Post on 31-Jan-2021
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
RHIC France meeting, Etretat, June 15, 2004
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).
N. BORGHINI, Anisotropic flow and jet quenching – p.2/23
RHIC France meeting, Etretat, June 15, 2004
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!
N. BORGHINI, Anisotropic flow and jet quenching – p.3/23
RHIC France meeting, Etretat, June 15, 2004
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
N. BORGHINI, Anisotropic flow and jet quenching – p.4/23
RHIC France meeting, Etretat, June 15, 2004
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
Q
The difference between bothmeasurements is due to “non-flow” effects that contaminatethe standard method
♥ v2 sign measured recently (STAR, Oct. 2003): v2 > 0
N. BORGHINI, Anisotropic flow and jet quenching – p.5/23
RHIC France meeting, Etretat, June 15, 2004
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
N. BORGHINI, Anisotropic flow and jet quenching – p.6/23
RHIC France meeting, Etretat, June 15, 2004
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)!
N. BORGHINI, Anisotropic flow and jet quenching – p.7/23
RHIC France meeting, Etretat, June 15, 2004
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)
N. BORGHINI, Anisotropic flow and jet quenching – p.8/23
RHIC France meeting, Etretat, June 15, 2004
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)
N. BORGHINI, Anisotropic flow and jet quenching – p.8/23
RHIC France meeting, Etretat, June 15, 2004
A new observable: v4STAR Collaboration, charged particles, minimum bias, 200 GeV
N. BORGHINI, Anisotropic flow and jet quenching – p.9/23
RHIC France meeting, Etretat, June 15, 2004
A new observable: v4STAR Collaboration, charged particles, minimum bias, 200 GeV
N. BORGHINI, Anisotropic flow and jet quenching – p.9/23
RHIC France meeting, Etretat, June 15, 2004
Jet quenching
proton-proton
vs. nucleus-nucleus: medium effect?
figures courtesy of F. GELIS
N. BORGHINI, Anisotropic flow and jet quenching – p.10/23
RHIC France meeting, Etretat, June 15, 2004
Jet quenching
proton-proton vs. nucleus-nucleus: medium effect?
figures courtesy of F. GELIS
N. BORGHINI, Anisotropic flow and jet quenching – p.10/23
RHIC France meeting, Etretat, June 15, 2004
“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
N. BORGHINI, Anisotropic flow and jet quenching – p.11/23
RHIC France meeting, Etretat, June 15, 2004
“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
|
RHIC France meeting, Etretat, June 15, 2004
Jet quenching
Extreme scenario:
Only the jets formed close to the edge manageto get out of the medium
Is this supported by QCD?
N. BORGHINI, Anisotropic flow and jet quenching – p.13/23
RHIC France meeting, Etretat, June 15, 2004
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
N. BORGHINI, Anisotropic flow and jet quenching – p.14/23
RHIC France meeting, Etretat, June 15, 2004
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
N. BORGHINI, Anisotropic flow and jet quenching – p.15/23
RHIC France meeting, Etretat, June 15, 2004
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”
N. BORGHINI, Anisotropic flow and jet quenching – p.16/23
RHIC France meeting, Etretat, June 15, 2004
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”
N. BORGHINI, Anisotropic flow and jet quenching – p.16/23
RHIC France meeting, Etretat, June 15, 2004
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
N. BORGHINI, Anisotropic flow and jet quenching – p.17/23
RHIC France meeting, Etretat, June 15, 2004
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
N. BORGHINI, Anisotropic flow and jet quenching – p.17/23
RHIC France meeting, Etretat, June 15, 2004
v2 at high transversemomentum
A first idea: v2 from jet quenching
For a given high-pT parton, the amount of jet quenching dependson the length of the in-medium path:
(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
N. BORGHINI, Anisotropic flow and jet quenching – p.18/23
RHIC France meeting, Etretat, June 15, 2004
v2 at high transversemomentum
A first idea: v2 from jet quenching
For a given high-pT parton, the amount of jet quenching dependson the length of the in-medium path:
(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
N. BORGHINI, Anisotropic flow and jet quenching – p.18/23
RHIC France meeting, Etretat, June 15, 2004
RHIC v2 results [3]
STAR Collaboration, charged particles, 200 GeV
N. BORGHINI, Anisotropic flow and jet quenching – p.19/23
RHIC France meeting, Etretat, June 15, 2004
RHIC v2 results [3 bis]
PHENIX Collaboration, 200 GeV
N. BORGHINI, Anisotropic flow and jet quenching – p.20/23
RHIC France meeting, Etretat, June 15, 2004
v2 at high transversemomentum
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
N. BORGHINI, Anisotropic flow and jet quenching – p.21/23
RHIC France meeting, Etretat, June 15, 2004
v2 at high transversemomentum
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
)
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
/n (GeV/c)TpTransverse Momentum
N. BORGHINI, Anisotropic flow and jet quenching – p.21/23
RHIC France meeting, Etretat, June 15, 2004
v2 at high transversemomentum
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
N. BORGHINI, Anisotropic flow and jet quenching – p.21/23
RHIC France meeting, Etretat, June 15, 2004
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???
N. BORGHINI, Anisotropic flow and jet quenching – p.22/23
RHIC France meeting, Etretat, June 15, 2004
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
N. BORGHINI, Anisotropic flow and jet quenching – p.23/23
RHIC France meeting, Etretat, June 15, 2004
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
Problem: the measurement is contaminated by other sources oftwo-particle correlations: quantum (HBT) effects, minijets, etc.
systematic uncertainty
better methods:cumulants of multiparticle correlations
4-, 6-particle cumulants ⇒ nonflow effects reducedLee–Yang zeroes: probe collective effects (flow!)
⇔ “infinite-order” cumulant
N. BORGHINI, Anisotropic flow and jet quenching – p.23/23
RHIC France meeting, Etretat, June 15, 2004
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
Problem: the measurement is contaminated by other sources oftwo-particle correlations: quantum (HBT) effects, minijets, etc.
systematic uncertainty
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