wojciech broniowski · standardmodeloflittlebangs wojciech broniowski ifj pan & ujk ncbj,...

Standard Model of Little Bangs

Wojciech Broniowski

IFJ PAN & UJK

NCBJ, 27.03.17

WB (IFJ PAN & UJK) SM of Little Bangs NCBJ, 27.03.17 1 / 43

Little Bangs


[U. Heinz 2000]: analogous to . . . Big Bang . . . the Hubble expansion (which goeson until today), the cosmic microwave background of thermal photons (whichdecoupled when our universe was about 300,000 years old), and the measuredabundances of light atomic nuclei . . .


Analogy of fluctuations in Little Bangs to the Face of God – the CMBinhomogeneities, originating from primordial fluctuations during the inflationphase


3 stages of the “Standard Model”

time −→partons hydrodynamization quark-gluon plasma freeze-out hadrons

1 Initial pre-equilibrium dynamics: instabilities [Mrówczyński 1988],AdS/CFT [. . . Janik, Heller, Spaliński . . . ], color glass condensate,wounded nucleon model [Białas, Błeszyński, Czyż 1976]

2 Collective evolution: hydrodynamics, large anisotropy [. . . Florkowski,Ryblewski . . . ], viscous, event-by-event [. . . Bożek . . . ]

3 Freeze-out and production of hadrons (hydrodynamics takes care ofthis by passing through the cross over, supported by the thermalmodel for hadron yields) [. . . Kraków, Wrocław . . . ]


Collectivity


Initial geometry

Au+Au collision at RHIC(view along the beam)

-10 -5 5 10x

-6

-4

-2

2

4

6

8

y

1 Participants determine the geometryof the overlap region

2 Initial entropy distribution in moremicroscopic approaches (IP Glasma)also follows the geometry of theoverlap region

3 Strong radial flow4 Initial eccentricity → anisotropic flow

of hadrons [Ollitrault 1992]


Initial geometry

Au+Au collision at RHIC(view along the beam)

-7.5 -5 -2.5 2.5 5 7.5x

-7.5

-5

-2.5

2.5

5

7.5

y

1 Participants determine the geometryof the overlap region

2 Initial entropy distribution in moremicroscopic approaches (IP Glasma)also follows the geometry of theoverlap region

3 Strong radial flow4 Initial eccentricity → anisotropic flow

of hadrons [Ollitrault 1992]


Rescattering/collectivity essential

[ALICE]

dN/dφ = A

(1 + 2

∑n

vn cos[n(φ−Ψn)]

)WB (IFJ PAN & UJK) SM of Little Bangs NCBJ, 27.03.17 7 / 43

Fluctuations

Collapse of the nuclear wavefunction → each Little Bangdifferent

-7.5 -5 -2.5 2.5 5 7.5x

-7.5

-5

-2.5

2.5

5

7.5

y 1 Higher Fourier components appear2 Odd harmonics also show up,

triangular flow3 Fluctuations dominant for central

A+A and for small systems, such asp+A

New thinking since [Miller and Snellings 2003]


Collectivity: shape/size – flow transmutation


Doppler effect

Emission from a fast movingelement of fluidCollimation of hadrons(increasing with mass)Thermal motion

Scan

ned

by C

amSc

anne

r

Multi-particle correlations in the azimuth are used in cumulant methods toextract flow coefficients without the non-flow contamination from jets orresonance decays

[Borghini, Ollitrault 2001]


Signatures of flow

1 Mass ordering in pT spectra from radial flow2 Mass ordering of harmonic flow coefficients vn3 Higher harmonics suppressed4 Near-side ridge (discussed later on) - the real “proof” of harmonic flow


Role of viscosity

perfect shear shear+bulk

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 0.5 fm/c, ideal

50

100

150

200

250

300

350

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 0.5 fm/c, shear

50

100

150

200

250

300

350

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 0.5 fm/c, shear/bulk

50

100

150

200

250

300

350

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 2 fm/c, ideal

5

10

15

20

25

30

35

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 2 fm/c, shear

5

10

15

20

25

30

35

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 2 fm/c, shear/bulk

5

10

15

20

25

30

35

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 6 fm/c, ideal

1

2

3

4

5

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 6 fm/c, shear

1

2

3

4

5

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]


1

2

3

4

5

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 10 fm/c, ideal

0.1

0.2

0.3

0.4

0.5

0.6

0.7

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]

= 10 fm/c, shear

0.1

0.2

0.3

0.4

0.5

0.6

0.7

5 0 5x [fm]

8

6

4

2

0

2

4

6

8

y[fm

]


0.1

0.2

0.3

0.4

0.5

0.6

0.7

Quenching of flow withviscosityIncreasing with theFourier rankSets limits on viscosity,which is close to the KSSbound η/s = 1/4π

... but many other modelparameters

Figure:[Bazow, Heinz, Strickland 2016]


Event-by-event pT fluctuations


Size – radial flow transmutation

smaller size → stronger flowlarger size → weaker flow

[WB, Chojnacki, Obara 2009]


E-by-e size fluctuations

[Bożek, WB 2012]

Same number of participants, NW = 100

Different size (and shape)


Transverse momentum fluctuations in Au+Au@200GeV

STAR PHENIXred points – model

Measure removes trivial fluctuations from finite sampling

Model overshoots the data by about 50% for most central collisions

Hydro response not modified by viscosity, freeze-out temperature, smearing,core-corona, total momentum conservation, centrality definition∆〈pT 〉/〈〈pT 〉〉 ' 0.4∆〈r〉/〈〈r〉〉Need to decrease the fluctuations in the initial state


Transverse momentum fluctuations with wounded quarks

Wounded quark model as implemented in [Bożek, WB, Rybczyński 2016]:more participants → less fluctuation

●●

●

●

●

■

■■

■■■

[email protected]

● quarks

■ nucleons

● ALICE

○○□□ [email protected]

○ quarks

□ nucleons

0 500 1000 15000.00

0.01

0.02

0.03

0.04

0.05

0.06

dNch/dη

<ΔpTΔpT>1/2/<<pT>>

[Bożek, WB 2017]



Wounded quark model as implemented in [Bożek, WB, Rybczyński 2016]:more participants → less fluctuation

●

●

●

●

●

■

■■

■■■

[email protected]

● quarks

■ nucleons

● ALICE

○○□□

[email protected]

(a)

○ quarks

□ nucleons

10 50 100 500 1000

0.01

0.02

0.05

0.10

dNch/dη

<ΔpTΔpT>1/2/<<pT>>

[Bożek, WB 2017]



Nontrivial dependence on multiplicity

●

●

●●

●

■■

■

■

■

■

○○□□

(b)

0 500 1000 1500

0.2

0.3

0.4

0.5

0.6

dNch/dη

<ΔpTΔpT>1/2(dNch/dη)1

/2/<<pT>>

Excludes independent production from sources (would be flat)


Size – flow anti-correlation

Very strong e-by-e anti-correlation of size and 〈pT 〉

▫

▫▫

▫

▫

▫

▫

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▫

Pb+Pb 10-20%(b)

quarksnucleons

-0.2 -0.1 0.0 0.1 0.2-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

Δ(<r>/N1/3)/<<r>/N1/3>

<ΔpT>/<<pT>>

This is the mechanism for pT fluctuations!


Back to harmonic flow . . .


Proportionality of flow to eccentricity

0.1 0.2 0.3 0.4 0.5 0.6ǫ2

0.02

0.04

0.06

0.08

0.10

v 2

c(ǫ2 ,v2 ) =0.996

C2 =0.153

sWN η/s=0.16

20−30 %

(c)

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40ǫ3

0.005

0.010

0.015

0.020

0.025

0.030

0.035

v 3

c(ǫ3 ,v3 ) =0.973

C3 =0.093

sWN η/s=0.16

20−30 %

(c)

[Niemi, Denicol, Holopainen, Huovinen 2012]

vn = κnεn

Allows us to build scale-less combinations independent of the responsecoefficient κn


Flow fluctuations

←√

4/π − 1

[WB 2007]


Flow fluctuations

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300 350 400

σ(vn

)/〈v n〉

Nw

σ (v2) /〈v2〉σ (v3) /〈v3〉

σ (ε2) /〈ε2〉 (mixed+Γ)σ (ε3) /〈ε3〉 (mixed+Γ)σ (ε2) /〈ε2〉 (mixed)σ (ε3) /〈ε3〉 (mixed)

←√

4/π − 1

[ WB, Rybczyński 2016]


Flow fluctuations

Fn =

√εn{2}2 − εn{4}2εn{2}2 + εn{4}2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 50 100 150 200 250 300 350 400

F

Nw

F (v2) (ALICE)F (v2) (CMS)F (v2) (ATLAS cum.)F (v2) (ATLAS EbyE)

F (ε2) (mixed+Γ)F (ε2) (mixed)

[ WB, Rybczyński 2016]WB (IFJ PAN & UJK) SM of Little Bangs NCBJ, 27.03.17 22 / 43

Flow fluctuations

Fn =

√εn{2}2 − εn{4}2εn{2}2 + εn{4}2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 50 100 150 200 250 300 350 400

F

Nw

F (v3) (ATLAS)F (v3) (CMS)

F (ε3) (mixed+Γ)F (ε3) (mixed)

[ WB, Rybczyński 2016]WB (IFJ PAN & UJK) SM of Little Bangs NCBJ, 27.03.17 22 / 43

Going longitudinal


Non-flow events


Factorization of the transverse and longitudinal distributions

left-moving participants strings right-moving participants


Factorization of the transverse and longitudinal distributions

left-moving participants strings right-moving participants

Approximate (up to fluctuations) alignment of F and B event planesCollimation of flow at very distant longitudinal separations → ridges!


Surfers - the near-side ridge


Ridge

Near-side ridge indicates collectivity

Total surprise in p-p!


Triangles

Extracted from the d-Au collisions at RHIC:

[Białas, Czyż 2004]

Source emits mostly in its own froward hemisphereWB (IFJ PAN & UJK) SM of Little Bangs NCBJ, 27.03.17 28 / 43

Triangles


Triangles

[. . . Bierlich, Gustafson, Lönnblad 2016, Monnai, Schenke 2015, Schenke,Schlichting 2016 . . . Brodsky, Gunion, Kuhn, 1977]


Torque


Torque effect (event-by-event)

Transverse sections with triangles e-by-e longitudinal twist (a few degrees)

Scan

ned

by C

amSc

anne

r

Both e-by-e fluctuations and longitudinal asymmetry of the emissionprofile needed

[prediction in PB, WB, Moreira 2010 & PB, WB, Olszewski 2015, PB, WB 2016]


Fluctuating strings


Torque in Pb+Pb

aη0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

)b η,a η( nr

0.8

0.85

0.9

0.95

1 < 5bη(b) c=20-30% [email protected] 4.4 <

thin - trianglesthick - string breaking

v2 and v3

rn(ηa, ηb) =〈〈cos(n[φi(−ηa)− φj)ηb)])〉〉〈〈cos(n[φi(ηa)− φj)ηb)])〉〉


Torque in p-Pb

aη0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

)b η,-a η

(- 2)

rb η,a η( 2r

0.7

0.75

0.8

0.85

0.9

0.95

1

< 150offlinetrk

CMS, 120 < Ntorque model, c=0-3.4%model w/ no length fluct.

< 5bη [email protected] 4.4 <

String breaking essential to describe torque in p-Pb

With triangles:

Scan

ned

by C

amSc

anne

r


Slope of rn

●●●●●●●●

●

● ■■■

■■■■■

▽▽▽▽

▽

▲▲▲

● n=2, Pb+Pb

■ n=3, Pb+Pb

▽ n=2, p+Pb

▲ n=4 (x1/4), Pb+Pb

200 500 1000 2000 50000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Ntrk

Fnη

Fair description of mid-central collisionsWay too much decorrelation in central collisionsF4 ' 4F2


Small systems


d-A

d has an intrinsic dumbbell shape with a 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 analysis(geometry + fluctuations)


Collectivity in p+A

Practically no geometry, only fluctuations

0 50 100 150 200 250 300 3500

0.02

0.04

0.06

0.08

0.1

0.12p-Pb 5.02TeVCMS

|>2η∆ |{2}2v

<20 sub.track

|>2, Nη∆ |{2}2v

|>2 3+1D Hydroη∆ |{2}2v

trackN

2v

[Bożek, WB, Torrieri 2013]


Collectivity in p+A

Practically no geometry, only fluctuations

0 50 100 150 200 250 300 3500

0.01

0.02

0.03

0.04p-Pb 5.02TeVCMS

|>2η∆ |{2}3v

<20 sub.track

|>2, Nη∆ |{2}3v

|>2 3+1D Hydroη∆ |{2}3v

trackN

3v

[Bożek, WB, Torrieri 2013]


3He-Au at RHIC

φ∆1− 0 1 2 3 4 5η∆

3.8−3.6−

3.4−3.2−

3−

)φ∆, η∆C

(

0.980.99

11.011.021.03

a) Au-side 0-5%

φ∆1− 0 1 2 3 4 5η∆

33.2

3.43.6

3.84

)φ∆, η∆C

(

0.980.99

11.011.021.03

He-side 0-5%3b)

● ●●

●● ●

●●

● ●●

●

●

●● ●

●

●

●

●●

□□□□□

□□□

□□□□

□

□□

□□

□□□

□□□□□

a) Au-side 0-5%

-3.7<η assoc<-3.1

● PHENIX Data

0.98

0.99

1.00

1.01

1.02

C(Δϕ)

● ● ● ● ● ● ● ● ● ●●

●●

● ● ●●

●●

●●□□□

□□□□

□□□□

□□□

□□□□□□

□

□□□

□

b) 3He-side 0-5%

1GeV<pT,trig <3GeV, |η trig |<0.350.1GeV<pT,assoc<5GeV, 3.1<η assoc<3.9

□ 3+1D hydro

-1 0 1 2 3 4

0.98

0.99

1.00

1.01

1.02

Δϕ

C(Δϕ)

(seen on both pseudorapidity sides) [Bożek, WB 2015]WB (IFJ PAN & UJK) SM of Little Bangs NCBJ, 27.03.17 38 / 43

12C-Pb – role of α clusters

Nuclear structure from ultra-relativistic collisions!Probe to what degree 12C is made of three α’s

Specific features of the 12C collisions with a “wall”:

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


Ellipticity and triangularity vs multiplicity

wN

20 30 40 50 60 70 80

0.2

0.25

0.3

0.35

0.4

0.45

0.5wounded nucleon model

> (BEC)22∈<> (BEC)2

3∈<> (uniform)2

2∈<> (uniform)2

3∈<

10% 1% 0.1%

wounded nucleon model


Ellipticity and triangularity vs multiplicity

wN

20 30 40 50 60 70 80

0.5

0.6

0.7

0.8

0.9

1

(wounded){2}n/v{4}nv

n=2, BECn=3, BECn=2, VMCn=3, VMC

10%

1%0.1%

(wounded){2}n/v{4}nv


Conclusions


Conclusions

Standard model (almost) works!Collectivity in A+A beyond doubtExplanation of the near-side ridgeCognitive role of e-by-e fluctuationsMechanism for pT fluctuations (seem too much for central)Torque (event-plane angles decorrelation)Torque in p-Pb → longitudinal fluctuations (string breaking). . .

Not mentioned:

Jet quenching by the mediumEarly probesFemtoscopyChiral magnetic effectVorticity and Λ polarization. . .

[RHIC simulation, Pang et al. 2016]


Thank you!


wojciech broniowski · standardmodeloflittlebangs wojciech broniowski ifj pan & ujk ncbj,...

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