How to measure elliptic flow in

Transcription

1 How to measure elliptic flow in Jovan Milošević University of Oslo, Norway FIS, 26-th Sep. 27, Iriški Venac p.1/12

2 A schematic view of a non-central nucleus-nucleus collision Does in TeV regime proton-proton collision looks like that? With an increase of the incident energy the edge of the overlapping region becomes sharper and the smearing of it, due to the strong QCD interactions, becomes smaller K. Boreskov, A. B. Kaidalov and O. Kancheli, Elliptic flow in pp collisions, in preparation FIS, 26-th Sep. 27, Iriški Venac p.2/12

3 Building of the anisotropic flow Asymmetry in coordinate space (overlap region) develops into an asymmetry in momentum space due to the collective interactions (pressure gradients) reaction plane The initial compression pressure p collective flow space asymmetry Non-central collisions px > p y anisotropic flow y P max x P= reaction plane Fourier decomposition: dn/dφ = N {1 + P + n= 2v n cos[n(φ Φ)]} Quadrupole component = cos[2(φ Φ)] is called elliptic flow momentum asymmetry FIS, 26-th Sep. 27, Iriški Venac p.3/12

4 Simulated data Flow + Hijing simulation On Hijing Jet data (J) are randomly added soft Flow particles (F) where: M F 1.2M J FIS, 26-th Sep. 27, Iriški Venac p.4/12

5 Simulated data Flow + Hijing simulation On Hijing Jet data (J) are randomly added soft Flow particles (F) where: M F 1.2M J Flow particles have similar pseudorapidity and p T distributions. The distribution of the laboratory azimuthal angles of particles, φ lab, are made in a way to be random (and isotropic) in the laboratory frame and to have an (elliptic) flow pattern with respect to the true reaction plane FIS, 26-th Sep. 27, Iriški Venac p.4/12

6 Simulated data Flow + Hijing simulation On Hijing Jet data (J) are randomly added soft Flow particles (F) where: M F 1.2M J Flow particles have similar pseudorapidity and p T distributions. The distribution of the laboratory azimuthal angles of particles, φ lab, are made in a way to be random (and isotropic) in the laboratory frame and to have an (elliptic) flow pattern with respect to the true reaction plane The intention is to check could LYZ Method remove the contribution of Jet (Hijing) particles from the flow. FIS, 26-th Sep. 27, Iriški Venac p.4/12

7 Two particle azimuthal distributions Flow particles Jet particles Jet+Flow particles dn d φ 18 dn d φ 18 dn d φ normalized to N trigg <N part < φ φ φ Simulated event: Huge elliptic flow signal (left) is hidden by the signal coming from the jet particles (middle) in the final distributions of both kind of particles taken together Real event: Strictly speaking, there is no possibility, by means of cuts, to distinguish between flow and jet particles FIS, 26-th Sep. 27, Iriški Venac p.5/12

8 Lee-Yang Zero Method Integrated flow V 2 = M j=1 w j cos[2(φ j Φ)] is connected with the Fourier coefficient via: V 2 = M w, where M w = M j=1 w j. N.Borghini, R.S.Bhalerao, and J.-Y.Ollitrault, nucl-th/4253 (24) FIS, 26-th Sep. 27, Iriški Venac p.6/12

9 Lee-Yang Zero Method Integrated flow V 2 = M j=1 w j cos[2(φ j Φ)] is connected with the Fourier coefficient via: V 2 = M w, where M w = M j=1 w j. for each event one calculates the complex-valued function g θ (ir) = M j=1 {1 + irw j cos[2(φ j θ)]} for various values of the real positive variable r and of the reference angle θ ( θ π/2). The φ j is the measured laboratory azimuthal angle of a particle and the product goes over all detected particles. N.Borghini, R.S.Bhalerao, and J.-Y.Ollitrault, nucl-th/4253 (24) FIS, 26-th Sep. 27, Iriški Venac p.6/12

10 Lee-Yang Zero Method Integrated flow V 2 = M j=1 w j cos[2(φ j Φ)] is connected with the Fourier coefficient via: V 2 = M w, where M w = M j=1 w j. for each event one calculates the complex-valued function g θ (ir) = M j=1 {1 + irw j cos[2(φ j θ)]} for various values of the real positive variable r and of the reference angle θ ( θ π/2). The φ j is the measured laboratory azimuthal angle of a particle and the product goes over all detected particles. One has to average g θ (ir) over events for each value of r and θ: G θ (ir) g θ (ir) = 1 N events gθ (ir) N.Borghini, R.S.Bhalerao, and J.-Y.Ollitrault, nucl-th/4253 (24) FIS, 26-th Sep. 27, Iriški Venac p.6/12

11 Lee-Yang Zero Method For each θ, the position of r θ of the first minimum of the modulus G θ (ir) has to be found. Then the estimate of the integrated flow V 2 is given by: V2 θ { } j 1 where r θ j is the first zero of the Bessel function J. FIS, 26-th Sep. 27, Iriški Venac p.7/12

12 Lee-Yang Zero Method For each θ, the position of r θ of the first minimum of the modulus G θ (ir) has to be found. Then the estimate of the integrated flow V 2 is given by: V2 θ { } j 1 where r θ j is the first zero of the Bessel function J. Once the integrated flow is obtained, the differential flow analysis can be done. v θ 2{ } = V θ 2 { } J 1(j 1 ) J 2 (j 1 ) Re( gθ(irθ ) cos(2(ψ θ)) 1+ir θ w ψ cos(2(ψ θ)) θ ) w j cos(2(φ j θ)) 1+ir θ ) evts w j cos(2(φ j θ)) g θ (ir θ ) P j FIS, 26-th Sep. 27, Iriški Venac p.7/12

13 Lee-Yang Zero Method For each θ, the position of r θ of the first minimum of the modulus G θ (ir) has to be found. Then the estimate of the integrated flow V 2 is given by: V2 θ { } j 1 where r θ j is the first zero of the Bessel function J. Once the integrated flow is obtained, the differential flow analysis can be done. v θ 2{ } = V θ 2 { } J 1(j 1 ) J 2 (j 1 ) Re( gθ(irθ ) cos(2(ψ θ)) 1+ir θ w ψ cos(2(ψ θ)) θ ) w j cos(2(φ j θ)) 1+ir θ ) evts w j cos(2(φ j θ)) g θ (ir θ ) P j The necessary statistics is given by the following inequality: v2 θ > j 1 2MlnN where M is multiplicity and N is the number of events. FIS, 26-th Sep. 27, Iriški Venac p.7/12

14 True and reconstructed coefficients vs η and p T very peripheral semicentral rather central 15 < N part < < N part < < N part < jet; true RP 2 flow; true RP jet; reco. RP η η η pt(gev/c) pt(gev/c) pt(gev/c) FIS, 26-th Sep. 27, Iriški Venac p.8/12

15 Generating functions Only when both, the magnitude of v2 and the multiplicity are high enough, the generating function show a sharp minimum close to zero Graph Graph G 2 1 G 2 1 G <N part <18 θ= jet flow jet+flow 21<N part < <N part <3 θ= θ= r r FIS, 26-th Sep. 27, Iriški Venac p.9/12

16 LYZ reconstructed coefficients 27<N part < <N part < <N part < η η η.8 jet part flow part jet+flow part pt(gev/c) pt(gev/c) pt(gev/c) FIS, 26-th Sep. 27, Iriški Venac p.1/12

17 True and LYZ reconstructed coefficients <N part < <N part <24 4 flow; true RP 2 flow; reco. LYZ jet+flow; reco LYZ η η η <N part < pt(gev/c) pt(gev/c) pt(gev/c) FIS, 26-th Sep. 27, Iriški Venac p.11/12

18 Conclusion and outlook Preliminary results on the feasibility of the Lee-Yang Zero method applied on HIJING are presented FIS, 26-th Sep. 27, Iriški Venac p.12/12

19 Conclusion and outlook Preliminary results on the feasibility of the Lee-Yang Zero method applied on HIJING are presented The LYZ method doesn t work for very peripheral events (due to the small multiplicity) and for rather central events (where one suppose a small anisotropy and consequently a small magnitude) FIS, 26-th Sep. 27, Iriški Venac p.12/12

20 Conclusion and outlook Preliminary results on the feasibility of the Lee-Yang Zero method applied on HIJING are presented The LYZ method doesn t work for very peripheral events (due to the small multiplicity) and for rather central events (where one suppose a small anisotropy and consequently a small magnitude) In between these two extremes the shape of the differential has been reconstructed but it undershoots the true flow due to the multiplicity fluctuations and unremoved jet remnants FIS, 26-th Sep. 27, Iriški Venac p.12/12

21 Conclusion and outlook Preliminary results on the feasibility of the Lee-Yang Zero method applied on HIJING are presented The LYZ method doesn t work for very peripheral events (due to the small multiplicity) and for rather central events (where one suppose a small anisotropy and consequently a small magnitude) In between these two extremes the shape of the differential has been reconstructed but it undershoots the true flow due to the multiplicity fluctuations and unremoved jet remnants If the theoretically predicted really exists in pp@lhc it will be a difficult task to extract it from the huge jet contribution which hides the flow FIS, 26-th Sep. 27, Iriški Venac p.12/12