Analisi del flow con il metodo dei coefficienti di Fourier Francesco Prino –INFN Torino 1° Convegno nazionale sulla fisica di Alice Catania 11-12 gennaio 2005 Physics motivation Few experimental results Description of the analysis method

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

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

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

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

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

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

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

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

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, 031902(R)) F. Prino Catania, Jan 2005

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

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

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

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

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

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

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

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

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

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

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

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

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

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