o Impact of different Geant4 effects and Genfit MSC models on Si-tracking Moritz Nadler Institute of High Energy Physics Austrian Academy of Sciences March 2012 Moritz Nadler 1 HEPHY Wien & BELLE Collaboration
Overview I will mainly present 2 studies: simulation only study investigating scattering angles of Pions tracking study about the effect of different scattering models in Geant4 and Genfit for Pions and Muons Moritz Nadler 2 HEPHY Wien & BELLE Collaboration
Other stuff the Genfit RKTrackRep needs modification to deal with arbitrary curling tracks: I hope to discuss this with Johannes Rauch my Genfit hit sorting for curling tracks made problems with root I/O so it had to go, but will be reintroduced soon the segmentation faults in the vertexing module were fixed by Patrick but no further development and testing was done Moritz Nadler 3 HEPHY Wien & BELLE Collaboration
Note on multiple scattering models for track fit MSC formula implemented in Genfit: ln(159 Z − 1 / 3 ) Genfit = 225 · 10 − 6 Z σ 2 X p 2 β 2 ln(287 Z − 1 / 2 ) Z + 1 Highland formula (from PDG book, H. Ozaki proposed to try it): HL = 0 . 0136 2 σ 2 p 2 β 2 X (1 + 0 . 038 ln( X )) both describe electro-magnetic multiple scattering the ratio σ HL /σ Gf is 0.92, 0.75, 0.69 for X = 1 , 320 µm Si, 75 µm Si Genfit formula should give a best σ for the whole scattering angle distribution; Highland a best σ for the core theoretically σ HL ≈ σ Gf at X = 1 Moritz Nadler 4 HEPHY Wien & BELLE Collaboration
Aim and method of scattering angles study Aim: determine strength of electro-magnetic and other effects on scattering at different energies estimate number of Pion tracks lost for reconstruction because of material interaction in sensors Method: simulated 100000 tracks with different effect and momentum combinations: all, only MSC, and no MSC calculated ∆ φ and ∆ θ of entry and exit points of the active sensor materials (used info from TrueHits) looked at standard deviation of whole samples, of a Gaussian fit of whole sample, and of Gaussian fit after cuts determined by ± 5 σ of first fit. calculated ratio of sample size before and after cuts Moritz Nadler 5 HEPHY Wien & BELLE Collaboration
pGun parameters for simulation only studies If not stated otherwise: p fixed at 1 GeV or 100 MeV, Φ ∈ [0 ◦ 360 ◦ ] uniformly distributed, θ = 90 ◦ π + , π − uniformly distributed no other material/detectors than the SVD and PXD detectors no magnetic field after 15 cm only tracks with exactly one hit in every layer 100000 tracks simulated ≈ 66000 tracks used Moritz Nadler 6 HEPHY Wien & BELLE Collaboration
Results: Details I An example: whole ∆ φ sample of layer 4 with all Pion (1 GeV) effects on: histTitle histTitle hist Entries 66906 2500 Mean -1.106e-05 RMS 0.002334 χ 2 / ndf 444.2 / 190 2000 ± Constant 2420 11.9 ± Mean 1.328e-06 2.255e-06 ± Sigma 0.0005813 0.0000017 1500 1000 500 0 -0.3 -0.2 -0.1 0 0.1 x in rad Moritz Nadler 7 HEPHY Wien & BELLE Collaboration
Results: Details II same as last slide but a cut of 5 σ applied to the sample histTitle histTitle hist 300 Entries 66791 Mean 9.132e-07 RMS 0.0005962 250 χ 2 / ndf 934.2 / 828 ± Constant 266.4 1.3 ± Mean 2.186e-06 2.239e-06 200 ± Sigma 0.0005734 0.0000017 150 100 50 0 -0.002 -0.001 0 0.001 0.002 x in rad Moritz Nadler 8 HEPHY Wien & BELLE Collaboration
Results: Details III σ of ∆ φ in layer 4 (all σ in mrad) 1 GeV 1 GeV 1 GeV 100 MeV 100 MeV 100 MeV all only msc no msc all only msc no msc whole 2.3 0.62 2.3 12 12 8.4 fit 0.58 0.57 × 9.9 9.9 × a. cut 0.57 0.57 × 9.8 9.8 × ratio − 1 1.7‰ 1.5‰ × 1.4‰ 1.2‰ × comparison with track fit MSC formulas: Highland: 0.63, 11 (1 GeV, 100 MeV) Genfit: 0.84, 14 (1 GeV, 100 MeV) Moritz Nadler 9 HEPHY Wien & BELLE Collaboration
Overview of results and conclusions the outlier ratio is between 1.2‰ and 2.4‰ per layer = ⇒ ≈ 2‰ of Pion tracks might be lost per Si sensor layer even with 66000 tracks hadronic scattering does not form a recognizable distribution at 1 GeV hadronic effects dominate the sample σ and produce most outliers at 100 MeV EM-MSC dominates and hadronic effects become relatively unimportant the Highland formula seems to produce a σ closer to the σ of Geant4’s EM-MSC than Genfit Moritz Nadler 10 HEPHY Wien & BELLE Collaboration
Aim and method of tracking study Aim: determine the consequences on track fit quality of different scattering effects and their description in Genfit Method: 8 different samples of 10000 tracks were fitted with 2 different MSC formulas in Genfit (Genfit and Highland) = ⇒ 16 different fitted track samples Pions (normal and only EM effects) and Muons (with and without Wentzel model) at 1 GeV and 100 MeV afterwards the p-value distributions (from total χ 2 ), the pulls of p p p and x x x of the track extrapolated to the origin with respect to the true values and other distributions were investigated Moritz Nadler 11 HEPHY Wien & BELLE Collaboration
pGun parameters for tracking studies If not stated otherwise: p fixed at 1 GeV or 100 MeV, Φ ∈ [0 ◦ , 360 ◦ ] uniformly distributed, θ = 90 ◦ either µ + , µ − uniformly distributed or π + , π − uniformly distributed no other material/detectors than the SVD and PXD detectors no magnetic field after 15 cm truth information used as starting values for track fit and “pattern recognition” other condition also optimal, e.g. only Gaussian smearing, detector resolution the same in digitizer and Genfit 10000 tracks simulated Moritz Nadler 12 HEPHY Wien & BELLE Collaboration
Result I: p-value/pulls oddity 1 when using the Genfit MSC model with 1 GeV EM effects only Pions p values are very good but pulls are to small (reason for H. Ozaki trying Highland) when using Highland formula pulls are good but p-values get worse pValue_bu.data pValue_bu.data htemp htemp htemp htemp Entries Entries 10000 10000 Entries Entries 10000 10000 250 160 Mean Mean 0.5036 0.5036 Mean Mean 0.4684 0.4684 RMS RMS 0.2938 0.2938 RMS RMS 0.2962 0.2962 140 200 120 100 150 80 100 60 40 50 20 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 pValue_bu.data pValue_bu.data σ of pulls: 0.8 – 0.91 σ of pulls: 1.01 – 1.02 Moritz Nadler 13 HEPHY Wien & BELLE Collaboration
Result I: p-value/pulls oddity 2 not caused by extrapolation to origin, already present in layer wise tests cause seems to be very subtle and connected to the off diagonal elements of the Genfit covariance matrices exactly the same effect is present when looking at Muons without Wentzel when fitting with both MSC models in Genfit Moritz Nadler 14 HEPHY Wien & BELLE Collaboration
Result II: Genfit overestimates the MSC σ at low p at low energies the Genfit formula for MSC clearly overestimates the MSC σ below a comparison of p values of 100 MeV Pions fitted with both models pValue_bu.data pValue_bu.data htemp htemp htemp htemp Entries Entries 9851 9851 700 Entries Entries 9899 9899 500 Mean Mean 0.7171 0.7171 Mean 0.4689 Mean 0.4689 RMS 0.2739 RMS 0.2739 RMS 0.3187 RMS 0.3187 600 400 500 300 400 300 200 200 100 100 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 pValue_bu.data pValue_bu.data σ of pulls: 0.7 – 0.86 σ of pulls: 0.94 – 1.12 Moritz Nadler 15 HEPHY Wien & BELLE Collaboration
Result III: p dependency of different outlier producing effects at 100 MeV it has no effect on tracking results if Pions uses only EM effects or all effects = ⇒ hadronic effects become irrelevant at low p the first study already suggested this but Wentzel model’s impact grows at low p example: Muons at 100 MeV w/wo Wentzel, Highland for fitting pValue_bu.data pValue_bu.data htemp htemp htemp htemp 700 Entries Entries 9984 9984 Entries Entries 9982 9982 Mean 0.4485 Mean 0.4485 Mean 0.3463 Mean 0.3463 1400 RMS 0.3113 RMS 0.3113 RMS 0.3124 RMS 0.3124 600 1200 500 1000 400 800 300 600 200 400 100 200 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 pValue_bu.data pValue_bu.data Moritz Nadler 16 HEPHY Wien & BELLE Collaboration
Conclusions and things to do the current Genfit MSC implementation should be modified investigate the p-value/pull oddity at low momenta in combination with thin sensor modules standard Geant4 MSC model (Urban) produces some outlier tracks with very strong scattering angles with further tracking studies I will more clearly determine the quantity of “kinky” tracks for different particles and p ranges we have several ideas how to deal with them (e.g. importing Gaussian sum filter like features) the effort put into “outlier fitting” strongly depends on the number of “kinky” tracks surviving the pattern recognition again: get into contact with Geant4 developers about Wentzel effect (also for Pions?) Moritz Nadler 17 HEPHY Wien & BELLE Collaboration
The End Any advice, suggestions or comments are very welcome Moritz Nadler 18 HEPHY Wien & BELLE Collaboration
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