Anisotropic flow and jet quenching - Fakultät für Physikborghini/Physics/... · 2007. 4. 5. · STAR Collaboration, charged particles, minimum bias, 200 GeV N. B ORGHINI , Anisotropic

RHIC France meeting, Etretat, June 15, 2004

Anisotropic flow and jet quenching

Nicolas BORGHINI

SPhT, CEA Saclay

N. BORGHINI, Anisotropic flow and jet quenching – p.1/23


Anisotropic flow

Non-central collision:

φ

b

yΦ

R

x

−

The particle source is anisotropic(and around it there is only vacuum)

⇒ the pressure gradient along theimpact parameter direction XXXzis stronger than the gradientperpendicular to the reactionplane

XXXXz

⇒ anisotropic particle emission: FLOW?

in momentum space

Particles mainly emitted in-plane (φ = ΦR)rather than out-of-plane (φ − ΦR = 90o).



Anisotropic flow

Flow is a collective effect- affects (almost) all particles

Measures bulk property of the medium: equation of state

Anisotropy quantified by a Fourier expansion:

dN

dφ∝ 1 + 2 v1 cos(φ − ΦR) + 2 v2 cos 2(φ − ΦR) + . . .

v1: “directed flow”, v2: “elliptic flow”

A priori, vn(centrality, pT , y, PID)⇒ differential measurements needed!



Elliptic flow v2

v2 = 〈cos 2(φ − ΦR)〉

Predictions (Jean-Yves OLLITRAULT, 1992):

At ultrarelativistic energies, particles are emitted “in-plane”(φ − ΦR = 0 or 180o)

⇒ v2 > 0

Hydrodynamical model(= assuming many collisions and anequation of state)

⇒ v2 linear function of centrality,up to very peripheral collisions

Fig.3



RHIC v2 results [1]

♥ Centrality dependence of elliptic flow in 130 GeV collisions:

max/nchn0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

2v

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08{2}2v

{4}2v

��9 using the “standard” method� using an improved method of analysis

QQ

QQ

QQ

QQ

Q

The difference between bothmeasurements is due to “non-flow” effects that contaminatethe standard method

♥ v2 sign measured recently (STAR, Oct. 2003): v2 > 0



RHIC v2 results [2]

Transverse momentum & particle type dependence of elliptic flow(200 GeV collisions, PHENIX data):

pT (GeV/c)

0

0.1

0.2

0.3

0 1 2 3 4

p pbarK+ K−π+ π−

hydro πhydro Khydro p

v 2

pT (GeV/c)

v/n

Hydrodynamical model: (Huovinen et al)

1st order phase transition,

freeze-out temperature 120 MeV

⇒ reproduces the mass-dependent v2pattern, up to ∼ 2 GeV

For v2 at high transverse momenta (pT & 2 GeV), see later



v1: a simple model,“antiflow”

Assumptions: incomplete baryon stoppingposition-momentum correlation

4 44

4

4

4

3

4

3332 32 3

1

2 21

z

xx

x , p

rapidity

21

x

4

z 3

P

12T

34

4

��

less stopping here

@@Imore stopping here

�' pT v1

⇒ Proton v1 negative just above midrapidity

R.J.M. Snellings et al, Phys. Rev. Lett. 84 (2000) 2803

Note: v1 = 0 at midrapidity for identical nuclei (symmetry)!



v1 at RHIC: first results

STAR Collaboration, Oct. 2003: charged particles, 10–70% centrality

Run 4 statistics... differential measurements of v1 (and smaller error bars)



A new observable: v4STAR Collaboration, charged particles, minimum bias, 200 GeV



Jet quenching

proton-proton

vs. nucleus-nucleus: medium effect?

figures courtesy of F. GELIS



Jet quenching

proton-proton vs. nucleus-nucleus: medium effect?

figures courtesy of F. GELIS



“Jets” in Au-Au collisions atRHIC

Nuclear modification factor RAA ≡1

Ncoll

d2NAAdpT dy

d2NppdpT dy

(GeV/c)Tp0 2 4 6 8 10

AA

R

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8 (0-10%)0πCentral

(80-92%)0πPeripheral pQCD-II (Vitev&Gyulassy)

PHENIX

〉part N〈0 50 100 150 200 250 300 350

AA

R

0

0.2

0.4

0.6

0.8

1

1.2

1.4

〉part N〈0 50 100 150 200 250 300 350

AA

R

0

0.2

0.4

0.6

0.8

1

1.2

1.40π±h

PHENIX

> 4.5 GeV/c)T(p > 4.5 GeV/c)T(p



“Jets” in Au-Au collisions atRHIC

Azimuthal correlations:k1. Choose leading particle (pT max): origin of azimuthsk2. Count associated particles (pT cut < pT < pT max): azimuth φ

(radians)φ ∆-3 -2 -1 0 1 2 3

)φ ∆

dN

/d(

TR

IGG

ER

1/N 1.4

1.6

|


Jet quenching

Extreme scenario:

Only the jets formed close to the edge manageto get out of the medium

Is this supported by QCD?



Jet quenching

Fast parton energy loss dominated by the emission of soft gluons

Soft gluon formation time

tform ∼ω

k2⊥

Model of the medium:mean free path λscreening mass µ

Multiple scatterings: λ � tform

ωE’

E

q⊥p⊥

Ncoh ∼ tform/λ coherent scatterings

Accumulated k⊥ : k2⊥ ∼ Ncohµ2

}Ncoh ∼

√ω

λµ2



Jet quenching

Coherence length for soft gluon emission `coh ∼

√λω

µ2

⇒ spectrum of energy loss, per unit length:

ω dI

dω dz≈

1

`cohαS ∼ αS

√q̂

ωwith q̂ ∼ µ2/λ

For a path length L:ω dI

dω∼ αS

√q̂

ωL

Average medium-induced energy loss:

∆E ∼

∫ ωm ω dIdω

dω ∼ αS q̂ L2



Jet quenching

∆E ∼ αS q̂ L2

∆E goes like L2: strong attenuation

“Transport coefficient” q̂:

0.1 1 10 1000.01

0.1

1.0

10.0

(GeV/fm3) q (GeV2/fm)

q̂ = ρ

∫dq2

⊥q2⊥

dσ

dq2⊥

in cold nuclear matter:q̂cold ∼ 0.05 GeV2/fmin a QGP at T = 250 MeV:q̂hot ∼ 1 GeV2/fm

expanding medium: effective q̂

- L = 5 fm, k⊥ . 10 GeV: 80–90% quenching: “OK”



Azimuthally dependentjet quenching

Let’s come back to non-central collisions

For a given high-pT parton, the amount of jet quenching dependson the length of the in-medium path:

∆E ∼ αS q̂ L2

⇒ less jet quenching in-plane than out-of-plane



v2 at high transversemomentum

A first idea: v2 from jet quenching


(pT )measured ≈ (pT )emitted − a + b cos 2(φ − ΦR)

⇒ measured momentum larger in-plane than out-of-plane

Detected distribution:dN

dpT(pT ) ≈ f0((pT )em.) + f

′

0((pT )em.) [−a + b cos 2(φ − ΦR)]HY emitted distribution

⇒ v2(pT ) ∝

∫dN

dpTcos 2(φ − ΦR) ≈

f ′0((pT )em.)

f0((pT )em.)b

v2(pT ) ≈f ′0((pT )em.)

f0((pT )em.)b

f0 exponential → v2(pT ) constant

f0 (inverse) power law → v2(pT ) decreasing with pT




A first idea: v2 from jet quenching


(pT )measured ≈ (pT )emitted − a + b cos 2(φ − ΦR)

⇒ measured momentum larger in-plane than out-of-plane

v2(pT ) ≈f ′0((pT )em.)

f0((pT )em.)b

f0 exponential → v2(pT ) constant

f0 (inverse) power law → v2(pT ) decreasing with pT



RHIC v2 results [3]

STAR Collaboration, charged particles, 200 GeV



RHIC v2 results [3 bis]

PHENIX Collaboration, 200 GeV




Second idea: hadrons from parton recombination

At hadronization, two quark/antiquark (resp. three quarks) with momentumpT /2 (resp. pT /3) coalesce into a meson (resp. baryon) with momentum pT

⇒ vmeson2 (pT ) ' 2 vq2

(pT2

), vbaryon2 (pT ) ' 3 v

q2

(pT3

)

/n 2v

0 1 2 3

0

0.05

0.1

0.15

=2)n (0SK =3)n (Λ+Λ

/n (GeV/c)TpTransverse Momentum







(pT2


q2

(pT3

)

0 1 2 3 4 5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

pT/nquark [GeV/c]

v 2/n

qu

ark

Min. Bias+π PHENIX -π PHENIX 0π PHENIX

+ PHENIX K- PHENIX K

S0 STAR K

PHENIX p

p PHENIX

Λ+Λ STAR

d PHENIX d+

/n 2v

0 1 2 3

0

0.05

0.1

0.15

=2)n (0SK =3)n (Λ+Λ








(pT2


q2

(pT3

)

/n 2v

0 1 2 3

0

0.05

0.1

0.15

=2)n (0SK =3)n (Λ+Λ




Summary

Runs 1 & 2 (3): beautiful data

Run 4: high statistics? Differential measurements!non-ambiguous v2, v4(PID), v1

→ Jérôme, il faut qu’on cause...jet quenching: azimuthal dependence, as a function of PID��)

Omitted topics:“dead-cone effect” for heavy quarksvarying the cut in jet quenching studies (especially for backjet: where has momentum gone?)rapidity dependences???



Methods of flow analysis

Measuring anisotropic flow is a complicated issue:vn = 〈cosn(φ − ΦR)〉

��lab. frame @I not measured!

“standard” method: extract flow from two-particle correlations

Idea: 2 particles are correlated together because each of them is

correlated to the reaction plane by flow.

Problem: the measurement is contaminated by other sources of

two-particle correlations: quantum (HBT) effects, minijets, etc.

systematic uncertainty

better methods:

cumulants of multiparticle correlations

4-, 6-particle cumulants ⇒ nonflow effects reduced

Lee–Yang zeroes: probe collective effects (flow!)

⇔ “infinite-order” cumulant







Problem: the measurement is contaminated by other sources oftwo-particle correlations: quantum (HBT) effects, minijets, etc.


better methods:cumulants of multiparticle correlations

4-, 6-particle cumulants ⇒ nonflow effects reducedLee–Yang zeroes: probe collective effects (flow!)

⇔ “infinite-order” cumulant







Problem: the measurement is contaminated by other sources oftwo-particle correlations: quantum (HBT) effects, minijets, etc.


better methods:cumulants of multiparticle correlations

4-, 6-particle cumulants ⇒ nonflow effects reducedLee–Yang zeroes: probe collective effects (flow!)

⇔ “infinite-order” cumulantN. BORGHINI, Anisotropic flow and jet quenching – p.23/23

ed Anisotropic flowed Anisotropic flowed Elliptic flow $v_2$RHIC {ed $v_2$} results [1]RHIC {ed $v_2$} results [2]{ed $v_1$}: a simple model, ``{ed antiflow}''{ed $v_1$} at RHIC: first resultsA new observable: {ed $v_4$}avy Jet quenching{``{avy Jets}''} in Au-Au collisions at RHIC{``{avy Jets}''} in Au-Au collisions at RHICavy Jet quenchingavy Jet quenchingavy Jet quenchingavy Jet quenchingAzimuthally dependent \ avy jet quenching{ed $v_2$} at high transverse momentumRHIC {ed $v_2$} results [3]RHIC {ed $v_2$} results [3 bis]{ed $v_2$} at high transverse momentumSummaryhypertarget {methods}{Methods} of {ed flow} analysis

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Anisotropic flow and jet quenching - Fakultät für Physikborghini/Physics/... · 2007. 4. 5. · STAR Collaboration, charged particles, minimum bias, 200 GeV N. B ORGHINI , Anisotropic