hydrodynamics overview - cern indico

Overview Initial Stages Equations of Motion Exp. Observables Transport Coefficients Small Systems Beam Energy Scan Backup

Hydrodynamics Overview

Jacquelyn Noronha-HostlerUniversity of Houston

Hot Quarks 2016- South Padre IslandSept. 13th 2016


“Standard Model" of Hydrodynamics in Heavy IonCollisions

Initial StatePre-equilibrium state (generate initial flow... full Tµν)Event-by-Event Relativistic Viscous Hydrodynamics (shearη/s(T ) and bulk ζ/s(T ) viscosities)Hadronization via Cooper Frye Freeze-outHadronic Afterburner (Decays, Transport)


Initial Conditions effects on Collective Flow

The distribution of particles can be written as a Fourier series

Ed3Nd3p

=1

2πd2N

pT dpT dy

[1 +

∑n

2vn cos [n (φ− ψn)]

]

Flow Harmonics at mid-rapidity

vn(pT ) =

∫ 2π0 dφ dN

pT dpT dφcos [n (φ−Ψn)]∫ 2π0 dφ dN

pT dpT dφ

where Ψn = 1n arctan 〈sin[(nφ)]〉

〈cos[(nφ)]〉


When you need to start somewhere...

from Abstruse Goose


Hydrodynamics: eccentric initial state to elliptical flow

Assuming Gold ions arespheres...

Cold AtomsLarge pressure

gradients

Elliptical Shape in pT


Centrality


Flow Harmonics across Centrality

ALICE Phys.Rev.Lett. 107 (2011) 032301


Same density (centrality), different shapes

Centrality bins by the density, but for the same density..


Flow Harmonics distribution within a centrality

Large fluctuations in flow harmonics for the same denisty

ATLAS JHEP 1311, 183 (2013)


Outline

1 Overview

2 Initial Stages

3 Equations of Motion

4 Exp. Observables

5 Transport Coefficients

6 Small Systems

7 Beam Energy Scan

8 Backup


Energy Density Scales of the Initial Condition

JNH, Noronha, Gyulassy Phys.Rev. C93(2016) no.2, 024909

Sensitivity at most tosub-leading modesA. Mazeliauskas and D. Teaney, Phys.Rev. C 93, no. 2, 024913 (2016)

Small scale fluctuationsnot relevant to final flowharmonicsJNH, Noronha, Gyulassy Phys.Rev.C93 (2016) no.2, 024909

Eccentricites bestpreditor of final flowharmonicsGardim et al,Phys.Rev. C85 (2012)024908 ; Phys.Rev. C91 (2015) no.3,034902, Niemi et al Phys.Rev. C87(2013) no.5, 054901


Types of Initial Conditions

Wounded Nucleons Color Glass Condensate

Hadronic Cascades

+

Glauber

MCKLN

Gluon Saturation

IP-Glasma

Partonic StringsNeXuS/EPOS

UrQMD

Trento, supersonicEKRT

DIPSY

Initial Flow

3D (longitudinal)

BAMPS


Eccentricities

Eccentricities:

εn,meiΦn,m =

∫d2r rm einφ ε(τ0, r)∫

d2r rm ε(τ0, r)

in the center of mass frame.Also, define εn = εn,n

Variance in the EccentricitiesLeads to differences in the finalflow harmonics. Different intialconditions leads to differentparameters in thehydrodynamics itself.

RHIC

0.1

0.2

0.3

0.4

0.5

0.6

0.7

¶2

rcbk+NBDrcbkmcklnEKRTIP-GlasmaGlauber

20 40 60

0.1

0.2

0.3

0.4

0.5

Centrality %¶

3


Outline

1 Overview

2 Initial Stages


4 Exp. Observables


6 Small Systems

7 Beam Energy Scan

8 Backup


Equations of Motion

Conservation of Energy and Momentum

∂µTµν = 0

Ideal Energy momentum TensorTµν = εuνuν − p∆µν

where ∆µν = gµν − uµuν

Coordinate System: xµ = (τ, x , y , η) where τ =√

t2 − z2 andη = 0.5 ln

(t+zt−z

)


Equations of Motion


∂µTµν = 0

Shear Energy momentum TensorTµν = εuνuν − p∆µν + πµν

with the shear stress tensor πµν where ∆µν = gµν − uµuν


t2 − z2 andη = 0.5 ln

(t+zt−z

)


Equations of Motion


∂µTµν = 0

Shear+Bulk Energy momentum Tensor

Tµν = εuνuν − (p + Π) ∆µν + πµν

with the shear stress tensor πµν and bulk dissipative term Πwhere ∆µν = gµν − uµuν


t2 − z2 andη = 0.5 ln

(t+zt−z

)


Outline

1 Overview

2 Initial Stages


4 Exp. Observables


6 Small Systems

7 Beam Energy Scan

8 Backup


Dissecting the Flow Harmonic Distribution


Reality is a bit more complicated...

Experimentally, v2{2} is a two particle correlation whereissues like non-flow effects (decays, jets etc) existRather, we use multiparticle cumulants v2{n} wheren = 2,4,6 . . . indicate the number of correlated particlesIf non-flow can be eliminated (minimized via a rapidity gap)we expect v2{4} ∼ v2{6} ∼ v2{8} . . .Then, v2{4}/v2{2} indicates magnitude of fluctuations

Good references: Ante Bilandzic Ph.D Thesis and Luzum andPetersen J.Phys. G41 (2014) 063102


We fit all the things...

0

0.05

0.1

0.15

0.2

0 0.5 1 1.5 2

⟨vn

2⟩1

/2

pT [GeV]

ATLAS 10-20%, EP

η/s =0.2

v2 v3 v4 v5

Gale et al, Phys.Rev.Lett. 110 (2013) no.1, 012302

∼ 5% changes across energies

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)

ALICE Phys.Rev.Lett. 116 (2016) no.13, 132302Hydro: JNH, Luzum, Ollitrault Phys.Rev. C93 (2016) no.3,034912 ; Niemi et al Phys.Rev. C93 (2016) no.1, 014912


We fit all the things...

0

0.05

0.1

0.15

0.2

0 0.5 1 1.5 2

⟨vn

2⟩1

/2

pT [GeV]

ATLAS 10-20%, EP

η/s =0.2

v2 v3 v4 v5

Gale et al, Phys.Rev.Lett. 110 (2013) no.1, 012302

∼ 5% changes across energies


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)

ALICE Phys.Rev.Lett. 116 (2016) no.13, 132302Hydro: JNH, Luzum, Ollitrault Phys.Rev. C93 (2016) no.3,034912 ; Niemi et al Phys.Rev. C93 (2016) no.1, 014912Taken from Hyperbole and a Half


But what can be learned from this?Gardim,JNH,Luzum,Grassi PRC91(2015)3,034902

εn and vn are strongly correlatedperfect estimation Qn → 1

0 10 20 30 40 50 600.85

0.9

0.95

1

% centrality

Q2

NeXSPheRIO

shear ∆f

shearbulk ∆f

bulk ∆f

ideal

¶2

0 10 20 30 40 50 60

0.7

0.8

0.9

1

% centrality

Q3

NeXSPheRIO

shear ∆f

shearbulk ∆f

bulk ∆f

ideal

¶3

Fitting the flow harmonics, gives us a good estimate of theinitial state, however, viscosity also plays a role...


Complications with mapping between ε2 → v2

1.0 0.5 0.0 0.5 1.0 1.5δε2 , δv2

10-2

10-1

100

P(δv 2

), P(δε 2

)

5−10 %

(a)

δv2

δε12

δε2

ATLAS

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40ε2

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

v 2

5−10 %

(b)

LHC 2.76 TeV Pb +Pb

1.0 0.5 0.0 0.5 1.0 1.5δε2 , δv2

10-2

10-1

100

P(δv 2

), P(δε 2

)

55−60 %

(g)

δv2

δε12

δε2

ATLAS

0.0 0.2 0.4 0.6 0.8ε2

0.00

0.05

0.10

0.15

0.20

0.25

v 2

55−60 %

(h)

LHC 2.76 TeV Pb +Pb

Niemi,Eskola, Paatelainen,arXiv:1505.02677, also Schenke,Tribedy,Venugopalan, Nucl. Phys. A 926, 102 (2014)


Linear+Cubic Response

Linear responsef (εn) = κnεn

Teaney,Yan,PRC83(2011)064904;Gardim,et al,PRC85(2012)024908;PRC91(2015)3,034902

Linear+cubic response

f (εn) = κnεn + κ′n|εn|2εn

JNH,Yan,Gardim,Ollitrault Phys.Rev. C93 (2016) no.1, 014909

Cubicresponse

Avg. Initial Condition


Skewness and higher order cumulants

Difference between cumulantsdue to skewness of vxdistribution

v2{4} − v2{6} = − s1

3〈vx〉2

where s1 = 〈(vx − 〈vx〉)3〉 0

200

400

600

800

1000

Nevents

(a)

50-55%

vyκ εy

0

200

400

600

800

1000

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Nevents

(b)50-55%

vxκ εx

Giacolone et alarXiv:1608.01823


Event-by-event flow harmonics fluctuations

SC(n,m) =〈v2

n v2m〉 − 〈v2

n 〉〈v2m〉

Elliptical and triangularflow are anti-correlatedSC(3,2)→ initial stateeffectv4 is correlated with v2 andexperiences non-lineareffectsη/s(T ) dependencies inSC(4,2) diminished by exp.effects Gardim et al arXiv:1608.02982

Previous studies: ATLAS Phys.Rev.C92 (2015) no.3, 034903

ALICE arXiv:1604.07663


Outline

1 Overview

2 Initial Stages


4 Exp. Observables


6 Small Systems

7 Beam Energy Scan

8 Backup


Bulk Viscosity in Heavy-Ion Collisions

Resistance against thedeformation of a fluidΠµν

Navier−Stokes ∼ η∂〈µuν〉

æ

æ

æ

æ ææ æ

æ ææ

æ æææ ææ æ

æ æ ææ æ æ

æ ææ

æ

à àààà

àà

àà à à à

UrQMDPHSD kubo kin.

AdS�CFT

HRG+HS+QGP

semiQGP

DS YangMills

BAMPS

monopoles

100 150 200 250 300 350 4000.0

0.5

1.0

1.5

T HMeVL

Η�s

Resistance against theradial expansion of a fluidΠNavier−Stokes ∼ −ζ(∂µuµ)

æææ

æ

æ

æ

æ

æ

æ

æ

æ

æ

ææ

æææææ

ææ

à

à

à

à

à à

à àà à àà

à àà à à à

à à àà

ì

ì

HRG+HS

PHSD

pQCD

nonconf. AdS

14 mom.

100 150 200 250 300 350 4000.00

0.05

0.10

0.15

0.20

0.25

0.30

T HMeVL

Ζ�s

JNH arXiv:1512.06315 for references


Viscosity in Heavy-Ion Collisions

Given a lumpy initial condition τ = 1fm


Viscosity in Heavy-Ion Collisions


Viscosity kills off higher order flow harmonics

Higher order vn’s more strongly affected by η/s and ζ/s

Schenke, Jeon, Gale Phys.Rev.C85 (2012) 024901

JNH, Noronha, Grassi Phys.Rev. C90 (2014) no.3,034907

Depends on correction terms, nocorrection also shows ⇑

Bernhard et al Phys.Rev. C94 (2016) no.2, 024907

Another type shows ⇓Ryu et al Phys.Rev.Lett. 115 (2015) no.13, 132301


η/s(T ) sensitive observablesVarying η/s: Niemi et al. Phys.Rev. C93 (2016) no.2, 024907

100 150 200 250 300 350 400 450 500T [MeV]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

η/s

η/s=0.20

η/s=param1

η/s=param2

η/s=param3

η/s=param4

Event Plane Cor. sensitive to η/s(T )

0 10 20 30 40 50 60 70 80centrality [%]

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

v 2{ 2} ,v 2

{ 4} /2

(a)

LHC 2.76 TeV Pb +Pb

pT =[0.2 5.0] GeV

η/s=0.20

η/s=param1

η/s=param2

η/s=param3

η/s=param4

RPRP

ALICE v2

{2}

ALICE v2

{4}/2

RHIC sensitive to hadronic shear viscosity


Outline

1 Overview

2 Initial Stages


4 Exp. Observables


6 Small Systems

7 Beam Energy Scan

8 Backup


Applicability of hydrodynamics in PbPb: Part IKnudsen number in PbPb, JNH, Noronha, Gyulassy, Phys.Rev. C93 (2016) no.2, 024909

Tim

e Knθ

= lmicro

/Lmacro

→ τπ θ


Applicability of hydrodynamics in pPb

Only very small region with a "good" Knudsen number

Niemi and Denicol arXiv:1404.7327


Yet, Glauber+Negative Binomial Distributions fit pPb

Kozlov, Luzum, Denicol, Jeon,Gale arXiv:1405.3976

Bozek and Broniowski Phys.Rev. C88 (2013) no.1,014903

Kozlov, Luzum, Denicol, Jeon, Gale arXiv:1405.3976


Outline

1 Overview

2 Initial Stages


4 Exp. Observables


6 Small Systems

7 Beam Energy Scan

8 Backup


Phase Diagram

What happens to hydrodynamics at finite µB?

LHC

RHIC


Hydrodynamics at Finite µB

2+1 Dimensions→ 3+1 DimensionsEquation of State (Lattice QCD runs into the Fermi-SignProblem)→ Critical Point?Thermal fluctuationsBaryon diffusion (and Strangeness diffusion and Chargediffusion)- Temperature dependence? Rougemont et al Phys.Rev.Lett. 115

(2015) no.20, 202301 , Lattice QCD: Aarts et al JHEP 1502 (2015) 186

Transport Coefficients depend on T and µB,η/s(T )→ η/s(T , µB) and ζ/s(T )→ ζ/s(T , µB)


Triangular Flow at finite µB

v3 disappears at low energies

Auvinen and Petersen Phys.Rev. C88 (2013) no.6, 064908


v3 disappears at low energies


Do we still have perfect fluidity at finite µB?

Divergence of transport coef. depend on the universality classCP (Class B- no divergence)

Rougemont, Noronha, JNH to appear shortly

No CP

Kadam, Mishra Nucl.Phys. A934 (2014) 133-147See also Denicol, Jeon, Gale, Noronha Phys.Rev. C88

(2013) no.6, 064901

Class H- diverges at CP


Baryon/Charge Diffusion

Talk from Chun Shen at the BEST collaboration

Still waiting to see howDiffusion effects v2 vs. v3

Hadronic phase diminisheseffects of Diffusion

D(T) still needed

100 150 200 250 300 350 400

T [MeV]

0.0

0.5

1.0

1.5

2.0

2.5

2πTD

0.75 1.00 1.25 1.50 1.75 2.00

T/Tc

Aarts et al JHEP 1502 (2015) 186

CFT limit

μB=0

μB=100MeV

μB=200MeV

μB=300MeV

μB=400MeV

150 200 250 3000.00

0.05

0.10

0.15

T [MeV]

TDB(T,μB)

Rougemont et al Phys.Rev.Lett. 115 (2015) no.20,202301


Conclusions

Relativistic hydrodynamics has done an extraordinarilygood job at describing flow harmonics, particle spectra,and event-by-event sensitive observablesMany interesting open ended questions remain:

Can the initial state be determined separately from viscosityeffects?Are we seeing fluid-like behavior in small systems?What are the implications of the vanishing v3 at the BeamEnergy Scan?

Topics to be further explored at Hot Quarks: initial stages,transport coefficients, jets+hydrodynamics, anisotropichydrodynamics, magnetohydrodynamics, and the chiralmagnetic effect


Outline

1 Overview

2 Initial Stages


4 Exp. Observables


6 Small Systems

7 Beam Energy Scan

8 Backup


Mapping of the Initial State onto the Flow HarmonicsGardim et al, PRC85(2012)024908, Gardim,JNH,Luzum,Grassi PRC91(2015)3,034902

How do the eccentricitiesrelate to the flow harmonics?

εn,meiΦn,m = −{rmeinφ}{rm}

Define Quality of Estimator:

Qn =Re⟨VnV ∗est ,n

⟩√〈|Vn|2〉〈|Vest ,n|2〉

Estimator as a perturbativeseries in powers of

azimuthally asymmetriccumulants:

Vest,n =

mmax∑m=n

kn,mWn,m

+

mmax∑l=1

mmax∑m=l

mmax∑m′=|n−l|

Kl,m,m′Wl,mWn−l,m′

+O(W 3)

As Qn → 1, the εn,m ’s predict thecorresponding vn’s


Longitudinal Twists

Taken from W. Li INT 2015 Talk


Equations of Motion

Projecting Tµν in the parallel uν∂µTµν and perpendicular∆αν ∂µTµν direction (for µB = 0)

Israel-Stewart Equations

Dε+ (ε+ p)∂µuµ − Πµν∇(µuν) = 0 ,(ε+ p)Duα −∇αp + ∆α

ν ∂µΠµν = 0 (1)

where Πµν is the total viscous stress tensor (includes shear,bulk etc)


Second-order Transport Coefficients

Equations of Motion - 2nd orderDenicol et all, PRD85(2012)114047

Π̇ +Π

τΠ= −ζ/s

τΠθ +−δΠΠΠθ + λΠππ

µνσµν

+ φ1Π2 + φ3πµνπµν (2)

π̇〈µν〉 +πµν

τπ=

2η/sτπ

σµν − 43πµνθ

+ 2π〈µα ων〉α + φ7π

〈µα π

ν〉α + λπΠΠσµν − τπππ〈µα σν〉α

+ φ6Ππµν (3)

Shear and Bulk only - in blackCurrently used - redNot yet tested - gray


Shear+Bulk Direct Coupling Terms

φ6Ππµν λπΠΠσµν λΠππµνσµν

in πµν evolution in πµν evolution in Π evolution

nonconf. AdS

150 200 250 300 350 400

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

T HMeVL

Φ6

14 mom

nonconf. AdS

150 200 250 300 350 4000.0

0.2

0.4

0.6

0.8

1.0

T HMeVL

ΛΠ

P

14 mom

150 200 250 300 350 4000.0

0.1

0.2

0.3

0.4

T HMeVL

ΛP

Π

Finazzo et al, JHEP 1502 (2015) 051 Denicol et al, PRC90(2014)024912 Denicol et al, PRC90(2014)024912

Molnar et al, PRD89(2014)074010 Molnar et al, PRD89(2014)074010

hydrodynamics overview - cern indico

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