Likelihood Methods for Beam Particle Identification at the Experiment Tobias Weisrock for the Collaboration Graduate School Symmetry Breaking Johannes Gutenberg-Universität Mainz SPIN-Praha-22 July 7,22 International Summer School Symmetries, Fundamental Interactions and Cosmology Frauenchiemsee Bavaria, Germany September 6, 2 Dear Summer School Participant, Having provided you with some detailed information about our school in our first circular, this final
Outline The Experiment Hadron Physics @ Beam Particle Identification @ Beam Particle Identification using Likelihoods Efficiency and Purity of the Likelihood Method
The Experiment The Experiment I COmmon Muon and Proton Apparatus for Structure and Spectroscopy I Located at SPS at CERN Tobias Weisrock (JGU Mainz) July 7, 22 / 26
The Experiment The Experiment I COmmon Muon and Proton Apparatus for Structure and Spectroscopy I Located at SPS at CERN 2.4% K 97% π 9 GeV/c Tobias Weisrock (JGU Mainz) July 7, 22 / 26
The Experiment The Experiment I COmmon Muon and Proton Apparatus for Structure and Spectroscopy I Located at SPS at CERN 2.4% K 97% π 9 GeV/c CEDARs Tobias Weisrock (JGU Mainz) July 7, 22 / 26
The Experiment The Experiment I COmmon Muon and Proton Apparatus for Structure and Spectroscopy I Located at SPS at CERN 2.4% K 97% π 9 GeV/c CEDARs Target Tobias Weisrock (JGU Mainz) July 7, 22 / 26
The Experiment The Experiment I COmmon Muon and Proton Apparatus for Structure and Spectroscopy I Located at SPS at CERN 2.4% K 97% π 9 GeV/c Small Angle Spectrometer Large Angle Spectrometer CEDARs Target RICH Tobias Weisrock (JGU Mainz) July 7, 22 / 26
Hadron Physics @ Hadron Physics @ Very broad program Tobias Weisrock (JGU Mainz) July 7, 22 2 / 26
Hadron Physics @ Hadron Physics @ Very broad program Spectroscopy Different final states 3π, 5π, Kππ,... Search for exotic states Tobias Weisrock (JGU Mainz) July 7, 22 2 / 26
Hadron Physics @ Hadron Physics @ Very broad program Spectroscopy Different final states 3π, 5π, Kππ,... Search for exotic states Primakoff program πp πγp Measure pion/kaon polarizabilities Tobias Weisrock (JGU Mainz) July 7, 22 2 / 26
Hadron Physics @ Hadron Physics @ Very broad program Spectroscopy Different final states 3π, 5π, Kππ,... Search for exotic states Primakoff program πp πγp Measure pion/kaon polarizabilities Example: Kππ analysis Analysis of diffractive dissociation of K into K π + π on a liquid hydrogen target at the spectrometer, PhD Thesis P. Jasinski (JGU Mainz) Tobias Weisrock (JGU Mainz) July 7, 22 2 / 26
Hadron Physics @ Event Selection Incoming kaon Primary vertex in target with 3 outgoing charged tracks Four momentum transfer.7 < t [GeV 2 /c 2 ] <.7 One negative particle identified with RICH ] 2 Events / [MeV/c 3 3.5 3 2.5 2.5.5 K (27) K (4) 28 negative hadron beam K p K π + π p recoil preliminary not acceptance corrected K 2 (77).5.5 2 2.5 2 M (K π + π )[GeV/c ] ] 2 Events / 2 [MeV/c 3 25 2 5 5 3 K*(892) 28 negative hadron beam K p K π + π p recoil preliminary not acceptance corrected K* 2 (43).2.4.6.8.2.4.6.8 2 2 M (K π + )[GeV/c ] Tobias Weisrock (JGU Mainz) July 7, 22 3 / 26
Hadron Physics @ Partial Wave Analysis disentangle Kππ spectrum several resonances found further investigation needed (mass dependent fits) ] 2 Events / [MeV/c 3 3.5 3 2.5 2.5.5 K (27) K (4) 28 negative hadron beam K p K π + π p recoil preliminary not acceptance corrected K 2 (77).5.5 2 2.5 2 M (K π + π )[GeV/c ] Tobias Weisrock (JGU Mainz) July 7, 22 4 / 26
Hadron Physics @ Partial Wave Analysis disentangle Kππ spectrum several resonances found further investigation needed (mass dependent fits) ] 2 Events / [MeV/c 3 3.5 3 2.5 2.5.5 K (27) K (4) 28 negative hadron beam K p K π + π p recoil preliminary not acceptance corrected K 2 (77).5.5 2 2.5 2 M (K π + π )[GeV/c ] J P mass (GeV/c 2 ) possible state.3 K(46) +.25 K (27) +.35 K (4) +.8 K (65).75 K (68) 2 +.44 K 2 (43) 2.7 K 2 (77) 2.85 K 2 (82) 2.9 2.2 several Tobias Weisrock (JGU Mainz) July 7, 22 4 / 26
Hadron Physics @ Partial Wave Analysis disentangle Kππ spectrum several resonances found further investigation needed (mass dependent fits) ] 2 Events / [MeV/c 3 3.5 3 2.5 2.5.5 K (27) K (4) 28 negative hadron beam K p K π + π p recoil preliminary not acceptance corrected K 2 (77).5.5 2 2.5 2 M (K π + π )[GeV/c ] J P mass (GeV/c 2 ) possible state.3 K(46) +.25 K (27) +.35 K (4) +.8 K (65).75 K (68) 2 +.44 K 2 (43) 2.7 K 2 (77) 2.85 K 2 (82) 2.9 2.2 several Only 5% of kaons used due to bad efficiency of beam particle identification. Tobias Weisrock (JGU Mainz) July 7, 22 4 / 26
Beam Particle Identification @ Beam Particle Identification @ Two CEDAR detectors 3 m upstream of the target Tobias Weisrock (JGU Mainz) July 7, 22 5 / 26
Beam Particle Identification @ How does a CEDAR work? CEDAR = ČErenkov Differential counters with Acromatic Ring focus Fast charged particles emit Čerenkov light with angle cos(θ) = nβ quarz window diaphragm lense PMT K π PMT condenser corrector vapour-deposit mirror Tobias Weisrock (JGU Mainz) July 7, 22 6 / 26
Beam Particle Identification @ How does a CEDAR work? Čerenkov light detected with 8 PMTs Particle identification using multiplicities, e.g. 6 of 8 PMTs cos(θ) = nβ quarz window diaphragm lense PMT K π PMT condenser corrector vapour-deposit mirror Tobias Weisrock (JGU Mainz) July 7, 22 6 / 26
Beam Particle Identification @ Influence of Beam Divergence beam tuned to traverse full spectrometer beam is not parallel in the CEDAR region Tobias Weisrock (JGU Mainz) July 7, 22 7 / 26
Beam Particle Identification @ Influence of Beam Divergence beam tuned to traverse full spectrometer beam is not parallel in the CEDAR region parallel beam Tobias Weisrock (JGU Mainz) July 7, 22 7 / 26
Beam Particle Identification @ Influence of Beam Divergence beam tuned to traverse full spectrometer beam is not parallel in the CEDAR region divergent beam Kaon ring leaves acceptance, pion ring enters Multiplicity method does not work for divergent beams Tobias Weisrock (JGU Mainz) July 7, 22 7 / 26
Beam Particle Identification @ Influence of Beam Divergence beam tuned to traverse full spectrometer beam is not parallel in the CEDAR region divergent beam Kaon ring leaves acceptance, pion ring enters Multiplicity method does not work for divergent beams Find a method which takes divergence into account Tobias Weisrock (JGU Mainz) July 7, 22 7 / 26
Beam Particle Identification using Likelihoods General Idea Look at response of single PMTs for kaon and pion seperately Take care of beam divergence Identify beam particles using likelihoods Tobias Weisrock (JGU Mainz) July 7, 22 8 / 26
Beam Particle Identification using Likelihoods General Idea Look at response of single PMTs for kaon and pion seperately Take care of beam divergence Identify beam particles using likelihoods 5 steps to take. Measure beam divergence 2. Create a pure kaonsample and a pure pionsample 3. Determine probabilities to have hits in PMTs for pion and kaon 4. Calculate likelihoods from probabilities 5. Use likelihoods to identify particles Tobias Weisrock (JGU Mainz) July 7, 22 8 / 26
Beam Particle Identification using Likelihoods Step : Measure beam divergence Measure beam position in front of (x, y ) and behind (x 2, y 2 ) CEDARs Calculate relative displacement x = Divergence θ x = arctan( x ) x x2 x 283,4 cm θ y (µrad) 2 5 5 4 8 7 χ 2 / ndf 7.3 / 47 Constant 778.8 ± 7.5 Mean 7.753 ±.525 Sigma 65.7 ±.36 5-5 - 3 2 6 5 4 3 2 8 7 6 5 χ 2 / ndf 667. / 47 Constant 837.5 ± 7.9 Mean 35.87 ±.5 Sigma 58.86 ±.3-5 4-2 -2-5 - -5 5 5 2 θ x (µrad) Preliminary -2-5 - -5 5 5 2 Preliminary θ x (µrad) 3 2-2 -5 - -5 5 5 2 Preliminary θ y (µrad) Tobias Weisrock (JGU Mainz) July 7, 22 9 / 26
Beam Particle Identification using Likelihoods Step 2: Create a pure Kaonsample and a pure Pionsample Create a Kaonsample and a Pionsample Kaonsample Use free Kaon decay K π π π + 3 outgoing particles with correct charged Primary vertex outside of the target Cut on transverse momentum and Kaon mass Pionsample Use diffractive production π p π π π + p 3 outgoing particles with correct charge Primary vertex inside the target Small angle to beam direction, similar momenta same mass In addition: Take a beamsample without any filtering for testing the method Tobias Weisrock (JGU Mainz) July 7, 22 / 26
Beam Particle Identification using Likelihoods Step 3: Determine probabilities to have hits in PMTs for π and K Example: Particle with divergence θ x, θ y produces signal in PMT i Question: Is it a kaon? Use Bayes Theorem: P i θ x,θ y (Kaon Signal) = Here: Tobias Weisrock (JGU Mainz) July 7, 22 / 26
Beam Particle Identification using Likelihoods Step 3: Determine probabilities to have hits in PMTs for π and K Example: Particle with divergence θ x, θ y produces signal in PMT i Question: Is it a kaon? Use Bayes Theorem: P i θ x,θ y (Kaon Signal) = Pi θ x,θ y (Signal Kaon) Here: P i θ x,θ y (Signal Kaon): Probability that Kaon at θ x, θ y produces signal in PMT i ( Kaonsample) Tobias Weisrock (JGU Mainz) July 7, 22 / 26
Beam Particle Identification using Likelihoods Step 3: Determine probabilities to have hits in PMTs for π and K Example: Particle with divergence θ x, θ y produces signal in PMT i Question: Is it a kaon? Use Bayes Theorem: P i θ x,θ y (Kaon Signal) = Pi θ x,θ y (Signal Kaon) P θx,θ y (Kaon) Here: P i θ x,θ y (Signal Kaon): P θx,θ y (Kaon): Probability that Kaon at θ x, θ y produces signal in PMT i Probability that Kaon has divergence θ x and θ y ( Kaonsample) ( Kaonsample) Tobias Weisrock (JGU Mainz) July 7, 22 / 26
Beam Particle Identification using Likelihoods Step 3: Determine probabilities to have hits in PMTs for π and K Example: Particle with divergence θ x, θ y produces signal in PMT i Question: Is it a kaon? Use Bayes Theorem: P i θ x,θ y (Kaon Signal) = Pi θ x,θ y (Signal Kaon) P θx,θ y (Kaon) P i θ x,θ y (Signal) Here: P i θ x,θ y (Signal Kaon): P θx,θ y (Kaon): P i θ x,θ y (Signal): Probability that Kaon at θ x, θ y produces signal in PMT i Probability that Kaon has divergence θ x and θ y Probability that signal in PMT i ist produced at θ x, θ y ( Kaonsample) ( Kaonsample) ( Beamsample) Tobias Weisrock (JGU Mainz) July 7, 22 / 26
Beam Particle Identification using Likelihoods Step 3 continued Pions and Kaons have the same divergence distribution: P θx,θ y (Kaon) = P θx,θ y (Pion) = P θx,θ y (Beam) P i θ x,θ y (Kaon Signal) and P i θ x,θ y (Pion Signal) have same normalization factor Pθx,θy (Beam) P i (Signal), thus θx,θy P i θ x,θ y (Kaon Signal) P i θ x,θ y (Signal Kaon) P i θ x,θ y (Pion Signal) P i θ x,θ y (Signal Pion) Also calculate P i θ x,θ y (Kaon Signal) and P i θ x,θ y (Pion Signal) Tobias Weisrock (JGU Mainz) July 7, 22 2 / 26
Beam Particle Identification using Likelihoods Probability Distributions 7 6 5 2 4 3 Tobias Weisrock (JGU Mainz) July 7, 22 3 / 26
Beam Particle Identification using Likelihoods Probability Distributions Pions 7 in µrad 25 2.9 6 θ y 5.8 5-5.7.6.5.4 5 -.3-5.2-2. 2-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 4 3 Tobias Weisrock (JGU Mainz) July 7, 22 3 / 26
θ y θ y θ y θ y θ y θ y θ y θ y Beam Particle Identification using Likelihoods Probability Distributions in µrad 25 2.9 5.8 Pions in µrad 25 2 5 5-5 - -5-2.9.8.7.6.5.4.3.2. 5-5 - -5 7-2. 5-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 5-5 -.7.6.5.4.3.2 in µrad 25 2 6.9.8.7.6.5.4.3-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad -5.2-2. in µrad 25 2 5.9.8-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 5-5 -.3-5.2-2. -25-25 -2-5 - -5 5 5 2 25 θ x in µrad.7.6.5.4 in µrad 25 2 5 5-5 - 5.9.8.7.6.5.4.3-5.2-2. in µrad 25 2.9-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 5.8.7 5.6.5 2-5.4 -.3 25-5.2 2-2. 5-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 5 in µrad -5 3.9.8.7.6.5.4 in µrad 25 2 5 5-5 4 -.3-5.2-2. -25-25 -2-5 - -5 5 5 2 25 θ x in µrad.9.8.7.6.5.4 -.3-5 -2.2. -25-25 -2-5 - -5 5 5 2 25 θ x in µrad Tobias Weisrock (JGU Mainz) July 7, 22 3 / 26
Beam Particle Identification using Likelihoods Probability Distributions Kaons 7 in µrad 25 2.9 6 θ y 5.8 5-5.7.6.5.4 5 -.3-5.2-2. 2-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 4 3 Tobias Weisrock (JGU Mainz) July 7, 22 3 / 26
θ y θ y θ y θ y θ y θ y θ y θ y Beam Particle Identification using Likelihoods Probability Distributions in µrad 25 2.9 5.8 Kaons in µrad 25 2 5 5-5 - -5-2.9.8.7.6.5.4.3.2. 5-5 - -5 7-2. 5-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 5-5 -.7.6.5.4.3.2 in µrad 25 2 6.9.8.7.6.5.4.3-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad -5.2-2. in µrad 25 2 5.9.8-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 5-5 -.3-5.2-2. -25-25 -2-5 - -5 5 5 2 25 θ x in µrad.7.6.5.4 in µrad 25 2 5 5-5 - 5.9.8.7.6.5.4.3-5.2-2. in µrad 25 2.9-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 5.8.7 5.6.5 2-5.4 -.3 25-5.2 2-2. 5-25 -25-2 -5 - -5 5 5 2 25 θ x in µrad 5 in µrad -5 3.9.8.7.6.5.4 in µrad 25 2 5 5-5 4 -.3-5.2-2. -25-25 -2-5 - -5 5 5 2 25 θ x in µrad.9.8.7.6.5.4 -.3-5 -2.2. -25-25 -2-5 - -5 5 5 2 25 θ x in µrad Tobias Weisrock (JGU Mainz) July 7, 22 3 / 26
Beam Particle Identification using Likelihoods Additional Cut Statistics bad for large divergences Cut out events with r = θx 2 + θ2 y < 2 6 About 2% of all events are lost this way θ y in µrad 25 2 5 5-5 - -5-2.9.8.7.6.5.4.3.2. -25-25 -2-5 - -5 5 5 2 25 θ x in µrad Tobias Weisrock (JGU Mainz) July 7, 22 4 / 26
Beam Particle Identification using Likelihoods Step 4: Calculate likelihoods from probabilities To obtain the log likelihood just add logarithms of probabilities log L(Kaon) = log P i θ x,θ y (Kaon Signal) i PMT with Signal Calculate the same for Pions. Compare them + log P j θ x,θ y (Kaon Signal) j PMT without Signal Tobias Weisrock (JGU Mainz) July 7, 22 5 / 26
Kaonsample Beam Particle Identification using Likelihoods log L(K) -2-4 -6 2-8 - -2-4 -6-8 -2-2 -8-6 -4-2 - -8-6 -4-2 log L(π) Tobias Weisrock (JGU Mainz) July 7, 22 6 / 26
Pionsample Beam Particle Identification using Likelihoods log L(K) -2-4 -6 2-8 - -2-4 -6-8 -2-2 -8-6 -4-2 - -8-6 -4-2 log L(π) Tobias Weisrock (JGU Mainz) July 7, 22 7 / 26
Beam Particle Identification using Likelihoods Step 5: Use likelihoods to identify particles Compare log likelihoods to get an ID for each CEDAR: log L K > log L π + A PID K log L π > log L K + B PID π else no PID given Tune A and B due to efficiency/purity. Tobias Weisrock (JGU Mainz) July 7, 22 8 / 26
Beam Particle Identification using Likelihoods Step 5: Use likelihoods to identify particles Compare log likelihoods to get an ID for each CEDAR: log L K > log L π + A PID K log L π > log L K + B PID π else no PID given Tune A and B due to efficiency/purity. Combine CEDARs afterwards C2 \ C? π K?? π K π π π? K K? K Tobias Weisrock (JGU Mainz) July 7, 22 8 / 26
Efficiency and Purity of the Likelihood Method Calculation of Purity Look at h p h K S p Then one knows (due to conservation of strangeness): h K π h π K Identify h using the RICH and count the wrong particles Tobias Weisrock (JGU Mainz) July 7, 22 9 / 26
Efficiency and Purity of the Likelihood Method Select h = π log2(p(k) / p(pi)) over momentum 4 3 2 hkprob Entries 22225 Mean x 3 Mean y.52 RMS x 43.69 RMS y.486 2 - -2-3 2 4 6 8 2 4 6 8 2 For CEDAR pions RICH should only see kaons (log 2 ( p(k)/p(π) ) > ) Look at events with p < 5 GeV, cut out ± Tobias Weisrock (JGU Mainz) July 7, 22 2 / 26
Efficiency and Purity of the Likelihood Method Purity of Pion Selection % 25 Graph Majority Likelihood 2 5 5 2 3 4 5 6 7 8 9 B Independent of likelihood cut 4% better than multiplicity Tobias Weisrock (JGU Mainz) July 7, 22 2 / 26
Efficiency and Purity of the Likelihood Method Select h = K log2(p(k) / p(pi)) over momentum 4 3 2 hkprob Entries 27 2 Mean x 89.4 Mean y -.435 RMS x 4 RMS y.6368 - -2-3 2 4 6 8 2 4 6 8 2 For CEDAR pions RICH should only see pions (log 2 ( p(k)/p(π) ) < ) Look at events with p < 5 GeV, cut out ± Tobias Weisrock (JGU Mainz) July 7, 22 22 / 26
Efficiency and Purity of the Likelihood Method Purity of Kaon Selection % 25 Graph Majority Likelihood 2 5 5 2 3 4 5 6 7 8 9 A Independent of likelihood cut Compatible with multiplicity method Compatible with pion purity Tobias Weisrock (JGU Mainz) July 7, 22 23 / 26
Efficiency and Purity of the Likelihood Method Calculation of Efficiency Look at expected number of particles in the beam 2.4% kaons, 97% pions Kaons Pions Efficiency 9 8 Efficiency 9 8 7 7 6 6 5 5 4 4 3 3 2 2 - A - B Efficiency of around 8% for pions and kaons Efficiency for kaons 6% better than for multiplicity method Tobias Weisrock (JGU Mainz) July 7, 22 24 / 26
Efficiency and Purity of the Likelihood Method Direct Comparison with multiplicity Method likelihood PID K 92 869 4 π 6839 62 3 no ID 2235 43 2 π K multiplicity PID Tobias Weisrock (JGU Mainz) July 7, 22 25 / 26
Efficiency and Purity of the Likelihood Method Direct Comparison with multiplicity Method likelihood PID K π 92 869 6839 62 4 Most of multiplicity kaons reproduced as kaons (896 of 74, 83%) 3 no ID 2235 43 2 π K multiplicity PID Tobias Weisrock (JGU Mainz) July 7, 22 25 / 26
Efficiency and Purity of the Likelihood Method Direct Comparison with multiplicity Method likelihood PID K π 92 869 6839 62 4 Most of multiplicity kaons reproduced as kaons (896 of 74, 83%) 3 92 additional kaons from multiplicity pions no ID 2235 43 2 π K multiplicity PID Tobias Weisrock (JGU Mainz) July 7, 22 25 / 26
Efficiency and Purity of the Likelihood Method Summary hadron beam consists of 97% pions and 2.4% kaons Pions and kaons have to be identified for analyses multiplicity method only identifies 5% of the kaons Problems with divergent beams Likelihood method improves identification for divergent beams Identifies 8% of the kaons with 87% purity. Tobias Weisrock (JGU Mainz) July 7, 22 26 / 26
Efficiency and Purity of the Likelihood Method Summary hadron beam consists of 97% pions and 2.4% kaons Pions and kaons have to be identified for analyses multiplicity method only identifies 5% of the kaons Problems with divergent beams Likelihood method improves identification for divergent beams Identifies 8% of the kaons with 87% purity. Outlook Adapt methods to 29/22 data taking Do finetuning using existing hadron analyses Redo Kππ analysis Tobias Weisrock (JGU Mainz) July 7, 22 26 / 26