embedding: add rfMirror option to transform input muon four-vectors

This mirrors the input muons along the plane defined by the Z axis and
the proton axis. In contrast to the rfRotation, this seems to preserve
the polarization of the Z boson.

TauAnalysis/MCEmbeddingTools/plugins/ParticleReplacerZtautau.cc

@@ -143,6 +143,7 @@ ParticleReplacerZtautau::ParticleReplacerZtautau(const edm::ParameterSet& cfg)
   }
 
   rfRotationAngle_ = cfg.getParameter<double>("rfRotationAngle")*TMath::Pi()/180.;
+  rfMirror_ = cfg.getParameter<bool>("rfMirror");
 
   std::string applyMuonRadiationCorrection_string = cfg.getParameter<std::string>("applyMuonRadiationCorrection");
   if ( applyMuonRadiationCorrection_string != "" ) {
@@ -872,6 +873,30 @@ namespace
     return p4_rotated;
   }
 
+  reco::Particle::LorentzVector mirror(const reco::Particle::LorentzVector& p4, const reco::Particle::LorentzVector& zAxis, const reco::Particle::LorentzVector& pAxis)
+  {
+    typedef ROOT::Math::DisplacementVector3D<ROOT::Math::Cartesian3D<double>, ROOT::Math::DefaultCoordinateSystemTag> RotVector3;
+
+    // Make zAxis and pAxis orthogonal:
+    // (this is not strictly needed)
+    const RotVector3 pAxisOrtho = pAxis.Vect() - pAxis.Vect().Dot(zAxis.Vect().Unit()) * zAxis.Vect().Unit();
+    assert(fabs(pAxisOrtho.Dot(zAxis.Vect())) < 1e-3);
+
+    // Define a cartesian coordinate system such that the X axis is in the projected proton momentum direction,
+    // the Z axis is in the Z boson direction and the Y axis is orthogonal on the two:
+    const RotVector3 x = pAxisOrtho.Unit();
+    const RotVector3 z = zAxis.Vect().Unit();
+    const RotVector3 y = x.Cross(z).Unit();
+
+    // Mirror the vector on the x-z plane
+    const double ycomp1 = p4.Vect().Dot(y);
+    const RotVector3 y1 = p4.Vect() - 2 * ycomp1 * y;
+    assert(fabs(ycomp1 + y1.Dot(y)) < 1e-3);
+
+    const reco::Particle::LorentzVector p4Mirrored(y1.x(), y1.y(), y1.z(), p4.energy());
+    return p4Mirrored;
+  }
+
   void print(const std::string& label, const reco::Particle::LorentzVector& p4, const reco::Particle::LorentzVector* p4_ref = 0)
   {
     std::cout << label << ": En = " << p4.E() << ", Pt = " << p4.pt() << " (Px = " << p4.px() << ", Py = " << p4.py() << ")," 
@@ -917,11 +942,21 @@ void ParticleReplacerZtautau::transformMuMu2LepLep(CLHEP::HepRandomEngine& rando
       double u = randomEngine.flat();
       rfRotationAngle_value = 2.*TMath::Pi()*u;
     }
-    
+
     muon1P4_rf = rotate(muon1P4_rf, zP4_lab, rfRotationAngle_value);
     muon2P4_rf = rotate(muon2P4_rf, zP4_lab, rfRotationAngle_value);
   }
 
+  if ( rfMirror_ ) {
+    double protonEn = beamEnergy_;
+    double protonPz = sqrt(square(protonEn) - square(protonMass));
+    const reco::Particle::LorentzVector pplus_lab(0., 0., protonPz, protonEn);
+    const reco::Particle::LorentzVector pplus_rf = boost_to_rf(pplus_lab);
+
+    muon1P4_rf = mirror(muon1P4_rf, zP4_lab, pplus_rf);
+    muon2P4_rf = mirror(muon2P4_rf, zP4_lab, pplus_rf); 
+  }
+
   double muon1P_rf2 = square(muon1P4_rf.px()) + square(muon1P4_rf.py()) + square(muon1P4_rf.pz());
   double lep1Mass2 = square(targetParticle1Mass_);
   double lep1En_rf = 0.5*zP4_rf.E();

TauAnalysis/MCEmbeddingTools/plugins/ParticleReplacerZtautau.h

@@ -78,7 +78,9 @@ class ParticleReplacerZtautau : public ParticleReplacerBase
   bool useTauolaPolarization_;
   double rfRotationAngle_; // angle of rotation around Z-direction of embedded leptons wrt. reconstructed muons
                            // (used to "place" simulated leptons in a detector region different from reconstructed muons,
-                           //  while preserving Z/W-boson momentum and spin effects)
+                           // Note this does not preserve the Z polarization!!!
+  bool rfMirror_; // mirror the muon momentum vectors at the plane defined by the Z axis and the proton axis
+                  // This preserves the Z polarization from what we have seen so far.
 
   gen::TauolaInterfaceBase* tauola_;
   // keep track if TAUOLA interface has already been initialized.

TauAnalysis/MCEmbeddingTools/python/MCParticleReplacer_cfi.py

@@ -78,7 +78,8 @@
         PhotosOptions = cms.PSet(),
         filterEfficiency = cms.untracked.double(1.0),
         beamEnergy = cms.double(4000.), # GeV
-        rfRotationAngle = cms.double(90.),
+        rfRotationAngle = cms.double(0.),
+	rfMirror = cms.bool(True),
         applyMuonRadiationCorrection = cms.string(""),
         enablePhotosFSR = cms.bool(False),
         pythiaHepMCVerbosity = cms.untracked.bool(False),

TauAnalysis/MCEmbeddingTools/python/embeddingCustomizeAll.py

@@ -220,6 +220,9 @@ def customise(process):
   print "Setting rfRotationAngle to %1.0f" % process.customization_options.rfRotationAngle.value()
   process.generator.Ztautau.rfRotationAngle = process.customization_options.rfRotationAngle
 
+  print "Setting rfMirror to %s" % process.customization_options.rfMirror.value()
+  process.generator.Ztautau.rfMirror = process.customization_options.rfMirror
+
   print "Setting muon radiation corrections to \"%s\"" % process.customization_options.applyMuonRadiationCorrection.value()
   process.generator.Ztautau.applyMuonRadiationCorrection = process.customization_options.applyMuonRadiationCorrection
 

TauAnalysis/MCEmbeddingTools/python/setDefaults.py

@@ -23,7 +23,8 @@ def setDefaults(process):
       mdtau                        = cms.int32(0),       # mdtau value passed to TAUOLA: 0=no tau decay mode selection,
       useTauolaPolarization        = cms.bool(False),    # disable tau polarization effects in TAUOLA, weight events by weights computed by TauSpinner instead
       transformationMode           = cms.int32(1),       # transformation mode: 0=mumu->mumu, 1=mumu->tautau
-      rfRotationAngle              = cms.double(90.),    # rotation angle around Z-boson direction, used when replacing muons by simulated taus
+      rfRotationAngle              = cms.double(0.),     # rotation angle around Z-boson direction, used when replacing muons by simulated taus
+      rfMirror                     = cms.bool(True),  # mirror at the Z-boson / proton plane
       embeddingMode                = cms.string("RH"),   # embedding mode: 'PF'=particle flow embedding, 'RH'=recHit embedding
       replaceGenOrRecMuonMomenta   = cms.string("rec"),  # take momenta of generated tau leptons from: 'rec'=reconstructed muons, 'gen'=generator level muons
       applyMuonRadiationCorrection = cms.string(""),     # should I correct the momementa of replaced muons for muon -> muon + photon radiation ?