UPDATES ON THE PION INCLUSIVE CROSS-SECTION ANALYSIS (MONTE CARLO - - PowerPoint PPT Presentation

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)

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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. Have been collaborating with Tingjun Yang on the analysis. 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:

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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. Wire numbers or w PeakTime or t In the figure aside, w represents the wire coordinate (it can be u, v

• r z depending on wire plane) and t represents the Peaktime.

w1=StartWire, w2=EndWire, t1=StartTick, t2=EndTick for a cluster (say corresponding to beam particle). Similarly, w3, w4, t3, t4 are corresponding quantities for any other cluster in the same TPC. Then the point of intersection (w, t) can be easily evaluated by solving sets of two linear equations in two variables. (w1,t1) (w2,t2) (w3,t3) (w4,t4) (w, t)

Removing Cosmic muon contamination:

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Plot on the right shows the number of cosmic tracks intersecting for each pi+.

Number of cosmic muons intersecting a beam particle

In the plot shown aside , 58% of pi+ track have no cosmic contamination. 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. dE/dx distribution of primary pi+ hits close to the point intersection (within ±2.5cm) with cosmic muons dE/dx distribution of all primary pi+ hits not within ±2.5cm from the point of intersection with cosmic muons Avg dE/dx = 2.79MeV/cm 5 Avg dE/dx = 8.1MeV/cm

Comparing the true and reconstructed Kinetic Energies:

Reconstructed Kinetic Energy vs true Kinetic Energy for all pi+ tracks

Reconstructed vs true Kinetic Energy for pi+ tracks with no cosmic contamination 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

KErec-KEtrue for all the hits in a pi+ track with no cosmic contamination:

(KErec-KEtrue) for all pi+ tracks at the interaction point

KErec-KEtrueat interaction point for tracks with no cosmic contamination

Left:all pi+ tracks and Right: pi+ tracks with no cosmic contamination 7

Mean=-4.85MeV/cm Mean=-31.35MeV/cm Mean=1.04MeV/cm Mean=-19.4MeV/cm

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 Peak time in ticks Z coordinate in cm

Z coordinate in cm

Y (cm) X (cm) XZ view YZ view If the daughter track scatters back towards the primary track at small angle, the charge deposition from the two tracks

• verlaps as shown in the Wire vs peak time distribution

above 8

Removing tracks with overlapping daughters: Find the angle between the projection of the primary and daughter tracks on the XZ plane. Z coordinate To calculate the angle I used the direction cosines of the primary track end and direction cosines of daughter track beginning. 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

• verlapping with the primary track.

XZ_theta for all pi+ tracks 9

Reco vs True Kinetic energy after removing overlapping tracks: (KErec-KEtrue) for all the hits in a pi+ track

(KErec-KEtrue) for all pi+ tracks at the interaction point Very few tracks (25 tracks out of 3276 tracks) with

• verlapping 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.

10 Mean=0.98MeV/cm

Mean=-19.62MeV/cm

Some more issues: Proton tail assigned to a primary muons: Event 1542, run 2.38 Event 1542, run 2.38 Often daughter protons are attached to the primary pi+ track. subsequently the dE/dx values becomes very high which results in wrong Kinetic Energy. 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: If (dE/dx for last hit<5MeV/cm and the mean value

• f 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. True pi+ Reco pi+

High dE/dx proton contamination

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KE reco vs KE true after removing the proton hits: (KErec-KEtrue) for all the hits in a pi+ track

(KErec-KEtrue) for all pi+ tracks at the interaction point

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. 12 Mean=1.2MeV/cm Mean=-2.6MeV/cm

Reco dE/dx distribution for all primary pi+ hits before applying any cut Reco dE/dx distribution for all primary pi+ hits after applying the cuts discussed in the previous slides

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. Summarizing energy deposition studies: 13 Mean=3.3MeV/cm Mean=2.33MeV/cm

Brief Update on Elastic scattering angle studies:

Elastic interaction vertices B C A D Fig:pi+ interaction event In the figure aside there are two Elastic interaction vertices (B and C) and one Inelastic interaction vertex D. True scattering angle at vertex B is found using: Cos(theta_B)=AB•BC/(|AB|*|BC|) Where theta_B is the scattering angle at vertex B, AB and BC are vectors in 3D space. Similary, Cos(theta_C)=BC•CD/(|BC|*|CD|) In Monte Carlo there is no break in true trajectory of the primary particle in case of Elastic interaction. 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. E F 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 well reconstructed

Reco EndZ-true interaction Z position True scattering angles (in degrees) Elastic interaction vertex reconstruction studies: From the plot aside we can see that for small scattering angles there is no correlation between the reconstructed Z position and the true Elastic interaction Z position. Often the interaction vertex is missed. 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 well, I will show some event displays in following slides which explains the cause. Scattering angle vs (Reco EndZ-true interation Z) 15

Elastic scattering vertex reconstruction as a function of scattering angle: Assumed vertex is well reconstructed if abs(reconstructed End Z –interaction Z)<10cm.

All Elastic scattering angles: These are all the scattering angle values until an interaction vertex is found at which abs(reconstructed Z –interaction Z)<10cm then we stop. Reconstructed Elastic angles: These are scattering angle corresponding to the vertex at which abs(reconstructed End Z –interaction Z)<10cm. Reconstruction Efficiency: Ratio of number of reconstructed vertex to the total number of Elastic interaction vertex for a particular angle bin.(I used 10 deg bins) As we go to higher and higher scattering angles number of entries is very few.

Vertex reconstruction efficiency as a function of Elastic scattering angle

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Big scattering angles not reconstructed: This tracks is broken at the APA boundary, although the scattering angle at 270.8cm appears to be reconstructed well the primary track breaks much before the interaction vertex. Z coordinate X coordinate Event: 1323 Run: 2.27 Reconstructed EndPosition Z=236cm True InteractionZ=270.8 True Elastic Scattering angle=109 deg Primary pi+ broken 17

Event 886, run 2.30, reconstructed primary EndPositionZ=262.36cm , true interaction Z=273.7, Elastic scat angle=149deg True pi+ Reco End True interaction point Here are the different views of the same event, we can see some part of the primary track is not reconstructed, possibly a backward scattered daughter proton is creating issues with reconstruction although scattering angle is big. XZ plane view YZ plane view Wire vs time view 18

Event 1274, run 2.46, reco End pointZ=155.67cm, true interaction Z=119.238cm, scattering angle​=45.5deg Reco End Point True Elastic Interaction vertex In this example we clearly see a kink around Z=119cm (true interaction vertex). But the track continues further, although the true angle at the interaction vertex is big, the angle in the XZ doesn't seem too big, which could be a possible reason for the track not ending at the interaction vertex. XZ view YZ view 19

SUMMARY:

• We identified the cosmic contaminated hits. After removing tracks with cosmic intersection the Kinetic Energy

reconstruction shows significant improvement. Plans are to correct dE/dx for contaminated hits using neighbouringdE/dx values.

• Removed tracks overlapping with daughters.
• Removed proton hits attached to the end of the primary pi+.
• At small scattering angles (<30deg, not so small infact) Elastic scattering vertex are often not reconstructed, we

are looking for ways to address this issue.

• We are now ready to calculate the pi+ inclusive cross-section (Inelastic scattering + Elastic scattering greater than

~30deg?) for SCE OFF sample.

• Soon we will start looking into Energy reconstruction status in SCE ON samples and protoDUNE data.

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THANKS

BACKUP SLIDES==>>

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all hits No cosmic contamination

Plot of Reco KE-true KE for all hit positions before and after removing cosmic contamination

Normalised entries all hits

No cosmic contamination

Plot of Reco KE-true KE for interaction point before and after removing cosmic contamination KE true vs KE reco comparisons before and after removing cosmic contamination 22

Backup Slides: Event 746, run 2.1, angle 58.6, true int Z=149.127, reco EndPositionZ=185.97 This plot contains only reco tracks This plot contains only true tracks We can see the scattering angle in the XZ view is very small, that could be the possible reason for missing Elastic int vertex. Primary pi+ Primary pi+ Interaction vertex missed 23

Some study to remove high dE/dx values attached to primary pi+: As 1GeV pi+ interact much before they can reach their full range, so it's reasonable to assume they are not in Bragg peak region, so the average dE/dx will be closer to MIP (2.1MeV/cm).

This is reco dE/dx values for reco hits between true EndPoint and 2.5 cm further than true end point (if reco track stops at

• r before true Endpoint there won't be any

entries here for that track). This histogram has dE/dx values for all reco hits 2.5cm to 0cm before the true EndPoint, there is still some contamination in this histogram, so high average dE/dx This histogram has dE/dx values for all reco hits 5.0 cm to 2.5 cm before the true EndPoint. This histogram has dE/dx values for all reco hits before 7.5cm to 5.0 cm from true EndPoint

Reco pi+ end points are often contaminated with a daughter proton or another pi+. The 4th histogram shows a very high dE/dx compared to other 3, this is possible only if proton hits are attached to the end. To remove proton hit, 1.)I check the last hit on the track, if it's less than 5MeV/cm, I calculate the avg dE/dx of the last 3 hits and if that is less than 3MeV/cm, I assume the last hit is not contaminated with proton hits and stop. Else I go to the 2nd last hits. And repeat the same process as in 1) for 2nd last hit. I repeat this until I find a hit satisfying above criteria. Taking average is necessary as there is always some fluctuation in dE/dx values.

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25 Implementing proton hit removing algorithm

Evt:241 run 2.41, before applying proton hits removal cut Evt:241 run 2.41, after applying proton hits removal cut Evt:1754 run 2.48, before applying proton hits removal cut Evt:1754 run 2.48, after applying proton hits removal cut

Left are plots before applying proton hits removal algorithm, Right are plots after applying the algorithm. The algorithm not only improves KE reconstruction but also shifts the reco end position closer to true EndPosition.