UPDATES ON THE PION INCLUSIVE CROSS-SECTION ANALYSIS (MONTE CARLO STUDY) Ajib Paudel Graduate Student Kansas State University Date: May 9, 2019 (ProtoDUNE Analysis Meeting) 1
Have been collaborating with Tingjun Yang on the analysis. Outline of the talk: • Brief review of the issues with Kinetic Energy reconstruction. • Possible solutions and remaining issues. • A brief status of the Elastic interaction vertex reconstruction, which will be very important for inclusive cross-section measurements. Note: throughout the analysis I will be using "1GeV histat SCE OFF sample" previous talk the link to my previous talk where I have talked about the KE reconstruction issues in detail. 2
Screenshot from previous talk: I discussed a few issues with energy reconstruction: 3
Removing Cosmic muon contamination: Developed an algorithm to identify all the intersection points of cosmic muons with the beam particle: • Identify the recob::Cluster in the collection plane associated with our beam particle. • Find the StartWire, EndWire, StartTick and EndTick of the recob::Cluster (for beam particle). • Loop over all the remaining clusters in the same TPC and plane as the beam particle and identify the StartWire, Endwire, StartTick and EndTick of all those recob::Cluster. (w4,t4) In the figure aside, w represents the wire coordinate (it can be u, v or z depending on wire plane) and t represents the Peaktime. PeakTime or t (w2,t2) w1=StartWire, w2=EndWire, t1=StartTick, t2=EndTick for a cluster (say corresponding to beam particle). (w, t) Similarly, w3, w4, t3, t4 are corresponding quantities for any other (w1,t1) cluster in the same TPC. (w3,t3) Then the point of intersection (w, t) can be easily evaluated by solving sets of two linear equations in two variables. Wire numbers or w 4
Plot on the right shows the number of cosmic tracks intersecting for each pi+. In the plot shown aside , 58% of pi+ track have no cosmic contamination. Number of cosmic muons intersecting a beam particle From the plots below we can see that hits near the cosmic contamination has a very high dE/dx values compared to the rest of the part of the track. We plan to replace the dE/dx values around the cosmic contamination with average dE/dx values from neighboring region. Avg dE/dx = 8.1MeV/cm Avg dE/dx = 2.79MeV/cm dE/dx distribution of primary pi+ hits close dE/dx distribution of all primary pi+ hits not to the point intersection (within ± 2.5cm) within ± 2.5cm from the point of with cosmic muons intersection with cosmic muons 5
Comparing the true and reconstructed Kinetic Energies: Reconstructed vs true Kinetic Energy for pi+ tracks with no cosmic contamination Reconstructed Kinetic Energy vs true Kinetic Energy for all pi+ tracks We can see that if we remove the tracks with cosmic contamination the reco vs true Kinetic Energy distribution looks much better. There are still some tracks which shows a steep decrease in reconstructed Kinetic Energy, which needs further investigation. 6
KErec-KEtrue for all the hits in a pi+ track with no cosmic contamination: (KErec-KEtrue) for all the hits in a pi+ track Mean=1.04MeV/cm Mean=-4.85MeV/cm KErec-KEtrueat interaction point for tracks with no cosmic contamination (KErec-KEtrue) for all pi+ tracks at the interaction point Mean=-31.35MeV/cm Mean=-19.4MeV/cm Left:all pi+ tracks and Right: pi+ tracks with no cosmic contamination 7
Significant improvement is observed in the energy reconstruction once the issue with cosmic contamination is solved or those tracks are removed. There are still many tracks with big gap between true and reco KE. Other common issues are primary tracks overlapping with daughter tracks. Wire no XZ view Peak time in ticks X (cm) Z coordinate in cm Y (cm) If the daughter track scatters back towards the primary track YZ view at small angle, the charge deposition from the two tracks overlaps as shown in the Wire vs peak time distribution above Z coordinate in cm 8
Removing tracks with overlapping daughters: Find the angle between the projection of the primary and daughter tracks on the XZ plane. To calculate the angle I used the direction cosines of the primary track end and direction cosines of daughter track beginning. XZ_theta for all pi+ tracks Z coordinate XZ_theta in degrees I removed tracks with abs(XZ_theta)>0.94 and abs(primaryEndPositionZ-daughterStartPostionZ)<5cm and primaryEndPositionZ-daughterEndPosition>5cm Pandora reconstruction does not always identify the correct daughter particle so I require daughter track to start close to where the primary track ends and also daughter should have a lower endZ than primary particle to make sure it's 9 overlapping with the primary track.
Reco vs True Kinetic energy after removing overlapping tracks: Very few tracks (25 tracks out of 3276 tracks) with overlapping daughter tracks. So it does not make a big change in the plots. For comparison from slide 8, after removing cosmic contamination: Mean KErec-KEtrue for all hits=1.04MeV/cm Mean KErec-KEtrue for hits at interaction vertex=- 19.4MeV/cm For interaction vertex KErec-KEtrue seems to get slightly worse. (KErec-KEtrue) for all pi+ tracks at the interaction point (KErec-KEtrue) for all the hits in a pi+ track Mean=-19.62MeV/cm Mean=0.98MeV/cm 10
Some more issues: Proton tail assigned to a primary muons: Often daughter protons are attached to the primary pi+ track. Event 1542, run 2.38 subsequently the dE/dx values becomes very high which results in wrong Kinetic Energy. Reco pi+ True pi+ As 1GeV pions interaction much before they stop, so we can easily distinguish between pion and proton hits based on the dE/dx values. After doing some study (described in backup slide with some results) I wrote a simple algorithm to remove proton hits. Start from the last hit of the primary track: Event 1542, run 2.38 If (dE/dx for last hit<5MeV/cm and the mean value of last hit and two following hits is less than 3MeV/cm) then keep EndPoint, else go to next hit and repeat the above process until we find a hit satisfying above condition. In short, if there are high dE/dx hits at the end we remove those hits. High dE/dx proton contamination 11
KE reco vs KE true after removing the proton hits: As the proton hits are attached at the end on the pi+ tracks, hits near the interaction vertex are affected. For comparison from slide 10: Mean KErec-KEtrue for all hits=0.98MeV/cm Mean KErec-KEtrue for hits at interaction vertex=-19.62MeV/cm After proton hits removal KErec-KEtrue values at the interaction vertex shows a big improvement. While the KErec-KEtrue including all hits gets slightly worse. (KErec-KEtrue) for all the hits in a pi+ track (KErec-KEtrue) for all pi+ tracks at the interaction point Mean=1.2MeV/cm Mean=-2.6MeV/cm 12
Summarizing energy deposition studies: Reco dE/dx distribution for all Reco dE/dx distribution for all primary pi+ hits before applying primary pi+ hits after applying any cut the cuts discussed in the previous slides Mean=2.33MeV/cm Mean=3.3MeV/cm After removing the cosmic contamination, proton hits and overlapping tracks the mean dE/dx value gets much lower and closer to dE/dx in the MIP region. Majority of high dE/dx values disappears Still there are many very high dE/dx values, which escaped our cuts. Planning to have another look on how much further we can improve, finally we can set a cut on maximum allowed dE/dx values if we still have a significant number hits with high dE/dx hits. 13
Brief Update on Elastic scattering angle studies: Fig:pi+ interaction event In the figure aside there are two Elastic interaction vertices (B and C) and one Inelastic interaction vertex D. Elastic interaction vertices True scattering angle at vertex B is found using: A Cos(theta_B)= AB • BC/ (| AB| * |BC| ) Where theta_B is the scattering angle at vertex B, AB B and BC are vectors in 3D space. Similary, Cos(theta_C)= BC • CD/ (| BC| *| CD| ) D E C In Monte Carlo there is no break in true trajectory of the primary particle in case of Elastic interaction. F The primary particle trajectory stops if its KE energy drops to 0 (stopping pion) or the first inelastic Scattering occurs. In the fig aside, from A to D we have the same true trajectory while DE and DF are different trajectories. While reconstructed primary trajectory may or may not end at the elastic interaction vertex depending on the elastic scattering angle or other criteria set in the reconstruction algorithms. 14
Elastic interaction vertex reconstruction studies: Scattering angle vs (Reco EndZ-true interation Z) From the plot aside we can see that for small Reco EndZ-true interaction Z position scattering angles there is no correlation between the reconstructed Z position and the true Elastic interaction Z position. Often the interaction vertex is missed. Elastic Interaction well reconstructed As we go to higher and higher scattering angles there is a higher chance of reconstructed vertex matching with true vertex. There are some very high scattering angle vertex which have not been reconstructed True scattering angles (in degrees) well, I will show some event displays in following slides which explains the cause. 15
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