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phi-meson helicity frame spin alignment and off diagonal elements

Updated on Wed, 2024-08-21 20:50. Originally created by gwilks3 on 2024-08-20 13:38.
This blog is dedicated to the ongoing work to extract and correct the helicity frame spin density matrix elements from data. We extract these parameters with respect to pT and rapidity at the current time.

Rapidity (y) dependent study (1.2 < pT < 4.2 GeV/c, 20-60% centrality):

Procedure:
  1. Fill invariant mass histograms for kaon pairs in the same event (SE) and from mixing events (ME).
    • 9 bins in cos(theta*) = [-1,1]
    • 12 bins in phi' = [0,2pi]
    • 10 bins in rapidity = [-1,1]
  2. We normalize the mixed event pairs distribution to the same event pairs distributions in the region M(K+,K-) = [1.04,1.05] and then fill distributions for SE - ME. STAR/system/files/userfiles/6551/Rapidity2DHelicityOffDiag_InvMassDistributions_19GeV_Order2_Cent9.pdf
  3. Fit SE - ME distributions integrated over cos(theta*) and phi' with Breit-Wigner + Poly1, where the Poly 1 handles residual background. 
  4. Then fix the phi-meson mass and the width parameter (Γ) from this fit and refit each individual combination of bins to calculate the normalization and Poly1 for these bins. STAR/system/files/userfiles/6551/RapidityHelicity2D_OffDiag_allThetaYieldsPhi_19GeV_Order2_cent9_eta1_eta1_pTdependence_Norm0_Poly1.pdf
  5. Yields are extracted from (integrated Breit-Wigner + Poly1) - (integrated Poly1).
  6. Run simulation with Pythia decay for corrections with the following settings:
    • Preliminary v2
    • input pT spectra from data in region |y| < 0.5
    • flat rapidity spectra
    • no input global or helicity frame spin alignment
  7. Calculate the efficiency in 2D bins of cos(theta*) vs phi' for each rapidity bin from RC/MC, where RC includes the following effects: 
    • Acceptance |eta| < 1 for kaons
    • phi-meson TPC tracking efficiency from embedding
    • TOF Matching efficiency for kaons  
    • m^2 PID efficiency for kaons
    • nsigma_kaon PID efficiency for kaons
  8. Divide raw 2D yields by 2D efficiency and fit with the following function (3/8pi) is replaced by a normalization constant (N): 

  9. Plot final extracted parameters for each term as a function of rapidity: STAR/system/files/userfiles/6551/RapidityHelicity2DCorrected_OffDiag_ExtractedSpinDensityElements_19GeV_Order2.pdf
We also have additional QA plots for the raw yields, efficiency, corrected yields, fits in 1D and 2D:

pT dependent study (|y| < 1, 20-60% centrality):

Procedure:
  1. Fill invariant mass histograms for kaon pairs in the same event (SE) and from mixing events (ME).
    • 9 bins in cos(theta*) = [-1,1]
    • 12 bins in phi' = [0,2pi]
    • 12 bins in pT: bin edges = {1.2,1.4,1.6,1.8,2.0,2.2,2.4,2.6,2.8,3.0,3.4,3.8,4.2} Gev/c
  2. We normalize the mixed event pairs distribution to the same event pairs distributions in the region M(K+,K-) = [1.04,1.05] and then fill distributions for SE - ME. STAR/system/files/userfiles/6551/2DHelicityOffDiag_InvMassDistributions_19GeV_Order2_Cent9.pdf
  3. Rebin SE - ME to 4 pT bins with the following bin edges: {1.2,1.8,2.4,3.0,4.2} GeV/c.  STAR/system/files/userfiles/6551/2DHelicityOffDiag_InvMassBackgroundSubtracted_Rebinned_19GeV_Order2_Cent9.pdf
  4. Fit rebinned SE - ME distributions integrated over cos(theta*) and phi' with Breit-Wigner + Poly1, where the Poly 1 handles residual background.
  5. Then fix the phi-meson mass and the width parameter (Γ) from this fit and refit each individual combination of bins to calculate the normalization and Poly1 for these bins. STAR/system/files/userfiles/6551/Helicity2D_OffDiag_allThetaYieldsPhi_19GeV_Order2_cent9_eta1_eta1_pTdependence_Norm0_Poly1.pdf
  6. Yields are extracted from (integrated Breit-Wigner + Poly1) - (integrated Poly1).
  7. Run simulation with Pythia decay for corrections with the following settings:
    • Preliminary v2
    • input pT spectra from data in region |y| < 0.5
    • flat rapidity spectra
    • no input global or helicity frame spin alignment
  8. Calculate the efficiency in 2D bins of cos(theta*) vs phi' for each pT bin from RC/MC, where RC includes the following effects:
    • Acceptance |eta| < 1 for kaons
    • phi-meson TPC tracking efficiency from embedding
    • TOF Matching efficiency for kaons  
    • m^2 PID efficiency for kaons
    • nsigma_kaon PID efficiency for kaons
  9. Divide raw 2D yields by 2D efficiency and fit with the following function (3/8pi) is replaced by a normalization constant (N): 

  10. Plot final extracted parameters for each term as a function of pT:STAR/system/files/userfiles/6551/Helicity2DCorrected_OffDiag_ExtractedSpinDensityElements_19GeV_Order2.pdf
 We also have additional QA plots for the raw yields, efficiency, corrected yields, fits in 1D and 2D:

Embedding Results:

Rapidity (y) dependent study (1.2 < pT < 4.2 GeV/c, 20-60% centrality):

Plot final corrected parameters for each term as a function of rapidity using corrections from embedding: STAR/system/files/userfiles/6551/RapidityHelicity2DCorrected_OffDiag_ExtractedSpinDensityElements_19GeV_Order2_Embed.pdf

We also have additional QA plots for the raw yields, efficiency, corrected yields, fits in 1D and 2D:
pT dependent study (|y| < 1, 20-60% centrality):

Plot final corrected parameters for each term as a function of pT using corrections from embedding: STAR/system/files/userfiles/6551/Helicity2DCorrected_OffDiag_ExtractedSpinDensityElements_19GeV_Order2_Embed.pdf

We also have additional QA plots for the raw yields, efficiency, corrected yields, fits in 1D and 2D:
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