collective flow in 2.76 and 5.02 a tev pb+pb...

Collective flow in 2.76 and 5.02 A TeV Pb+Pb collisions

Wenbin Zhao

Collaborators: Haojie-Xu, Huichao SongarXiv:1703.10792Peking University

July 25th 2017

Wenbin Zhao (Collaborators: Haojie-Xu, Huichao Song arXiv:1703.10792 Peking University)Collective flow in 2.76 and 5.02 A TeV July 25th 2017 1 / 36

Outline

1 Introduction

2 Motivation

3 Model and Set up

4 Results and Discussion

5 Summary


Introduction

Introduction


Introduction

The process of heavy-ion collisions

U. W. Heinz, hep-ph/0407360.Wenbin Zhao (Collaborators: Haojie-Xu, Huichao Song arXiv:1703.10792 Peking University)Collective flow in 2.76 and 5.02 A TeV July 25th 2017 4 / 36

Introduction

Collective flow

Pressure gradients (larger in -plane) push bulk “out”− >”flow”:

leading to the “double peaks” structure:

The internal pressure gradientslead to strong anisotropic flow.


Introduction

Higher order flow harmonics

In experimental, the initial statesfluctuate event-by-event.

One can get higher order flow harmonics by Fourier unfolding of thefinal observed momentum distribution dN/(pTdpTdydφ):

dNi

pTdpTdydφ=

1

2π

dNi

pTdpTdy[1 + 2v i2(pT )cos(2φp)

+ 2v i3(pT )cos(3φp) + 2v i4(pT )cos(4φp) + ...]. (1)


Introduction

Other flow observables

Many other detailed flow observables can reflect the fluctuations ofinitial states, non-linear response, flow angle correlations,mode-coupling effects and factorizations breaking effects of thesystem:

event-by-event vn distributionsevent-plane correlationsSymmetric Cumulantnon-linear response coefficientsflow factorizations ratio

A systematic study of these flow observables can help to test themodel calculations and the extracted QGP viscosity as well as tofurther evaluate and constrain the initial condition models.


Motivation

Collective flow in 2.76 and 5.02 ATeV Pb+Pb collisions


Motivation

Motivationintegrated-vn

Centrality percentile0 10 20 30 40 50 60 70 80

nv

0.05

0.1

0.15 5.02 TeV|>1}η∆{2, |2 v|>1}η∆{2, |3 v|>1}η∆{2, |4 v

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

2.76 TeV|>1}η∆{2, |2 v|>1}η∆{2, |3 v|>1}η∆{2, |4 v

{4}2 v

5.02 TeV, Ref.[27]|>1}η∆{2, |2 v|>1}η∆{2, |3 v

ALICE Pb-Pb Hydrodynamics

(a)


Rat

io

1

1.1

1.2 /s(T), param1η/s = 0.20η

(b)

Hydrodynamics, Ref.[25]2 v 3 v 4 v


Rat

io

1

1.1

1.2

(c)

vn(pT ) for all charged

0 1 2 3 4 5

| >

1.0

}η ∆

{2, |

nv

0

0.1

0.2

5.02 TeV|>1}η∆{2, |2v|>1}η∆{2, |3v|>1}η∆{2, |4v

2.76 TeV|>1}η∆{2, |2v|>1}η∆{2, |3v|>1}η∆{2, |4v

ALICE Pb-Pb 0-5% (a)

)c (GeV/T

p0 1 2 3 4 5

| >

1.0

}η ∆

{2, |

nv

0

0.1

0.2

30-40% (b)

ALICE PRL 13, 132302 (2016)

These can fix parameters in hydro model then to calculate otherobservables.


Model and Set up

Model and Set up


Model and Set up

Heavy-ion collisions process:

Hydrodynamics simualtions:

C. Shen, Z. Qiu, H. Song, J. Bernhard, S. Bass and U. Heinz. Comput. Phys.Commun. 199, 61 (2016)


Model and Set up

VISHNU hybrid model

For hydrodynamics part, VISHNU solves Tµν , πµν and Π:

∂µTµν(x) = 0, Tµν = euµuν − (p + Π)∆µν + πµν ,

Π̇ = − 1

τΠ

[Π + ζθ + ΠζT∂µ

(τΠuµ

2ζT

)], (2)

∆µα∆νβπ̇αβ = − 1

τπ

[πµν − 2η∇〈µuν〉 + πµνηT∂α

(τπuα2ηT

)],

Switch from hydrodynamics to hadron cascade (Cooper-Frye formula):

Ed3Ni

d3p(x) =

gi(2π)3

p · d3σ(x) fi (x , p) (3)

Hadron cascade simulated by UrQMD by:

dfi (x , p)

dt= Ci (x , p) (4)

H. Song, S. A. Bass and U. Heinz, PRC 83, 024912 (2011).C. Shen, Z. Qiu, H. Song, J. Bernhard, S. Bass and U. Heinz, Comput. Phys.Commun. 199, 61 (2016)


Model and Set up

Initial conditions

TRENTo parameterizes initial entropy density by:

s = s0

(T̃ pA + T̃ p

B

2

)1/p

. (5)

where T̃ (x , y) =∑Npart

i=1 γi Tp(x − xi , y − yi ),

Tp(x , y) = 12πw2 exp(− x2+y2

2w2 ) and turing p makes TRENTo match KLN,EKRT, WN, etc.

AMPT construct energy density by energy decompositions of individualpartons via a Gaussian smearing:

ε = K∑i

E ∗i2πσ2τ0∆ηs

exp (−(x − xi )2 + (y − yi )

2

2σ2), (6)

J. S. Moreland, J. E. Bernhard and S. A. Bass, PRC 92 (2015) no.1, 011901.H. j. Xu, Z. Li and H. Song, PRC 93, no. 6, 064905 (2016)


Model and Set up

Set up

iEBE-VISHNU + TRENTo / AMPT

TRENTo : η/s(T ) and ζ/s(T ) (para-I) .

AMPT: η/s ≡ 0.08 and ζ/s ≡ 0 (para-II).

/sη /sζ

T [GeV] T [GeV]0.15 0.2 0.25

0

0.1

0.2

0.3

0.4

(a)

Ι

ΙΙ

/s(T)η Ι 0.08≡/sη ΙΙ

0.15 0.2 0.25

Ι

ΙΙ

/s(T)ζ Ι 0.0≡/sζ ΙΙ

(b)


Results and Discussion




pT -spectra for 2.76 A TeV

(GeV)T

p

Pb + Pb 2.76 A TeV

0 0.5 1 1.5 2

The

ory/

Exp

.

0.6

0.8

1

1.2

0.5 1 1.5 2

The

ory/

Exp

.

0.6

0.8

1

1.2

0.5 1 1.5 2

The

ory/

Exp

.0.6

0.8

1

1.2

0.5 1 1.5 2

The

ory/

Exp

.

0.6

0.8

1

1.2

0 0.5 1 1.5 2

]-2 )c

dy)

[(G

eV/

Tp

/(d

N2)d

Tpπ

1/(2

1

10

210

310

10-20%

π

K

P

(a)

π K p

ALICE DATA2.76 A TeV

0.5 1 1.5 2

{2}

nv

-110

1

10

210

310

20-30%

π

K

P

(b)

π K p

iEBE-VISHNU2.76 A TeV

TRENTo AMPT

0.5 1 1.5 2

{2}

nv

-110

1

10

210

310

30-40%

π

K

P

(c)

0.5 1 1.5 2

{2}

nv

-110

1

10

210

310

40-50%

π

K

P

(d)

iEBE-VISHNU + TRENTo / AMPT describes π , K and proton data well.

W. Zhao, H. j. Xu and H. Song, arXiv:1703.10792 [nucl-th].



pT -spectra for 5.02 A TeV

(GeV)T

p

Pb + Pb 5.02 v.s.2.76 A TeV

0 0.5 1 1.5 2

The

ory/

Exp

.

0.6

0.8

1

1.2

0.5 1 1.5 2

The

ory/

Exp

.

0.6

0.8

1

1.2

0.5 1 1.5 2

The

ory/

Exp

.

0.6

0.8

1

1.2

0.5 1 1.5 2

The

ory/

Exp

.

0.6

0.8

1

1.2

0 0.5 1 1.5 2

]-2 )c

dy)

[(G

eV/

Tp

/(d

N2)d

Tpπ

1/(2

1

10

210

310

10-20%

π

K

P

(a)

π

K

p


TRENTo AMPT

0.5 1 1.5 2

{2}

nv

1

10

210

310

20-30%

π

K

P

(b)

π

K

p


TRENTo AMPT

0.5 1 1.5 2

{2}

nv

1

10

210

310

30-40%

π

K

P

(c)

0.5 1 1.5 2

{2}

nv

1

10

210

310

40-50%

π

K

P

(d)

Stronger radial flow is developed in systems of 5.02 A TeV collisionsenergy.




Q-cumulant

2-particle azimuthal correlations:

〈2〉|∆η|n,−n =QA

n · QB∗n

MA ·MB, (7)

flow harmonics:

cn{2, |∆η|} = 〈〈2〉〉|∆η|n,−n, vn{2, |∆η|} =√cn{2, |∆η|} (8)

where Qn =∑M

i=1 einϕi , and Qn can be Particles Of Interests (POIs)

to calculate vn(pT ).



vn(pT ) for all charged hadrons

Pb+Pb 2.76 A TeV

(GeV)T

p (GeV)T

p

Pb+Pb 5.02 A TeV

2v3v

4v

2v

3v

4v

2v3v

4v

2v

3v

4v

0 0.5 1 1.5 2

{2}

nv

0

0.05

0.1 {2}2 v{2}3 v{2}4 v

TRENToAMPTiEBE-VISHNU

0-5% (c)

{2}2 v{2}3 v{2}4 v

5.02 A TeVALICE DATA

0 0.5 1 1.5 2{2

}n

v0

0.1

0.2

30-40% (d)

0 0.5 1 1.5 2

{2}

nv

0

0.05

0.1 {2}2 v{2}3 v{2}4 v

TRENToAMPTiEBE-VISHNU

0-5% (a)

{2}2 v{2}3 v{2}4 v

2.76 A TeVALICE DATA

0 0.5 1 1.5 2

{2}

nv

0

0.1

0.2

30-40% (b)

iEBE-VISHNU + TRENTo / AMPT can describe vn(pT ) of Pb+Pb at2.76 and 5.02 A TeV well.




vn(pT ) for π,K and proton at 2.76 A TeVPb + Pb 2.76 A TeV

(GeV)T

p

0 0.5 1 1.5 2

2v

0

0.1

0.2

0.3

10-20%

(a-1)


π k p

TRENTo AMPT

0 0.5 1 1.5 2

2v

0

0.1

0.2

0.3

20-30%

(a-2)

π K p

ALICE DATA2.76 A TeV

0 0.5 1 1.5 2

2v

0

0.1

0.2

0.3

30-40%

(a-3)

0 0.5 1 1.5 2

2v

0

0.1

0.2

0.3

40-50%

(a-4)

0 0.5 1 1.5 2

3v

0

0.05

0.1

10-20%

(b-1)

0 0.5 1 1.5 2

2v

0

0.05

0.1

20-30%

(b-2)

0 0.5 1 1.5 2

2v

0

0.05

0.1

30-40%

(b-3)

0 0.5 1 1.5 20

0.05

0.1

40-50%

(b-4)

0 0.5 1 1.5 2

4v

0

0.02

0.04

0.06

0.08

10-20%

(c-1)

0.5 1 1.5 2

2v

0

0.02

0.04

0.06

0.08

20-30%

(c-2)

0.5 1 1.5 2

2v

0

0.02

0.04

0.06

0.08

30-40%

(c-3)

0.5 1 1.5 2

0

0.02

0.04

0.06

0.08

40-50%

(c-4)

iEBE-VISHNU + TRENTo / AMPT can describe π , K and proton datawell.

W. Zhao, H. j. Xu and H. Song, arXiv:1703.10792 [nucl-th].Wenbin Zhao (Collaborators: Haojie-Xu, Huichao Song arXiv:1703.10792 Peking University)Collective flow in 2.76 and 5.02 A TeV July 25th 2017 20 / 36


vn(pT ) for π,K and proton at 5.02 A TeVPb + Pb 5.02 v.s. 2.76 A TeV

(GeV)T

p

0 0.5 1 1.5 2

2v

0

0.1

0.2

0.3

10-20%

(a-1)


π k p

TRENTo AMPT

0 0.5 1 1.5 2

2v

0

0.1

0.2

0.3

π k p

TRENTo AMPT

20-30%

(a-2)


0 0.5 1 1.5 2

2v

0

0.1

0.2

0.3

30-40%

(a-3)

0 0.5 1 1.5 2

2v

0

0.1

0.2

0.3

40-50%

(a-4)

0 0.5 1 1.5 2

3v

0

0.05

0.1

10-20%

(b-1)

0 0.5 1 1.5 2

2v

0

0.05

0.1

20-30%

(b-2)

0 0.5 1 1.5 2

2v

0

0.05

0.1

30-40%

(b-3)

0 0.5 1 1.5 20

0.05

0.1

40-50%

(b-4)

0 0.5 1 1.5 2

4v

0

0.02

0.04

0.06

0.08

10-20%

(c-1)

0.5 1 1.5 2

2v

0

0.02

0.04

0.06

0.08

20-30%

(c-2)

0.5 1 1.5 2

2v

0

0.02

0.04

0.06

0.08

30-40%

(c-3)

0.5 1 1.5 2

0

0.02

0.04

0.06

0.08

40-50%

(c-4)

Mass-splitting between π and proton increased slightly at 5.02 A TeVcollisions energy.

W. Zhao, H. j. Xu and H. Song, arXiv:1703.10792 [nucl-th].Wenbin Zhao (Collaborators: Haojie-Xu, Huichao Song arXiv:1703.10792 Peking University)Collective flow in 2.76 and 5.02 A TeV July 25th 2017 21 / 36


Event-by-event vn distributions

The event-by-event vn distributions reflect the initial statesfluctuations, providing strong constraints for the initial conditionmodels

One need do standard Bayesian unfolding to suppress the non-flowand finite multiplicities effects.



Event-by-event vn distribution

>n/<vnv >n/<vnv

Pb+Pb 2.76 A TeV Pb+Pb 5.02A TeV v.s.2.76 A TeV

>n/<vnv0 1 2 3

>) 2/<

v2

p(v

-210

-110

1

10

(d-2)40-45%

2v2v

>n/<vnv0 1 2 3

>) 3/<

v3

p(v

-210

-110

1

10

(e-2)40-45%

3v

0 1 2 3

>) 4/<

v4

p(v

-210

-110

1

10

(f-2)40-45%

4v

>n/<vnv0 1 2 3

>) 2/<

v2

p(v

-210

-110

1

10

(d-1)0-5%

TRENTo

AMPT

iEBE-VISHNU2.76 A TeV 5.02 A TeV2v

>n/<vnv0 1 2 3

>) 3/<

v3

p(v

-210

-110

1

10

(e-1)0-5%

3v

0 1 2 3

>) 4/<

v4

p(v

-210

-110

1

10

(f-1)0-5%

4v

>n/<vnv0 1 2 3

>) 2/<

v2

p(v

-210

-110

1

10

(a-2)40-45%

2v

>n/<vnv0 1 2 3

>) 3/<

v3

p(v

-210

-110

1

10

(b-2)40-45%

3v

0 1 2 3

>) 4/<

v4

p(v

-210

-110

1

10

(c-2)40-45%

4v

>n/<vnv0 1 2 3

>) 2/<

v2

p(v

-210

-110

1

10

(a-1)0-5%

2v TRENTo

AMPT


ATLAS DATA2.76 A TeV

>n/<vnv0 1 2 3

>) 3/<

v3

p(v

-210

-110

1

10

(b-1)0-5%

3v

0 1 2 3

>) 4/<

v4

p(v

-210

-110

1

10

(c-1)0-5%

4v

iEBE-VISHNU + TRENTo / AMPT can fit scaled-vn distributions well.

The scaled vn distributions are insensitive to collision energy.W. Zhao, H. j. Xu and H. Song, arXiv:1703.10792 [nucl-th].



Event-plane correlationsEvent-plane correlations reveal the patterns of initial statefluctuations, and evaluate correlations of flow angles.

we use Scalar-Product:

cos [c1n1Ψn1 − c2n2Ψn2 ] =〈Q̃c1

n1AQ̃c2∗

n2B〉√

〈Q̃c1n1A

Q̃c1∗n1B〉√〈Q̃c2

n2AQ̃c2∗

n2B〉

cos [c1n1Ψn1 + c2n2Ψn2 − c3n3Ψn3 ]

=〈Q̃c1

n1AQ̃c2

n2AQ̃c3∗

n3B〉√

〈Q̃c1n1A

Q̃c1∗n1B〉〈Q̃c2

n2AQ̃c2∗

n2B〉〈Q̃c3

n3AQ̃c3∗

n3B〉, (9)

where Q̃n ≡ 1N

∑j e

inϕj .Wenbin Zhao (Collaborators: Haojie-Xu, Huichao Song arXiv:1703.10792 Peking University)Collective flow in 2.76 and 5.02 A TeV July 25th 2017 24 / 36


Event-plane correlations at 2.76 A TeVPb+Pb 2.76 A TeV

partN partN

0 100 200 300 400

0

0.5

1

TRENTo

AMPT

iEBE-VISHNU

ATLAS DATA

2.76 A TeV

2.76 A TeV

)>4Ψ-2Ψ<cos4(

(a-1)

0 100 200 300 400-0.2

-0.1

0

0.1

0.2 )>3

Ψ-2

Ψ<cos6(

(b-1)

0 100 200 300 400

0

0.5

1 )>6

Ψ-2

Ψ<cos6(

(c-1)

0 100 200 300 400

0

0.5

1 )>6

Ψ-3

Ψ<cos6(

(d-1)

0 100 200 300 400

0

0.5

1 )>5Ψ-53

Ψ+32

Ψ<cos(2

(e-1)

0 100 200 300 400-0.3

-0.2

-0.1

0)>4Ψ+4

3Ψ-6

2Ψ<cos(2

(f-1)

0 100 200 300 400

0

0.5

1 )>6

Ψ-64Ψ-42

Ψ<cos(10

(g-1)

0 100 200 300 400-0.2

-0.1

0

0.1

0.2 )>4Ψ-43

Ψ-62

Ψ<cos(10

(h-1)

iEBE-VISHNU + TRENTo / AMPT generately reproduce date.

Some correlations are sensitive to initial conditions.

W. Zhao, H. j. Xu and H. Song,. arXiv:1703.10792 [nucl-th].



Event-plane correlations at 5.02 A TeV

Pb+Pb 5.02 v.s.2.76 A TeV

partN partN

0 100 200 300 400

0

0.5

1

TRENTo

AMPT

iEBE-VISHNU

2.76 A TeV

)>4Ψ-2Ψ<cos4(

(a-2)

0 100 200 300 400-0.2

-0.1

0

0.1

0.2 )>3

Ψ-2

Ψ<cos6(

(b-2)

0 100 200 300 400

0

0.5

1 )>6

Ψ-2

Ψ<cos6(

(c-2)

0 100 200 300 400

0

0.5

1 )>6

Ψ-3

Ψ<cos6(

(d-2)

0 100 200 300 400

0

0.5

1 )>5Ψ-53

Ψ+32

Ψ<cos(2

(e-2)TRENTo

AMPT

iEBE-VISHNU

5.02 A TeV

0 100 200 300 400-0.3

-0.2

-0.1

0)>4Ψ+4

3Ψ-6

2Ψ<cos(2

(f-2)

0 100 200 300 400

0

0.5

1 )>6

Ψ-64Ψ-42

Ψ<cos(10

(g-2)

0 100 200 300 400-0.2

-0.1

0

0.1

0.2 )>4Ψ-43

Ψ-62

Ψ<cos(10

(h-2)

No significant difference between these two collision energies.




Symmetric Cumulants (SC (m, n))

SC (m, n) values correlations of flow harmonics:

SC v (m, n) = 〈〈cos(mϕ1+nϕ2−mϕ3 −nϕ4)〉〉c= 〈〈4〉〉n,m,−n,−m − 〈〈2〉〉n,−n · 〈〈2〉〉m,−m=

⟨v2mv

2n

⟩−⟨v2m

⟩ ⟨v2n

⟩. (10)

the Normalized Symmetric Cumulants:

NSC v (m, n) =SC v (m, n)

〈v2m〉〈v2

n 〉(11)

where 〈v2m〉 and 〈v2

n 〉 can be calculated by the 2-particle cumulants



Symmetric CumulantsPb+Pb 2.76 A TeV Pb+Pb 5.02A TeV v.s. 2.76 A TeV

Centrality %0 20 40 60

-3

-2

-1

0-610×

iEBE-VISHNU(2.76 A TeV)TRENTo AMPT

(4,2)vSC(3,2)vSC (a)

0 20 40 60

(m,n

)v

SC

0

1

2

3-610×

ALICE DATA 2.76 A TeV

(4,2)vSC(3,2)vSC


-3

-2

-1

0-610×


(4,2)vSC(3,2)vSC (c)

0 20 40 60

(m,n

)v

SC

0

1

2

3-610×


-0.3

-0.2

-0.1

0


(4,2)vNSC(3,2)vNSC (b)

0 20 40 60

(m,n

)v

NSC

0

0.5

1ALICE DATA 2.76 A TeV

(4,2)vNSC(3,2)vNSC


-0.3

-0.2

-0.1

0


(4,2)vNSC(3,2)vNSC (d)

0 20 40 60

(m,n

)v

NSC

0

0.5

1

iEBE-VISHNU + TRENTo / AMPT describe the (N)SC v (m, n) well.

NSC v (m, n) has no significant dependence on collision energies.W. Zhao, H. j. Xu and H. Song, arXiv:1703.10792 [nucl-th].



Non-linear response coefficients

For low harmonics, vn(n=2,3), magnitudes are linear in initial εn(n=2,3).

Higher harmonics, vn(n ≥ 4), receive contributions from mode-coupling.

Non-linear response coefficients evalue the mode-coupling effects:

V4 = V4L + χ422V22 , V5 = V5L + χ523V2V3,

V6 = V6L + χ624V2V4L + χ633V23 + χ6222V

32 ,

V7 = V7L + χ725V2V5L + χ734V3V4L + χ7223V22 V3 .

(12)

We implement Scalar-Product method to calculate these coefficients.



Non-linear response coefficients

Centrality %

Pb+Pb 2.76 A TeV v.s. 5.02 A TeV

0 10 20 30 40 50 60-10123456

422χ

(a)

0 10 20 30 40 50 60

-1

0

1

2

3

4

5

6

523χ

(b)

0 10 20 30 40 50 60

-1

0

1

2

3

4

5

6

624χ

(c)

TRENToAMPT

iEBE-VISHNU2.76 A TeV 5.02 A TeV

0 10 20 30 40 50 60-10123456

633χ

(d)

0 10 20 30 40 50 60-1

0

1

2

3

4

5

6

6222χ

(e)

0 10 20 30 40 50 60-1

0

1

2

3

4

5

6

7223χ

(f)

No obvious centrality or energy dependence;

It does depend on the initial conditions.




pT -dependent factorization ratio (r2,3(pT ))

Due to the initial state fluctuation, hadrons at different pT do notshare a common flow angle.

rn(pT ) evaluates the break-up of factorizations of flow harmonics:

rn(paT , pbT ) ≡

Vn∆(paT , pbT )√

Vn∆(paT , paT )Vn∆(pbT , p

bT ), (13)

where:

Vn∆ ≡ 〈〈cos(n∆φ)〉〉 = 〈Q̃a(b)n Q̃

a(b)∗n 〉, (14)

and Q̃a(b)n ≡ 1

N

∑j e

inϕj calculated within a specific pa(b)T bin .



Factorization ratio for 2.76 A TeVPb+Pb 2.76 A TeV

<1.5 GeV/caT1.0<P <2.0 GeV/ca

T1.5<P <2.5 GeV/caT2.0<P <3.0 GeV/ca

T2.5<P

Centrality %0 1 2

)b T

-pa T

(p 2r

0.85

0.9

0.95

1

1.05

(a-1)

TRENToAMPT

iEBE-VISHNU 2.76 A TeV

0-5%

Centrality %0 1 2

η/d

chdN

0.85

0.9

0.95

1

1.05

(a-2)

Centrality %0 1 2

η/d

chdN

0.85

0.9

0.95

1

1.05

(a-3)

Centrality %0 1 2

η/d

chdN

0.85

0.9

0.95

1

1.05

(a-4)

0 1 2

)b T

-pa T

(p 2r

0.85

0.9

0.95

1

1.05

(b-1)

CMS DATA

30-40%

2.76 A TeV

0 1 2

)b T

-pa T

(p 2r 0.85

0.9

0.95

1

1.05

(b-2)0 1 2

)b T

-pa T

(p 2r 0.85

0.9

0.95

1

1.05

(b-3)0 1 2

)b T

-pa T

(p 2r 0.85

0.9

0.95

1

1.05

(b-4)

Centrality %0 1 2

)b T

-pa T

(p 3r

0.6

0.7

0.8

0.9

1

(c-1)

0-5%

Centrality %0 1 2

η/d

chdN

0.6

0.7

0.8

0.9

1

(c-2)

Centrality %0 1 2

η/d

chdN

0.6

0.7

0.8

0.9

1

(c-3)

Centrality %0 1 2

η/d

chdN

0.6

0.7

0.8

0.9

1

(c-4)

bT

-paT

p0 1 2

)b T

-pa T

(p 3r

0.60.70.80.9

1

(d-1)

30-40%

bT

-paT

p0 1 2

)b T

-pa T

(p 3r 0.60.70.80.9

1

(d-2)

bT

-paT

p0 1 2

)b T

-pa T

(p 2r 0.60.70.80.9

1

(d-3)

bT

-paT

p0 1 2

)b T

-pa T

(p 2r 0.60.70.80.9

1

(d-4)

iEBE-VISHNU + TRENTo / AMPT describe r2 and r3 well;

r3 drop sharply at large paT − pbT , due to hadronic rescattering.




Factorization ratio for 5.02 A TeV

Pb+Pb 5.02 A TeV v.s.2.76 A TeV<1.5 GeV/ca

T1.0<P <2.0 GeV/caT1.5<P <2.5 GeV/ca

T2.0<P <3.0 GeV/caT2.5<P

Centrality %0 1 2

)b T

-pa T

(p 2r

0.85

0.9

0.95

1

1.05

TRENToAMPT


0-5%(a-1)

Centrality %0 1 2

η/d

chdN

0.85

0.9

0.95

1

1.05

(a-2)

Centrality %0 1 2

η/d

chdN

0.85

0.9

0.95

1

1.05

(a-3)

Centrality %0 1 2

η/d

chdN

0.85

0.9

0.95

1

1.05

(a-4)

0 1 2

)b T

-pa T

(p 2r 0.85

0.9

0.95

1

1.05

(b-1)

30-40%TRENToAMPT


0 1 2

)b T

-pa T

(p 2r 0.85

0.9

0.95

1

1.05

(b-2)

0 1 2

)b T

-pa T

(p 2r 0.85

0.9

0.95

1

1.05

(b-3)

0 1 2

)b T

-pa T

(p 2r 0.85

0.9

0.95

1

1.05

(b-4)

Centrality %0 1 2

)b T

-pa T

(p 3r

0.6

0.7

0.8

0.9

1

(c-1)

0-5%

Centrality %0 1 2

η/d

chdN

0.6

0.7

0.8

0.9

1

(c-2)

Centrality %0 1 2

η/d

chdN

0.6

0.7

0.8

0.9

1

(c-3)

Centrality %0 1 2

η/d

chdN

0.6

0.7

0.8

0.9

1

(c-4)

bT

-paT

p0 1 2

)b T

-pa T

(p 3r

0.6

0.7

0.8

0.9

1

(d-1)

30-40%

bT

-paT

p0 1 2

)b T

-pa T

(p 3r 0.60.70.80.9

1

(d-2)

bT

-paT

p0 1 2

)b T

-pa T

(p 2r 0.60.70.80.9

1

(d-3)

bT

-paT

p0 1 2

)b T

-pa T

(p 2r 0.60.70.80.9

1

(d-4)

r2 and r3 are close for two collision energies.



Summary

Summary


Summary

Summary

iEBE-VISHNU + TRENTo / AMPT with two forms of QGP transportcoefficients, we calculate:

integrated and differential vn, the event-by-event vn distributions, theevent-plane correlations, Symmetric Cumulant, the nonlinear responsecoefficients, pT -depentdent factorization ratio.

Raising from 2.76 to 5.02 A TeV, multiplicities increased by ∼ 30%,transport properties of the QGP do not change significantly.

Some observables are sensitive to initial conditions, such as:

Symmetric Cumulant SC v (4, 2),

Event plane correlations 〈cos6(Ψ2 −Ψ6)〉 and〈cos(10Ψ2 − 4Ψ4 − 6Ψ6)〉,The non-linear response coefficients χ624 and χ7223.


Summary

Thank You.


collective flow in 2.76 and 5.02 a tev pb+pb...

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