[PWGDQ] add variables for global polarization (#15713)

Co-authored-by: ypwangg <ypwangg@mail.ustc.edu.cn>

Author: zjxiongOvO

PWGDQ/Core/HistogramsLibrary.cxx

@@ -1347,6 +1347,9 @@ void o2::aod::dqhistograms::DefineHistograms(HistogramManager* hm, const char* h
         hm->AddHistogram(histClass, "CosThetaStarTPC", "", false, 100, -1.0, 1.0, VarManager::kCosThetaStarTPC);
         hm->AddHistogram(histClass, "CosThetaStarFT0A", "", false, 100, -1.0, 1.0, VarManager::kCosThetaStarFT0A);
         hm->AddHistogram(histClass, "CosThetaStarFT0C", "", false, 100, -1.0, 1.0, VarManager::kCosThetaStarFT0C);
+        hm->AddHistogram(histClass, "CosThetaStarRandom", "", false, 100, -1.0, 1.0, VarManager::kCosThetaStarRandom);
+        hm->AddHistogram(histClass, "Cos2ThetaStarFT0C_Mass", "", true, 50, 2.0, 4.0, VarManager::kMass, 100, -1.0, 1.0, VarManager::kCos2ThetaStarFT0C);
+        hm->AddHistogram(histClass, "Cos2ThetaStarRandom_Mass", "", true, 50, 2.0, 4.0, VarManager::kMass, 100, -1.0, 1.0, VarManager::kCos2ThetaStarRandom);
       }
       if (subGroupStr.Contains("upsilon")) {
         hm->AddHistogram(histClass, "MassUpsilon_Pt", "", false, 500, 7.0, 12.0, VarManager::kMass, 400, 0.0, 40.0, VarManager::kPt);

PWGDQ/Core/VarManager.cxx

@@ -1425,6 +1425,8 @@ void VarManager::SetDefaultVarNames()
   fgVariableUnits[kPsi2B] = "";
   fgVariableNames[kPsi2C] = "#Psi_{2}^{C} ";
   fgVariableUnits[kPsi2C] = "";
+  fgVariableNames[kRandomPsi2] = "Random #Psi_{2} ";
+  fgVariableUnits[kRandomPsi2] = "";
   fgVariableNames[kR2SP_AB] = "R_{2}^{SP} (AB) ";
   fgVariableUnits[kR2SP_AB] = "";
   fgVariableNames[kR2SP_AC] = "R_{2}^{SP} (AC) ";
@@ -1521,6 +1523,14 @@ void VarManager::SetDefaultVarNames()
   fgVariableUnits[kCosThetaStarFT0A] = "";
   fgVariableNames[kCosThetaStarFT0C] = "cos#it{#theta}^{*}_{FT0C}";
   fgVariableUnits[kCosThetaStarFT0C] = "";
+  fgVariableNames[kAbsCosThetaStarFT0C] = "|cos#it{#theta}^{*}_{FT0C}|";
+  fgVariableUnits[kAbsCosThetaStarFT0C] = "";
+  fgVariableNames[kCos2ThetaStarFT0C] = "cos^{2}#it{#theta}^{*}_{FT0C}";
+  fgVariableUnits[kCos2ThetaStarFT0C] = "";
+  fgVariableNames[kCosThetaStarRandom] = "cos#it{#theta}^{*}_{Random}";
+  fgVariableUnits[kCosThetaStarRandom] = "";
+  fgVariableNames[kCos2ThetaStarRandom] = "cos^{2}#it{#theta}^{*}_{Random}";
+  fgVariableUnits[kCos2ThetaStarRandom] = "";
   fgVariableNames[kCosPhiVP] = "cos#it{#varphi}_{VP}";
   fgVariableUnits[kCosPhiVP] = "";
   fgVariableNames[kPhiVP] = "#varphi_{VP} - #Psi_{2}";
@@ -2337,6 +2347,10 @@ void VarManager::SetDefaultVarNames()
   fgVarNamesMap["kCosThetaStarTPC"] = kCosThetaStarTPC;
   fgVarNamesMap["kCosThetaStarFT0A"] = kCosThetaStarFT0A;
   fgVarNamesMap["kCosThetaStarFT0C"] = kCosThetaStarFT0C;
+  fgVarNamesMap["kAbsCosThetaStarFT0C"] = kAbsCosThetaStarFT0C;
+  fgVarNamesMap["kCos2ThetaStarFT0C"] = kCos2ThetaStarFT0C;
+  fgVarNamesMap["kCosThetaStarRandom"] = kCosThetaStarRandom;
+  fgVarNamesMap["kCos2ThetaStarRandom"] = kCos2ThetaStarRandom;
   fgVarNamesMap["kCosPhiVP"] = kCosPhiVP;
   fgVarNamesMap["kPhiVP"] = kPhiVP;
   fgVarNamesMap["kDeltaPhiPair2"] = kDeltaPhiPair2;
@@ -2435,6 +2449,7 @@ void VarManager::SetDefaultVarNames()
   fgVarNamesMap["kPsi2ANEG"] = kPsi2ANEG;
   fgVarNamesMap["kPsi2B"] = kPsi2B;
   fgVarNamesMap["kPsi2C"] = kPsi2C;
+  fgVarNamesMap["kRandomPsi2"] = kRandomPsi2;
   fgVarNamesMap["kCos2DeltaPhi"] = kCos2DeltaPhi;
   fgVarNamesMap["kCos2DeltaPhiMu1"] = kCos2DeltaPhiMu1;
   fgVarNamesMap["kCos2DeltaPhiMu2"] = kCos2DeltaPhiMu2;

PWGDQ/Core/VarManager.h

@@ -775,6 +775,10 @@ class VarManager : public TObject
     kCosThetaStarTPC,
     kCosThetaStarFT0A,
     kCosThetaStarFT0C,
+    kAbsCosThetaStarFT0C,
+    kCos2ThetaStarFT0C,
+    kCosThetaStarRandom,
+    kCos2ThetaStarRandom,
     kCosPhiVP,
     kPhiVP,
     kDeltaPhiPair2,
@@ -880,6 +884,7 @@ class VarManager : public TObject
     kPsi2ANEG,
     kPsi2B,
     kPsi2C,
+    kRandomPsi2,
     kCos2DeltaPhi,
     kCos2DeltaPhiMu1, // cos(phi - phi1) for muon1
     kCos2DeltaPhiMu2, ////cos(phi - phi2) for muon2
@@ -2195,6 +2200,7 @@ void VarManager::FillEvent(T const& event, float* values)
     values[VarManager::kPsi2A] = Psi2A;
     values[VarManager::kPsi2B] = Psi2B;
     values[VarManager::kPsi2C] = Psi2C;
+    values[VarManager::kRandomPsi2] = gRandom->Uniform(-o2::constants::math::PIHalf, o2::constants::math::PIHalf);
 
     if constexpr ((fillMap & ReducedEventQvectorExtra) > 0) {
       values[kQ42XA] = event.q42xa();
@@ -5697,6 +5703,13 @@ void VarManager::FillPairVn(T1 const& t1, T2 const& t2, float* values)
 
     ROOT::Math::XYZVector zaxisFT0C = ROOT::Math::XYZVector(TMath::Cos(Psi2C), TMath::Sin(Psi2C), 0).Unit();
     values[kCosThetaStarFT0C] = v_CM.Dot(zaxisFT0C);
+    values[kAbsCosThetaStarFT0C] = std::abs(values[kCosThetaStarFT0C]);
+    values[kCos2ThetaStarFT0C] = values[kCosThetaStarFT0C] * values[kCosThetaStarFT0C];
+
+    // Randomize the event plane angle to check the unpolarized contribution
+    ROOT::Math::XYZVector zaxisRandom = ROOT::Math::XYZVector(TMath::Cos(values[kRandomPsi2]), TMath::Sin(values[kRandomPsi2]), 0).Unit();
+    values[kCosThetaStarRandom] = v_CM.Dot(zaxisRandom);
+    values[kCos2ThetaStarRandom] = values[kCosThetaStarRandom] * values[kCosThetaStarRandom];
   }
 
   //  kV4, kC4POI, kC4REF etc.