Rivet::Sphericity Class Referenceabstract Calculate the sphericity event shape. More...
Inheritance diagram for Rivet::Sphericity:
Detailed DescriptionCalculate the sphericity event shape. The sphericity tensor (or quadratic momentum tensor) is defined as \[ S^{\alpha \beta} = \frac{\sum_i p_i^\alpha p_i^\beta}{\sum_i |\mathbf{p}_i|^2} \] , where the Greek indices are spatial components and the Latin indices are used for sums over particles. From this, the sphericity, aplanarity and planarity can be calculated by combinations of eigenvalues. Defining the three eigenvalues \( \lambda_1 \ge \lambda_2 \ge \lambda_3 \), with \( \lambda_1 + \lambda_2 + \lambda_3 = 1 \), the sphericity is \[ S = \frac{3}{2} (\lambda_2 + \lambda_3) \] The aplanarity is \( A = \frac{3}{2}\lambda_3 \) and the planarity is \( P = \frac{2}{3}(S-2A) = \lambda_2 - \lambda_3 \). The eigenvectors define a set of spatial axes comparable with the thrust axes, but more sensitive to high momentum particles due to the quadratic sensitivity of the tensor to the particle momenta. Since the sphericity is quadratic in the particle momenta, it is not an infrared safe observable in perturbative QCD. This can be fixed by adding a regularizing power of \(r\) to the definition: \[ S^{\alpha \beta} = \frac{\sum_i |\mathbf{p}_i|^{r-2} p_i^\alpha p_i^\beta} {\sum_i |\mathbf{p}_i|^r} \] \(r\) is available as a constructor argument on this class and will be taken into account by the Cmp<Projection> operation, so a single analysis can use several sphericity projections with different \(r\) values without fear of a clash. Member Function Documentation◆ apply()
template<typename PROJ = Projection>
Apply the supplied projection on event evt. Apply the supplied projection on event evt (user-facing alias). Referenced by Rivet::ALICE::V0Trigger< MODE >::project(). ◆ axis1()
Axis accessors, in decreasing order of significance. The main axis. Implements Rivet::AxesDefinition. ◆ axis2()
The 2nd most significant ("major") axis. Implements Rivet::AxesDefinition. References sphericityMajorAxis(). ◆ axis3()
The least significant ("minor") axis. Implements Rivet::AxesDefinition. References sphericityMinorAxis(). ◆ before()
Determine whether this object should be ordered before the object p given as argument. If p is of a different class than this, the before() function of the corresponding type_info objects is used. Otherwise, if the objects are of the same class, the virtual compare(const Projection &) will be returned. ◆ calc()
Manually calculate the sphericity, without engaging the caching system. This one actually does the calculation ◆ clone()
Clone on the heap. Implements Rivet::Projection. ◆ compare()
Compare with other projections. Implements Rivet::Projection. ◆ declare() [1/2]
template<typename PROJ >
Register a contained projection (user-facing version)
Referenced by Rivet::CentralEtHCM::CentralEtHCM(), Rivet::CentralityEstimator::CentralityEstimator(), Rivet::ChargedLeptons::ChargedLeptons(), Rivet::ALICE::CLMultiplicity< INNER >::CLMultiplicity(), Rivet::DISDiffHadron::DISDiffHadron(), Rivet::DISFinalState::DISFinalState(), Rivet::DISKinematics::DISKinematics(), Rivet::DISLepton::DISLepton(), Rivet::EventMixingBase::EventMixingBase(), Rivet::GammaGammaKinematics::GammaGammaKinematics(), Rivet::GammaGammaLeptons::GammaGammaLeptons(), Rivet::GammaGammaLeptons::GammaGammaLeptons(), Rivet::GeneratedCentrality::GeneratedCentrality(), Rivet::HadronicFinalState::HadronicFinalState(), Rivet::HeavyHadrons::HeavyHadrons(), Rivet::Hemispheres::Hemispheres(), Rivet::InvisibleFinalState::InvisibleFinalState(), Rivet::LeadingParticlesFinalState::LeadingParticlesFinalState(), Rivet::LossyFinalState< FILTER >::LossyFinalState(), Rivet::LossyFinalState< FILTER >::LossyFinalState(), Rivet::MC_pPbMinBiasTrigger::MC_pPbMinBiasTrigger(), Rivet::MC_SumETFwdPbCentrality::MC_SumETFwdPbCentrality(), Rivet::ATLAS::MinBiasTrigger::MinBiasTrigger(), Rivet::MissingMomentum::MissingMomentum(), Rivet::NeutralFinalState::NeutralFinalState(), Rivet::NeutralFinalState::NeutralFinalState(), Rivet::NonHadronicFinalState::NonHadronicFinalState(), Rivet::ParisiTensor::ParisiTensor(), Rivet::PercentileProjection::PercentileProjection(), Rivet::PrimaryHadrons::PrimaryHadrons(), Rivet::PrimaryHadrons::PrimaryHadrons(), Rivet::SmearedMET::SmearedMET(), Rivet::SmearedMET::SmearedMET(), Rivet::Spherocity::Spherocity(), Rivet::ATLAS::SumET_PB_Centrality::SumET_PB_Centrality(), Rivet::ATLAS::SumET_PBPB_Centrality::SumET_PBPB_Centrality(), Rivet::TauFinder::TauFinder(), Rivet::TriggerCDFRun0Run1::TriggerCDFRun0Run1(), Rivet::TriggerCDFRun2::TriggerCDFRun2(), Rivet::UndressBeamLeptons::UndressBeamLeptons(), Rivet::ALICE::V0AndTrigger::V0AndTrigger(), Rivet::ALICE::V0Trigger< MODE >::V0Trigger(), Rivet::VetoedFinalState::VetoedFinalState(), Rivet::VisibleFinalState::VisibleFinalState(), Rivet::VisibleFinalState::VisibleFinalState(), Rivet::CentralityProjection::add(), Rivet::CentralityBinner< T, MDist >::setProjection(), and Rivet::VetoedFinalState::vetoFinalState(). ◆ declare() [2/2]
template<typename PROJ >
Register a contained projection (user-facing, arg-reordered version)
◆ get()
template<typename PROJ >
Get the named projection, specifying return type via a template argument (user-facing alias).
◆ getProjection() [1/2]
template<typename PROJ >
Get the named projection, specifying return type via a template argument.
References Rivet::ProjectionHandler::getProjection(), and Rivet::ProjectionApplier::getProjHandler(). Referenced by Rivet::CentralityProjection::compare(), Rivet::pcmp(), Rivet::pcmp(), Rivet::pcmp(), and Rivet::pcmp(). ◆ getProjection() [2/2]
Get the named projection (non-templated, so returns as a reference to a Projection base class). References Rivet::ProjectionHandler::getProjection(), and Rivet::ProjectionApplier::getProjHandler(). ◆ getProjectionFromDeclQueue()
template<typename PROJ >
Get a named projection from this projection appliers declqueue TODO for TP: Recursion? References MSG_ERROR. ◆ mkNamedPCmp()
Shortcut to make a named Cmp<Projection> comparison with the Referenced by Rivet::MC_SumETFwdPbCentrality::compare(), Rivet::MC_pPbMinBiasTrigger::compare(), Rivet::ATLAS::SumET_PB_Centrality::compare(), Rivet::ATLAS::SumET_PBPB_Centrality::compare(), Rivet::ATLAS::MinBiasTrigger::compare(), Rivet::BeamThrust::compare(), Rivet::CentralEtHCM::compare(), Rivet::DISFinalState::compare(), Rivet::EventMixingBase::compare(), Rivet::FParameter::compare(), Rivet::GammaGammaFinalState::compare(), Rivet::HeavyHadrons::compare(), Rivet::Hemispheres::compare(), Rivet::LossyFinalState< FILTER >::compare(), Rivet::PercentileProjection::compare(), Rivet::STAR_BES_Centrality::compare(), Rivet::BRAHMSCentrality::compare(), Rivet::Spherocity::compare(), Rivet::Thrust::compare(), Rivet::CentralityEstimator::compare(), and Rivet::GeneratedCentrality::compare(). ◆ mkPCmp()
Shortcut to make a named Cmp<Projection> comparison with the
Referenced by Rivet::ALICE::PrimaryParticles::compare(), Rivet::SmearedJets::compare(), Rivet::SmearedMET::compare(), Rivet::SmearedParticles::compare(), and Rivet::Correlators::compare(). ◆ name()
Get the name of the projection. Implements Rivet::ProjectionApplier. Referenced by Rivet::Projection::getLog(), Rivet::Projection::setName(), and Rivet::VetoedFinalState::vetoFinalState(). ◆ project()
Perform the projection on the Event. Implements Rivet::Projection. ◆ setProjectionHandler()
The documentation for this class was generated from the following file:
Generated on Thu Feb 29 2024 15:46:48 for Rivet by  1.9.8
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