Elliptic flow of  meson in Pb-Pb
Paola Pagano
09/12/2009
Paola Pagano
Università di Salerno & INFN
1
Elliptic flow
The flow is a collective motion
of the particles produced in the
ultrarelativistic nuclear reaction.
A non central collision produces
an anisotropic flow
in the transverse plane
spectators
z
participants
spectators
y
x
The anisotropic transverse flow, i.e. elliptic flow,
springs from the initial azimuthal asymmetry of the interaction region
09/12/2009
Paola Pagano
Università di Salerno & INFN
2
Elliptic flow
It has origin from the anisotropic nature of the overlap
region in the plane x-y with impact parameter b>0
b=0
The secondary interaction of particles converts the initial spatial
anisotropy in an observed momentum anisotropy in the final state
09/12/2009
Paola Pagano
Università di Salerno & INFN
3
Elliptic Flow
To measure the elliptic flow, we
need
first
reaction
to
distribution
the
Then
the
plane.
coefficients
expansion
estimate
of
of
of
the
the
y
2
Fourier
azimuthal
particles

with
x
respect to the reaction plane are
evaluated.
Poskanzer and Voloshin,
Phys. Rev. C58, 1998
N0
dN
1  2v1 cos(  2 )  2v2 cos2  2   ....

d (  2 ) 2
Elliptic flow coefficient
09/12/2009
Paola Pagano
Università di Salerno & INFN
4
Elliptic flow measurement:
recent results at RHIC
A scaling of the
elliptic flow
parameter v2 with
the number of
quarks is observed
To describe the observed scaling,
two different models have been
used:
•Quark recombination models
• Hadronic transport models.
2007
09/12/2009
In the context of both models, the
observed v2 values seem to indicate
that elliptic flow is built up prior to
hadronization, in the partonic phase.
Paola Pagano
Università di Salerno & INFN
5
 meson’s elliptic flow measurement :
recent results at RHIC (I)
2007
v2 of  meson increases
with the eccentricity of
the central region of
overlap (i.e. the reduction
of the centrality)
09/12/2009
Paola Pagano
Università di Salerno & INFN
6
 meson’s elliptic flow
measurement:
recent results at RHIC (II)
2007
NQ-scaling fit
-mesons are produced
via coalescence of seemingly
thermalized
quarks
in central Au+Au collisions.
phi meson
NQ = 2.3 ± 0.4
This observation implies that
hot and dense matter with
partonic collectivity
has been formed at RHIC
09/12/2009
Paola Pagano
Università di Salerno & INFN
7
How can we perform this measurement in ALICE?
Mass invariant method
1)
Mass invariant histogram for phi meson
2)
Estimation of Signal and Background:
fit with Breit-Wigner + polynomial
3)
Estimation of reaction plane angle for each event:

wi sin( 2i ) 
1
1 

 2  tan 
2
  wi cos( 2i ) 
09/12/2009
Paola Pagano
Università di Salerno & INFN
wi e i for the l’ith
particle of a given event
8
How can we perform this measurement in ALICE?
Mass invariant method (cont’d)
4)
Estimate of the opening angle for all K+K- pairs
for each event
5)
Histogram of v2(minv)= <cos2(KK-2)>
6)
Fit of the last histogram with the function:
v2(minv) = a(minv)v2S+[1-a(minv)]v2B(minv)
where v2(minv) = <cos2(KK-2)>
v2S is the v2 we are looking for
v2B is the v2 of combinatorial background
a(minv) = N(minv) / NK+ K_ (minv)
09/12/2009
Paola Pagano
Università di Salerno & INFN
9
Status of the analysis
• The analysis tools are ready.
• We are still producing a sufficient number of events
 Estimation: approximately 106 events.
• Two Productions:
- one official, managed by the collaboration, for the
production of the background, now I’m generating the signal
- one private, containing only the generated particles
without recostruction-> ongoing on the Salerno computer
cluster
• The time and space needed to perform this analysis, make
essential the use of the world computing Grid facility.
• Here we show some preliminary results for the estimation of:
- reaction plane angle
- v2 for all particles
09/12/2009
Paola Pagano
Università di Salerno & INFN
10
Reaction Plane Angle estimation:
checking the algorithm
Generated Particles
Reconstructed
Particles

wi sin( 2i ) 
1
1 

 2  tan 
2
  wi cos( 2i ) 
09/12/2009
Paola Pagano
Università di Salerno & INFN
11
v2 estimation:
checking the generator
After the determination of reaction plane angle Ψ2 , it’s possible to build
a global distribution dN/d(φ-Ψ2) using events with same multiplicity and
centrality.
This distribution can be interpolated with the function:
dN/dφ = cost.(1/2π) + 2 v2 cos2(φ-Ψ2)
v2: 0.02794 ± 0.0011
Generated Particles
v2: 0.03163 ±
0.0011
φ-Ψ2 (degree)
Reconstructed Particles
21/12/2015
12
φ-Ψ2 (degree)
The End
09/12/2009
Paola Pagano
Università di Salerno & INFN
13
Back up
Metodo della matrice di sfericità trasversa (I)
  i cos i

  sin  cos 
i
i
 i

sin  i cos i   S11

S

sin

 i i   12
i
S12 

S 22 
• Diagonalizzazione della matrice di sfericità
trasversa
S11  
S12
S12
S 22  
0
Metodo della matrice di sfericità trasversa (II)
S11  S 22  ( S11  S 22 )  4S
1, 2 
2
1  2
Il rapporto  
è proporzionale a v2
1  2
2
2
12
Dagli autovettori si ricava l’angolo del piano di reazione 2 :
  S12 

21  ATan2
 S11  1 