Physics Analysis Concepts with PandaRoot (4) PANDA Computing Week 2017 Nakhon Ratchasima, Thailand, July 3 - 7, 2017 Klaus Götzen GSI Darmstadt
Topics Event Filtering ( FairFilteredPrimaryGenerator ) • Useful Event and Kinematic Variables ( PndEventShape ) • Creating Output • – Simplified N-Tuple output ( RhoTuple ) – QA-Tools ( PndRhoTupleQA ) Simplified Analysis Tools • – Quick Analysis Tools ( quick(fsim)ana.C ) Multi Variate Analysis ( TMVATrainer/TMVATester ) • K. Götzen PANDA Computing Workshop - Thailand 2
EVENT FILTERING
Event Filtering Usually 𝜏 𝐶𝑏𝑑𝑙𝑠𝑝𝑣𝑜𝑒 ≫ 𝜏 𝑇𝑗𝑜𝑏𝑚 (e.g. ∼ mb vs. ∼n b) • Since (full) simulation of reactions computational intensive: • – Idea: Reject events already at generator level likely being rejected at reco/analysis level – Saves a lot of computing power! – Caveat: Due to missing secondaries, rejecting criteria must be chosen carefully Comprehensive tutorial at • https://panda-wiki.gsi.de/foswiki/bin/view/Computing/PandaRootEventFilterTutorial K. Götzen PANDA Computing Workshop - Thailand 4
Event Filter Usage - (Selected) Filters FairEvtFilterOnSingleParticleCounts • Each MinMax can also be Min or Max only, placing AndMinMaxAllParticles (min, max) – just one limit. AndMinMaxCharged (min, max, type) – • type: FairEvtFilter::kPlus / kMinus / kCharged / kNeutral AndMinMaxPdg (min, max, pdg1 [, pdg2, ..., pdg8]) – AndPRange / AndPtRange / AndPzRange (min, max) – AndThetaRange / AndPhiRange (min, max) – AndVzRange / AndVRhoRange / AndRadiusRange (min, max) – PndEvtFilterOnInvMassCounts • SetPdgCodesToCombine (pdg1, pdg2 [,pdg3, pdg4, pdg5]) – SetMinMaxInvMass (m min , m max ) – SetMinMaxCounts (min, max) – FairFilteredPrimaryGenerator (allows logical combination of filters) • AndFilter / AndNotFilter (filterName) – OrFilter / OrNotFilter (filterName) – AddVetoFilter (filterName) (has higher priority) – K. Götzen PANDA Computing Workshop - Thailand 5
Event Filter Usage Event filter setup in simulation macro (Full or Fast Simulation) • FairFilteredPrimaryGenerator* primGen = new FairFilteredPrimaryGenerator(); FairEvtFilterOnSingleParticleCounts* chrgFilter less than 4 charged = new FairEvtFilterOnSingleParticleCounts("chrgFilter"); chrgFilter->AndMaxCharge(3, FairEvtFilter::kCharged); FairEvtFilterOnSingleParticleCounts* neutFilter at most 6 neutral = new FairEvtFilterOnSingleParticlesCounts("neutFilter"); neutFilter->AndMaxCharge(6, FairEvtFilter::kNeutral); PndEvtFilterOnInvMassCounts* eeInv= new PndEvtFilterOnInvMassCounts("eeInvMFilter"); eeInv->SetPdgCodesToCombine( 11, -11); at least on e + e - cand. eeInv->SetMinMaxInvMass( 2.0, 4.0 ); with 2 < m < 4 GeV/c 2 eeInv->SetMinCounts(1); Vetos events with less than 4 charged primGen->AddVetoFilter(chrgFilter); primGen->AndFilter(neutFilter); Combine all with logical AND primGen->AndFilter(eeInv); Maximum tries before counted as failed primGen->SetFilterMaxTries(100000); K. Götzen PANDA Computing Workshop - Thailand 6
Event Filter Example: 𝑞 𝑞 → 𝜓 𝑑1 𝜌 + 𝜌 − Reconstruct 𝑞 𝑞 → 𝜓 𝑑1 𝜌 + 𝜌 − → (𝜒𝜌 + 𝜌 − )𝜌 + 𝜌 − → 𝐿 + 𝐿 − 2𝜌 + 2𝜌 − Filter: N(t + ) ≥ 3, N(t − ) ≥ 3, |m KK − m φ | < 50MeV, |m 2K2 π − m χ c | < 300MeV → Unfiltered DPM: 1.1M ev; filtered DPM: 0.1M ev ( → 11x less simulation!!) Signal MC Background (DPM) K. Götzen PANDA Computing Workshop - Thailand 7
Event Filter Example: 𝑞 𝑞 → 𝜓 𝑑1 𝜌 + 𝜌 − Reconstruct 𝑞 𝑞 → 𝜓 𝑑1 𝜌 + 𝜌 − → (𝜒𝜌 + 𝜌 − )𝜌 + 𝜌 − → 𝐿 + 𝐿 − 2𝜌 + 2𝜌 − Filter: N(t + ) ≥ 3, N(t − ) ≥ 3, |m KK − m φ | < 50MeV, |m 2K2 π − m χ c | < 300MeV → Unfiltered DPM: 1.1M ev; filtered DPM: 0.1M ev ( → 11x less simulation!!) Signal MC well sub.-combs consistent! Background differ! (DPM) K. Götzen PANDA Computing Workshop - Thailand 8
EVENT SHAPE VARIABLES
Event Shape Variables Sometimes signal and background differ in overall • event shape Useful Event Shape variables (always computed in CMS) are • – Thrust – Sphericity – (A)planarity – Circularity – Fox-Wolfram Moments K. Götzen PANDA Computing Workshop - Thailand 10
Thrust (- Vector) Thrust-axis = "Jet direction" of event • |𝑜 ∙ 𝑞 𝑗 | 𝑗 𝑈 = max |𝑞 𝑗 | 𝑜 =1 𝑗 1 isotropic with thrust axis 𝑜 and 2 ≤ 𝑈 ≤ 1 jet-like K. Götzen PANDA Computing Workshop - Thailand 11
Sphericity - (A)planarity - Circularity Base for all is the sphericity tensor 𝑇 𝛽𝛾 • 𝛽 ∙ 𝑞 𝑗 𝛾 𝑞 𝑗 𝑇 𝛽𝛾 = 𝑗 |𝑞 𝑗 | 2 𝑗 with 𝛽, 𝛾 = 1,2,3 and eigenvalues 𝜇 1 , 𝜇 2 , 𝜇 3 3 isotropic 2 (𝜇 2 + 𝜇 3 ) with 0 ≤ 𝑇 ≤ 1 Sphericity 𝑇 = • jet-like 3 1 2 isotropic Aplanarity 𝐵 = 2 𝜇 3 with 0 ≤ 𝐵 ≤ • planar 1 2 Planarity 𝑄 = 𝜇 2 − 𝜇 3 with 0 ≤ 𝑄 ≤ • 2∙min(𝜇 1 ,𝜇 2 ) with 0 ≤ 𝐷 ≤ 1 Circularity 𝐷 = • 𝜇 1 +𝜇 2 K. Götzen PANDA Computing Workshop - Thailand 12
Fox-Wolfram Moments Fox-Wolfram Moments are defined by • 𝐼 𝑚 = |𝑞 𝑗 | ∙ |𝑞 𝑘 | ∙ 𝑄 𝑚 (cos 𝜄 𝑗𝑘 ) 2 𝐹 𝑤𝑗𝑡 𝑗,𝑘 with – 𝜄 𝑗𝑘 = opening angle of particles i,j – 𝐹 𝑤𝑗𝑡 = visible energy – 𝑄 𝑚 (cos 𝜄 𝑗𝑘 ) = Legendre polynomials Balanced events: 𝐼 1 = 0 • Jet-like events: 𝐼 𝑚 ≈ 1 for l=even and 𝐼 𝑚 ≈ 0 for l=odd • K. Götzen PANDA Computing Workshop - Thailand 13
Sphericity - (A)planarity - Circularity - Fox Wolfram Mom K. Götzen PANDA Computing Workshop - Thailand 14
Event (Shape) Variables in PandaROOT/Rho Class PndEventShape offers many variables • PndEventShape(RhoCandList &all, TLorentzVector pbp_sys, double neutMinE=0, double chrgMinP=0) Global multiplictities: NParticles, NCharged, NNeutral • Event shape variables • Sphericity, Planarity, Aplanarity, Circularity, Thrust, ThrustVector – FoxWolfMomH(order), FoxWolfMomR(order) – Minimum/maximum energy and (transverse) momentum (lab, cms) • PmaxLab/Cms, PminLab/Cms, EmaxNeutLab/Cms, PmaxChrgLab/Cms,... – (Transverse) momentum and energy sums (lab, cms) • PtSumLab, NeutESumLab/Cms, ChrgPSumLab/Cms – Multiplicities with (transv.) min/max momentum/energy (lab, cms) • MultPminLab/Cms, MultPmaxLab/Cms, MultPtminLab/Cms, MultPtmaxLab/Cms – MultChrgPminLab/Cms, MultChrgPmaxLab/Cms, MultNeutEminLab/Cms – PID multiplicities with minimum probability and momentum (lab, cms) • MultElectronPminCms, MultMuonPminCms,.... – (Transv.) momentum and energy sums with min momentum/energy (lab, cms) • SumPminLab/Cms, SumNeutEminLab/Cms,... – K. Götzen PANDA Computing Workshop - Thailand 15
SPECIAL KINEMATICS
Special Kinematics Some signal reactions exhibt special properties for selection • Prominent cases are • – Double resonance production close to threshold , 𝑞 𝑞 → Λ 𝑑 𝑑 + Λ − , 𝑞 𝑞 → 𝐸𝐸 ∗ , ... Examples: 𝑞 𝑞 → 𝐸𝐸 – Cascaded decays with low momentum particle emission Example: 𝐸 ∗+ → 𝐸 0 𝜌 + , 𝐸 𝑡 ∗+ → 𝐸 𝑡 + 𝛿 , 𝜓 𝑑1 → 𝐾 𝜔 𝛿 K. Götzen PANDA Computing Workshop - Thailand 17
Double Resonance Production at Threshold Fixed and known E cm • → resolution of invariant mass correlates with missing mass 2 − 𝑞 2 𝑛 miss = 𝐹 𝑞𝑞 − 𝐹 rec 𝑞𝑞 − 𝑞 rec , 𝐸/𝐸 → 𝐿 ∓ 𝜌 ± @ E cm = 3.75 GeV Example: 𝑞 𝑞 → 𝐸𝐸 • – invariant mass and missing mass resolution about 24 MeV – but very narrow correlation ellipsis σ inv = 23 MeV σ mm = 24 MeV K. Götzen PANDA Computing Workshop - Thailand 18
Beam Energy Substituted Mass m ES ) In case of resonance - anti-resonance production (like 𝐸𝐸 • → can infer the resonance's energy from the beam energy So called energy-subsituted mass is (* = in cm-frame) • 2 2 ∗ ∗ 𝐹 cm 𝐹 cm ∗ 2 , combined with ∆𝐹 = − 𝐹 rec 𝑛 ES = − 𝑞 rec 2 2 Much better S:N and thus relative error! • σ ES = 2 MeV N = 12703 ± 139 σ Δ E = 24 MeV N = 12200 ± 427 K. Götzen PANDA Computing Workshop - Thailand 19
Double Resonance Production at Threshold Very similar result by using m inv and m miss directly • Works also for R ' production (e.g. D *) with different masses • Plot difference vs. sum (or for R sum/2; peaks at corr. mass) • σ sum =2 MeV K. Götzen PANDA Computing Workshop - Thailand 20
Double Resonance Production at Threshold Very similar result by using m inv and m miss directly • Works also for R ' production (e.g. D *) with different masses • Plot difference vs. sum (or for R sum/2; peaks at corr. mass) • Also works for other cases like e.g. 𝛭 𝑑 𝛭 𝑑 σ sum =2 MeV K. Götzen PANDA Computing Workshop - Thailand 21
Cascaded Decays with Slow Particles Consider decay 𝐸 ∗+ → 𝐸 0 𝜌 + • – Experimental resolution of D *+ dominated by that of D 0 due to combinatoric reconstruction – Strong correlation between mass distributions • very narrow correlation ellipsis σ D* = 32 MeV σ D = 24 MeV K. Götzen PANDA Computing Workshop - Thailand 22
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