The below calculations were done with 45k events simulated via HIJING + GEANT (starsim) + EPDFastSimMaker.
Simulated data are available at /star/data06/EPD/Simulations/Mate/

Obtaining the 2nd order Event Plane in the simulation

• Hits in the EPD: φ determined based on tile center
  • Took mPhiCenter[12][31][2] array from StEpdGeom
• Q-sums for the east and west (− and +) sides:
  • Q_(2,y)^±=∑_{(i∈{E/W hits})} sin2φ_i
  • Q_(2,x)^±=∑_{(i∈{E/W hits})} cos2φ_i
  • (where hits really mean particles that left a hit, i.e. sum goes over list of StEpdHit objects; and I exclude particles with deposited energy such that ADC<50)
• Event plane:
  • Ψ₂^±=1/2 tan^₋₁(Q_(2,y)^±/Q_(2,x)^±)
• (or in a code, the atan2 function can be used)
• For flow measurements, event plane resolution needed
• Might be approximated as: R=√<cos(2(Ψ₂⁺-Ψ₂⁻))>

Adding flow and reaction plane to Hijing

• Hijing has no flow (amazing), and has Ψ_RP=0 for all events
• How can we add a reaction plane?
  • Randomly choose Ψ_RP∈[−π,+π]
  • Shift all particles in φ by Ψ_RP
  • See below plot (on the left; red is Ψ₂⁺, black is Ψ₂⁻ ) for obtained reaction plane distributions, calculated from the Q-sums mentioned above
• How can we add flow?
  • Randomly suppressing particles by prob=(1+2⋅v₂⋅cos⁡2φ)/(1+2v₂) (dividing factor needed to have prob≤1)
  • Making v₂ depend on kinematics:
    • v₂= p_T/(500 MeV/c) (0.06−0.005⋅|η|)
    • First factor kept constant above 2 GeV/c
    • Second factor kept zero for |η|>12
  • Check by shifting particles as φ=φ_raw−Ψ_RP
  • See below plot (on the right) for obtained dN/dφ (red is raw phi distribution, black is true distribution, latter is fitted with a cosine); extracted v₂ is 0.052, in line with what was put in

Event Plane resolution

• The two sides (Ψ₊ and Ψ₋) are now correlated (45k events i.e. limited statistics), see below plot (on the left)
• Event plane resolution can be calculated, R=√0.114=0.338, see below plot (on the right)
  • For this v₂(η,p_T) and these events
  • Depends quite strongly on v₂(η)!