A π telescope for reconstructing ¯ H decays Håvard Gjersdal University of Oslo December 16, 2019 1/21
Outline ◮ Motivation for using a telescope ◮ Geometry ◮ Simulated performance with no B-field ◮ Simulated performance with B-field 2/21
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. 3/21
Telescope Absorber TEL1 TEL2 TEL3 ◮ We need 3 strip planes to measure estimate vertical position, angle and χ 2 . ◮ Simple simulations can give good idea of performance. ◮ Compact tracker (5mm, 20mm, 40mm), compromize between realustion and acceptance. 4/21
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 25 µ m / √ 12 ◮ No energy loss, constant plane thickness, 100% detection efficiency 5/21
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 6/21
Resolution with no B-field 30 25 Resolution[ µm ] 20 15 10 5 0 50 100 150 200 250 300 350 400 450 500 Pion energy [MeV] ◮ 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. 7/21
Acceptance with no B-field 12 10 Acceptance[%] 8 6 4 2 0 60 80 100 120 140 160 180 200 Pion energy [MeV] ◮ 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. 8/21
Estimated positions, 100um pitch, 200k pions 0 . 08 0 . 07 True 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 10 20 30 40 50 60 70 80 90 100 9/21
Estimated positions, 100um pitch, 200k pions 0 . 08 0 . 07 200MeV 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 10 20 30 40 50 60 70 80 90 100 9/21
Estimated positions, 100um pitch, 200k pions 0 . 08 0 . 07 150MeV 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 10 20 30 40 50 60 70 80 90 100 9/21
Estimated positions, 100um pitch, 200k pions 0 . 08 0 . 07 100MeV 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 10 20 30 40 50 60 70 80 90 100 9/21
Estimated positions, 100um pitch, 200k pions 0 . 08 0 . 07 50MeV 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 10 20 30 40 50 60 70 80 90 100 9/21
Pion energy from Germano Bonomi Linear probability distribution from 50MeV (max) to 550MeV(0) seems to be ok approxiamtion. 10/21
Reconstruction with momentum distribution, no B-field resX0 resX0 resX0 Entries Entries 19644 19644 600 Mean Mean 0.0304 0.0304 Std Dev Std Dev 18.26 18.26 0 . 08 True 500 0 . 07 Reconstructed 0 . 06 400 0 . 05 300 0 . 04 200 0 . 03 0 . 02 100 0 . 01 0 − − − − − 100 80 60 40 20 0 20 40 60 80 100 0 . 00 0 10 20 30 40 50 60 70 80 90 100 11/21
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. 12/21
Helix propagation, from presentation by Francesco Ragusa 13/21
B-field simulation 14/21
Curved tracks with straight line fitter, linear momentum distribution resX0 resX0 resX0 resX0 resX0 resX0 Entries Entries 19514 19514 Entries Entries 7591 7591 − − Mean Mean 0.4191 0.4191 Mean Mean 0.3862 0.3862 160 140 Std Dev Std Dev 43.54 43.54 Std Dev Std Dev 22.34 22.34 140 120 120 100 100 ⇒ 80 80 60 60 40 40 20 20 0 − − − − − − − − − − 100 80 60 40 20 0 20 40 60 80 100 100 80 60 40 20 0 20 40 60 80 100 ◮ 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% 15/21
Curved tracks with straight line fitter, linear momentum distribution When distance from peak to peak shortens, contrast vanishes. 0 . 08 0 . 07 150um 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 16/21
Curved tracks with straight line fitter, linear momentum distribution When distance from peak to peak shortens, contrast vanishes. 0 . 08 0 . 07 125um 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 16/21
Curved tracks with straight line fitter, linear momentum distribution When distance from peak to peak shortens, contrast vanishes. 0 . 08 0 . 07 100um 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 10 20 30 40 50 60 70 80 90 100 16/21
Curved tracks with straight line fitter, linear momentum distribution When distance from peak to peak shortens, contrast vanishes. 0 . 08 0 . 07 75um 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 10 20 30 40 50 60 70 16/21
Curved tracks with straight line fitter, linear momentum distribution When distance from peak to peak shortens, contrast vanishes. 0 . 08 0 . 07 50um 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 10 20 30 40 50 16/21
Curved tracks with straight line fitter, linear momentum distribution When distance from peak to peak shortens, contrast vanishes. 0 . 08 0 . 07 25um 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 5 10 15 20 25 16/21
Curved tracks with straight line fitter, linear momentum distribution Reconstructed sine pattern, 150um pitch, N decays frmo the absorber. 0 . 08 0 . 07 True 200k 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 17/21
Curved tracks with straight line fitter, linear momentum distribution Reconstructed sine pattern, 150um pitch, N decays frmo the absorber. 0 . 08 0 . 07 Reco 200k pions 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 17/21
Curved tracks with straight line fitter, linear momentum distribution Reconstructed sine pattern, 150um pitch, N decays frmo the absorber. 0 . 08 0 . 07 Reco 100k pions 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 17/21
Curved tracks with straight line fitter, linear momentum distribution Reconstructed sine pattern, 150um pitch, N decays frmo the absorber. 0 . 08 0 . 07 Reco 50k pions 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 17/21
Curved tracks with straight line fitter, linear momentum distribution Reconstructed sine pattern, 150um pitch, N decays frmo the absorber. 0 . 08 0 . 07 Reco 25k pions 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 17/21
Curved tracks with straight line fitter, linear momentum distribution Reconstructed sine pattern, 150um pitch, N decays frmo the absorber. 0 . 08 0 . 07 Reco 10k pions 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 17/21
Curved tracks with straight line fitter, linear momentum distribution Reconstructed sine pattern, 150um pitch, N decays frmo the absorber. 0 . 08 0 . 07 Reco 5k pions 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 17/21
Curved tracks with straight line fitter, linear momentum distribution Reconstructed sine pattern, 150um pitch, N decays frmo the absorber. 0 . 08 0 . 07 Reco 2.5k pions 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 17/21
Curved tracks with straight line fitter, linear momentum distribution Reconstructed sine pattern, 150um pitch, N decays frmo the absorber. 0 . 08 0 . 07 Reco 1k pions 0 . 06 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 0 . 00 0 20 40 60 80 100 120 140 17/21
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