A telescope for reconstructing H decays Hvard Gjersdal University - - PowerPoint PPT Presentation

A π telescope for reconstructing ¯ H decays

Håvard Gjersdal

University of Oslo

December 16, 2019

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Outline

◮ Motivation for using a telescope ◮ Geometry ◮ Simulated performance with no B-field ◮ Simulated performance with B-field

3/21

Motivation (from Helga Holmestad’s thesis)

Plasma effect, vocano effect, halo effect makes position estimation hard. Pions are emitted from decay position, reconstructing tracks can give good position estimates.

4/21

Telescope

Absorber TEL1 TEL2 TEL3

◮ We need 3 strip planes to measure estimate vertical position, angle and χ2. ◮ Simple simulations can give good idea of performance. ◮ Compact tracker (5mm, 20mm, 40mm), compromize between realustion and acceptance.

5/21

Telescope simulations

Absorber TEL1 TEL2 TEL3

◮ All planes are 5 cm in x, 9 cm in y ◮ Initial position is uniform i x, undulating intensity in y. ◮ Direction of pions is uniform on a half-sphere. ◮ 50% π−, 50% π+ ◮ Trakcer planes are 50um thick Si, amount of scattering calculated from Highland formula ◮ Measurement resolution 25µm/ √ 12 ◮ No energy loss, constant plane thickness, 100% detection efficiency

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Simulation of straight line tracks

# Position in absorber self.z = 0 self.x = random.random() * self.max_x while(True): # Undulating along Y p = random.random() self.y = random.random() * self.max_y limit = 0.5 + 0.5 * math.sin((math.pi * self.y * 2)/pitch) if (limit < p): return() # Initial angle self.phi = random.random() * math.pi * 2 # Initial phase of helix self.lmbda = math.pi * 0.5 - math.acos(random.random()) # Uniform on a sphere self.chrge = 1 if (random.random() > 0.5): self.chrge = -1 def scatter(self): """ Scattering in detector planes, 50 um thick. Highland formula. """ pion_mass = 139.0 radlength = 50e-6/0.1 # 50um / 10cm beta = self.ebeam/math.sqrt(self.ebeam * self.ebeam + pion_mass * pion_mass) theta = 13.6/(beta * self.ebeam) * math.sqrt(radlength) * (1.0 + 0.038 * math.log(radlength)) self.lmbda += numpy.random.normal(0, theta) self.phi += numpy.random.normal(0, theta)

Simulation code: https://github.com/hgjersdal/aegis-stuff/blob/master/helix.py Track fitter: https://github.com/hgjersdal/eigen-track-fitter

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Resolution with no B-field

Resolution[µm] Pion energy [MeV]

50 100 150 200 250 300 350 400 450 500 5 10 15 20 25 30

◮ Limited by multiple scattering. 50MeV pions are not very relativistic. ◮ Distance from absorber to firs plane should be as short as possible! ◮ Resolution can be improved a little by making a longer telescope.

8/21

Acceptance with no B-field

Acceptance[%] Pion energy [MeV]

60 80 100 120 140 160 180 200 2 4 6 8 10 12

◮ Acceptance is determined by geometry and approximately 10 % in this case ◮ Adding χ-cut makes it possible to reject some “bad” tracks from low energy pions. ◮ Moving the last telescope plane closer to absorber improves acceptance. ◮ Compromise between acceptance and resolution.

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Estimated positions, 100um pitch, 200k pions

True

10 20 30 40 50 60 70 80 90 100 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Estimated positions, 100um pitch, 200k pions

200MeV

10 20 30 40 50 60 70 80 90 100 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Estimated positions, 100um pitch, 200k pions

150MeV

10 20 30 40 50 60 70 80 90 100 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Estimated positions, 100um pitch, 200k pions

100MeV

10 20 30 40 50 60 70 80 90 100 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Estimated positions, 100um pitch, 200k pions

50MeV

10 20 30 40 50 60 70 80 90 100 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

10/21

Pion energy from Germano Bonomi

Linear probability distribution from 50MeV (max) to 550MeV(0) seems to be ok approxiamtion.

11/21

Reconstruction with momentum distribution, no B-field

resX0 Entries 19644 Mean 0.0304 Std Dev 18.26 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 100 200 300 400 500 600 resX0 Entries 19644 Mean 0.0304 Std Dev 18.26

resX0

True Reconstructed

10 20 30 40 50 60 70 80 90 100 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

12/21

B-field simulation

◮ Helix reconstruction needs (x, y, φ, θ, q/p), 6 strip planes or 3 pixel planes ◮ Sine propagator needs (y, scale, speed, phase), 5 strip planes ◮ If lines are sufficiently close to being straight, we can get away with 3 strip planes. The last case means the simplest telescope, the simplest reconstruction code.

13/21

Helix propagation, from presentation by Francesco Ragusa

14/21

B-field simulation

15/21

Curved tracks with straight line fitter, linear momentum distribution

resX0 Entries 19514 Mean 0.4191 Std Dev 43.54 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 20 40 60 80 100 120 140 160 resX0 Entries 19514 Mean 0.4191 Std Dev 43.54

resX0

⇒

resX0 Entries 7591 Mean 0.3862 − Std Dev 22.34 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 20 40 60 80 100 120 140 resX0 Entries 7591 Mean 0.3862 − Std Dev 22.34

resX0

◮ χ-cuts can be used to reject tracks with large curvature. ◮ Resolution can be kept reasonably high, at the cost of acceptance. ◮ Acceptance goes from around 10% to around 4%

16/21

Curved tracks with straight line fitter, linear momentum distribution

When distance from peak to peak shortens, contrast vanishes.

150um

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Curved tracks with straight line fitter, linear momentum distribution

When distance from peak to peak shortens, contrast vanishes.

125um

20 40 60 80 100 120 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Curved tracks with straight line fitter, linear momentum distribution

When distance from peak to peak shortens, contrast vanishes.

100um

10 20 30 40 50 60 70 80 90 100 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Curved tracks with straight line fitter, linear momentum distribution

When distance from peak to peak shortens, contrast vanishes.

75um

10 20 30 40 50 60 70 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Curved tracks with straight line fitter, linear momentum distribution

When distance from peak to peak shortens, contrast vanishes.

50um

10 20 30 40 50 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Curved tracks with straight line fitter, linear momentum distribution

When distance from peak to peak shortens, contrast vanishes.

25um

5 10 15 20 25 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

17/21

Curved tracks with straight line fitter, linear momentum distribution

Reconstructed sine pattern, 150um pitch, N decays frmo the absorber.

True 200k

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

17/21

Curved tracks with straight line fitter, linear momentum distribution

Reconstructed sine pattern, 150um pitch, N decays frmo the absorber.

Reco 200k pions

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

17/21

Curved tracks with straight line fitter, linear momentum distribution

Reconstructed sine pattern, 150um pitch, N decays frmo the absorber.

Reco 100k pions

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

17/21

Curved tracks with straight line fitter, linear momentum distribution

Reconstructed sine pattern, 150um pitch, N decays frmo the absorber.

Reco 50k pions

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

17/21

Curved tracks with straight line fitter, linear momentum distribution

Reconstructed sine pattern, 150um pitch, N decays frmo the absorber.

Reco 25k pions

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

17/21

Curved tracks with straight line fitter, linear momentum distribution

Reconstructed sine pattern, 150um pitch, N decays frmo the absorber.

Reco 10k pions

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

17/21

Curved tracks with straight line fitter, linear momentum distribution

Reconstructed sine pattern, 150um pitch, N decays frmo the absorber.

Reco 5k pions

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

17/21

Curved tracks with straight line fitter, linear momentum distribution

Reconstructed sine pattern, 150um pitch, N decays frmo the absorber.

Reco 2.5k pions

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

17/21

Curved tracks with straight line fitter, linear momentum distribution

Reconstructed sine pattern, 150um pitch, N decays frmo the absorber.

Reco 1k pions

20 40 60 80 100 120 140 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

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Curved tracks with straight line fitter, linear momentum distribution

True 200k 100k 50k 25k 10k 5k 2.5k 1k

20 40 60 80 100 120 140 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

19/21

Alignment

◮ Alignment for all planes need to be accurate to a few um. ◮ Absorber to be aligned with light, but ligt is not detectable

• n the telescope.

◮ Telescope can be aligned with pions, but pions from ¯ H have bad resolution in absorber. ◮ Maybe possible to align from pions from upstream ¯ H decays.

20/21

Summary

◮ Simulation is new, very simple, not properly vetted ◮ But it seems like a well aligned pion telescope made of three thin planes of 25um stips could work ◮ Potentially hard to align.

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Summary

◮ Simulation is new, very simple, not properly vetted ◮ But it seems like a well aligned pion telescope made of three thin planes of 25um stips could work ◮ Potentially hard to align.