1. Analisi del flow con il metodo dei coefficienti di Fourier
Francesco Prino –INFN Torino
1° Convegno nazionale sulla fisica di Alice
Catania gennaio 2005
Physics motivation
Few experimental results
Description of the analysis method

2. Flow in heavy ion collisions
Flow = collective motion of particles (due to high pressure arising from compression and heating of nuclear matter) superimposed on top of the thermal motion
Collective Motions
Longitudinal expansion
Transverse Plane
Beam direction
Radial Transverse Flow
Anisotropic Transverse Flow
F. Prino
Catania, Jan 2005

3. Anisotropic transverse flow
Correlation between azimuthal angles of outgoing particles and the direction of the impact parameter
Peripheral nucleus-nucleus collisions produce an asymmetric particle source x y z
“Almond-shaped” overlap region
Larger pressure gradient in x-z plane than in y direction
Pressure gradients in the transverse plane
Particle rescatterings
Convert the initial spatial anisotropy into an observed momentum anisotropy
Asymmetry disappears with time
Sensitive to the early stages of collision evolution EOS
F. Prino
Catania, Jan 2005

4. REACTION PLANE = plane defined by beam direction and impact parameter
Flow parametrization
Fourier expansion of azimuthal particle distribution (Poskanzer and Voloshin, Phys. Rev. C58, 1998) x y
YRP
REACTION PLANE = plane defined by beam direction and impact parameter
View along beamline
F. Prino
Catania, Jan 2005

5. Directed flow coefficient
View along beamline
Due to pressure built up between nuclei during the time of overlap
Affects mostly particles at forward and backward rapidities
Estabilished very early
Time scale = overlap time of the 2 nuclei (decreases with increasing beam energy)
F. Prino
Catania, Jan 2005

6. Directed flow coefficient
Isotropic
V1=10%
V1=25%
F. Prino
Catania, Jan 2005

7. Elliptic flow coefficient
View along beamline
IN PLANE
Due to azimuthal anisotropy of transverse pressure gradient caused by deformation of reaction region in the transverse plane
Strongest near midrapidity
Eliminates the geometrical asymmetry which generates it
Time scale > than for directed flow (hydrodynamics may describe it)
OUT OF PLANE
F. Prino
Catania, Jan 2005

8. Elliptic flow coefficient
Isotropic
V2=25%
V2=10%
F. Prino
Catania, Jan 2005

9. In Plane vs Out of Plane Elliptic flow coefficient:
v2>0 In plane elliptic flow
v2<0 Out of plane elliptic flow
Isotropic
V2=10%
V2= - 10%
F. Prino
Catania, Jan 2005

10. Higher order harmonics
Isotropic
V4=10%
V4=25%
Isotropic
V3=25%
V3=10%
Fourth order coefficient v4:
Restore the elliptically deformed shape of particle distribution
Magnitude and sign sensitive to initial conditions of hydro
Strong potential to constrain model calculations
Carry information on the dynamical evolution of the system
(Peter Kolb, PRC 68, (R))
F. Prino
Catania, Jan 2005

11. Directed + Elliptic flow
Flow vs. rapidity
NA49
Elliptic RHIC
Preliminary
Pb-Pb MB
Directed + Elliptic flow
@ √s = 17 GeV
Au-Au
(0-40% central)
F. Prino
Catania, Jan 2005

12. Elliptic flow vs. centrality
Observed elliptic flow depends on:
Eccentricity → Decreases with increasing centrality
Amount of rescattering → Increases with increasing centrality
F. Prino
Catania, Jan 2005

13. Elliptic flow vs. pT Elliptic flow v2:
grows with pT at low pT → consistent with hydro
saturates at high pT
F. Prino
Catania, Jan 2005

14. Elliptic flow vs. energy
Preliminary
Au+Au data
(0-40% central)
Different physical mechanisms in different energy regimes
Linear logarithmic growth with √s from SPS to RHIC
strong interacting system at RHIC energy
F. Prino
Catania, Jan 2005

15. Experimental measurement
Estimate the reaction plane
Reaction plane not directly measurable
Event plane = estimation of the reaction plane from the anisotropic flow itself (Poskanzer and Voloshin, Phys. Rev. C58, 1998)
Particle distributions with respect to the event plane
Avoid autocorrelations: do not use the same particle for event plane and flow determination
Correct for the limited resolution of the event plane
F. Prino
Catania, Jan 2005

16. Estimate the reaction plane
Event plane = estimation of the reaction plane from the anisotropic flow itself
Weights wi optimized to have the best possible resolution
wi=pT (momentum weighting) / wi=1 (number of particles weighting)
Event plane can be extracted from any harmonic
The event plane angle Yn from the n-th harmonic is in the range 0≤Yn≤2p/n
F. Prino
Catania, Jan 2005

17. Acceptance correction
Event plane distributions not isotropic due to detector acceptance and efficiency
Affects the measurement of the flow signal
Different correction methods (see Poskanzer and Voloshin, Phys. Rev. C58, 1998 and references therein)
Example from CERES flow analysis
F. Prino
Catania, Jan 2005

18. Particle distributions with respect to the event plane
Use the event plane (measured) angle instead of the reaction plane (unknown) angle
Fourier coefficient vn can be evaluated using the event plane from any harmonic m, if n is a multiple of m
Best accuracy obtained if k=1, i.e. with the event plane determined from the same harmonic n.
Avoid autocorrelations:
Correlate particles in a given h region with event plane of a separate h region
Correlate each particle with the event plane of all the other particles
Correlate particles of a given charge sign with event plane of particles of the opposite charge sign …
F. Prino
Catania, Jan 2005

19. Event plane resolution
The finite number of detected particles limits the resolution in the angle of the measured event plane
The event plane resolution depends on:
Amount of anisotropy
Number of particles used in the event plane calculation
Deviation between measured event plane and true reaction plane
F. Prino
Catania, Jan 2005

20. Event plane resolution Flow coefficients underestimated
The resolution in the event plane angle affects the measured values of the Fourier coefficients vn
Flow coefficients underestimated
F. Prino
Catania, Jan 2005

21. Resolution estimation
Unknown angle YRP still present in the formula:
Solution: use independent sub-events (a) and (b)
Assumption: no other correlations between these 2 sub-events are present except for the ones due to flow
F. Prino
Catania, Jan 2005

22. Resolution Correction
The event plane resolution depends on:
Amount of anisotropy
Number of particles used for the event plane calculation
F. Prino
Catania, Jan 2005

23. Non-flow correlations
The standard Fourier method:
Extract flow from two-particle correlations
Assume that the only azimuthal correlation between outgoing particles is due to their correlation to the reaction plane (i.e. to anisotropic flow)
Non-flow correlations due to:
Physics
Transverse momentum conservation
Affects only the measurement of directed flow
Quantum correlations due to HBT effect
Resonances decay (such as r→pp)
Jets
Apparatus and detector effects
”Cumulants” method developed (Borghini, Dinh, Ollitrault, Phys Rev C 63, 2001):
Extract flow from multi-particle correlation
Less biased by non-flow correlations
Drawbacks:
larger statistical errors
more sensitive to fluctuation effects
F. Prino
Catania, Jan 2005

24. back-to-back track pairs
Cumulant method
v2in=0.1
Standard method
back-to-back track pairs
embedded
4-th order cumulant
F. Prino
Catania, Jan 2005