ∆

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

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

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

< 4.0 GeVT

0.5 < p

c=0-3.4%

red - standard, blue - compact

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

v2, v3 vs CMS

0 50 100 150 200 250 300 3500

0.12p-Pb 5.02TeVCMS

|>2η∆ |22v

<20 sub.track

|>2, Nη∆ |22v

|>2 3+1D Hydroη∆ |22v

trackN

0 50 100 150 200 250 300 3500

0.04p-Pb 5.02TeVCMS

|>2η∆ |23v

<20 sub.track

|>2, Nη∆ |23v

|>2 3+1D Hydroη∆ |23v

trackN

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

LHC: v2 vs ATLAS

20 40 60 80 100 1200

0.12 p-Pb 5.02TeV ATLAS22v42v2PC2v

hydro Glauber22v hydro Glauber+NB22v hydro Glauber+NB42v

GeV⟩ EΣ ⟨

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

v2, v3 vs pT

0 1 2 3 40

0.2<150track N≤ CMS 1202nv

<20 sub.)track

CMS (N2nv 3+1D Hydro2nv

p-Pb 5.02TeVnv

[GeV/c]T

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

a) 3+1D Hydro

p-Pb 5.02 TeV

ALICE Data (preliminary)

ηdN/d

1.5 b) HIJING

-π+π

ηdN/d

Identified v2 and v3

0 0.5 1 1.5 20

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

[GeV/c]T

0 0.5 1 1.5 20

0.1p-Pb 5.02TeV 0-20%

3+1D Hydro3v

[GeV/c]T

Resonance decays affect the mass ordering in v3

α clusters

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

Generated by CamScanner from intsig.com

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

Present theory status

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

ground

Hoyle 0+

other excited, 2+ . . .

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

ground state excited

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, ...

Merge the two ideas: α’s and flow

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

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

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

(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

... more events

x [fm]

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

... more events

x [fm]

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

... more events

x [fm]

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

... more events

x [fm]

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

... more events

x [fm]

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

... more events

x [fm]

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

... more events

x [fm]

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

... more events

x [fm]

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

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

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

x [fm]

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

clustered unclustered

Constraints on 12C from EM form factor

0 1 2 3 40.000

r @fmD

0.0 0.5 1.0 1.5 2.0 2.5 3.010-5

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

12C from Wiringa’s MC

0 1 2 3 4 50.00

r (fm)

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

12C from Wiringa’s MC

0 1 2 3 4 50.00

r (fm)

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

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

x [fm]

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

Geometry of nucleus → geometry of fireball

x [fm]

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

x [fm]

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

intrinsic density of 12C → geometry of the fireball

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

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

x @fmD

(GeV/c)T

±hp0.5 1.0 1.5 2.0 2.5 3.0 3.5

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

Geometry vs multiplicity correlations in 12C-Pb

Specific feature of the 12C collisions:

The cluster plane parallel or perpendicular to the transverse plane:

higher multiplicity lower multiplicityhigher triangularity lower triangularitylower ellipticity higher ellipticity

Ellipticity and triangularity vs multiplicity

40 45 50 55 60 65 70 75 80

>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

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

Triangularity vs ellipticity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Clusters:Anticorrelation of ε2 and ε3

Dependence on the collision energy

40 45 50 55 60 65 70 75 80

0.5>3∈))/<

3∈(σ>2∈<>3∈<

=32mb, a=0.145inelNNσ

45 50 55 60 65 70 75 80 85

0.5>3∈))/<

3∈(σ>2∈<>3∈<

60 70 80 90 100 110

>3∈))/<3

∈(σ>2∈<>3∈<

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

Qualitative conclusions hold from SPS to the LHC

Other systems

Other systems (Wiringa’s distributions)

10 15 20 25 30 35 40 45 50 550.2

0.7 7Be-Pb, SPS>2∈<>3∈<>4∈<

10 15 20 25 30 35 40 45 50 550.2

0.7 9Be-Pb, SPS>2∈<>3∈<>4∈<

45 50 55 60 65 70 75 80 850.2

0.4 C-Au, RHIC>2∈<>3∈<>4∈<

45 50 55 60 65 70 75 80 850.2

0.4 O-Pb, tet., SPS>2∈<>3∈<>4∈<

45 50 55 60 65 70 75 80 850.2

0.4 O-Pb, sq., SPS>2∈<>3∈<>4∈<

[work with Maciej Rybczyński]

Conclusions

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

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

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

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