[PPT] - Vertex reconstruction Vertex reconstruction in large liquid PowerPoint Presentation

SLIDE 1

Vertex reconstruction Vertex reconstruction

in large liquid scintillator detectors in large liquid scintillator detectors

David Meyhöfer March 20, 2017 Universität Hamburg

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SLIDE 2

Vertex reconstruction

Why a vertex reconstruction?

Novel track reconstruction has been developed Holds great potential for any liquid scintillator detector Has a limited number of fundamental assumptions Gain topological energy deposition information Novel track reconstruction needs a reference point Providing vertex to the Novel track reconstruction

Currently for LENA(low energy neutrino astronomy) Operation in an energy range of a few MeV to GeV Also works with a start point near the track

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SLIDE 3

Vertex reconstruction MeV range

Time of flight

Time of flight for photon i ti = D(xi(0), xi(t)) vg ti ˆ = Time of flight for photon i vg ˆ = Group velocity D(xi(0), xi(t)) distance xi(0) to xi(t)

Figure : Time of flight for a photon.

Not considered Scattering Absorption with reemission Scintillation decay time Electronic effects

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SLIDE 4

Vertex reconstruction MeV range

Time difference histogram

ti,dif = ti,hit − ti ti,dif ˆ = Difference in time for photon i thit ˆ = Measured time for photon i ti ˆ = Time of flight for photon i

[ns] 100 − 50 − 50 100 [a.u.] 10 20 30 40 50 60 70 80

1,0,5

Entries 1280 Mean 18.39 Std Dev 25.88

(a) Near the true vertex

[ns] 100 − 50 − 50 100 [a.u.] 10 20 30 40 50 60 70 80

16,20,511

Entries 1280 Mean 16.53 Std Dev 27.1

(b) ∼5 m away from true vertex Figure : Examples for time difference histograms at the true vertex and 5 m aside from the true vertex.

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SLIDE 5

Vertex reconstruction MeV range

Grid

(a) First iteration (b) Following iteration Figure : 2 dimensional example grid to illustrate the vertex finding.

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SLIDE 6

Vertex reconstruction MeV range

Angular acceptance of PMTs

cos α =

p ·

n | p| · | n| α incident angle

n PMT normal vector
p incident vector

[rad] α 0.2 0.4 0.6 0.8 1 1.2 1.4 ) α (

a

P 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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SLIDE 7

Vertex reconstruction Time reconstruction

Time fitting and evaluation algorithm

[ns] 10 − 8 − 6 − 4 − 2 − 2 4 6 8 10 20 40 60 80 100

ToE Entries 1280 Mean 3.748 − Std Dev 2.79

(a) Histogram at determined vertex

[ns] 10 − 8 − 6 − 4 − 2 − 2 4 6 8 10 20 40 60 80 100

(b) Fit for (a)

The fit considers: Scintillation decay time PMT time resolution ti,dif = ti − ti,hit

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SLIDE 8

Vertex reconstruction GeV range

High energy event development

(a) A few nanoseconds after the events start (b) First hit distribution after the event Figure : Distribution of first hit information

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SLIDE 9

Results MeV range

LEVertex

Distance of MCVertex to RecoVertex [cm]

5 10 15 20 25 30 35 40 45 50

Energy [MeV]

1 2 3 4 5 6 7 8 9 10

Entries 10000 Mean x 14.06 Mean y 5.354 Std Dev x 9.016 Std Dev y 2.682 0 9199 801

10 20 30 40 50 60 70 80

Entries 10000 Mean x 14.06 Mean y 5.354 Std Dev x 9.016 Std Dev y 2.682 0 9199 801

Distance of MCVertex to RecoVertex per Energy

Figure

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SLIDE 10

Results MeV range

MeV positional reconstruction results

Entries 10000 Std Dev 12.95 Underflow 225 Overflow 225 / ndf

2

χ 916.7 / 91 Prob Constant 16.1 ± 984.4 Mean 0.07531 ± 0.08323 Sigma 0.086 ± 6.998 Distance of RecoX from TrueX [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 200 400 600 800 1000 1200 Entries 10000 Std Dev 12.95 Underflow 225 Overflow 225 / ndf

2

χ 916.7 / 91 Prob Constant 16.1 ± 984.4 Mean 0.07531 ± 0.08323 Sigma 0.086 ± 6.998 Entries 10000 Std Dev 12.83 Underflow 264 Overflow 220 / ndf

2

χ 943 / 90 Prob Constant 16.6 ± 972.1 Mean 0.07602 ± 0.04976 Sigma 0.093 ± 7.036 Distance of RecoY from TrueY [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 200 400 600 800 1000 1200 Entries 10000 Std Dev 12.83 Underflow 264 Overflow 220 / ndf

2

χ 943 / 90 Prob Constant 16.6 ± 972.1 Mean 0.07602 ± 0.04976 Sigma 0.093 ± 7.036 Entries 10000 Std Dev 15.28 Underflow 143 Overflow 163 / ndf

2

χ 559.2 / 96 Prob Constant 10.4 ± 704.4 Mean 0.10826 ± 0.03671 Sigma 0.11 ± 10.35 Distance of RecoZ from TrueZ [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 100 200 300 400 500 600 700 800 Entries 10000 Std Dev 15.28 Underflow 143 Overflow 163 / ndf

2

χ 559.2 / 96 Prob Constant 10.4 ± 704.4 Mean 0.10826 ± 0.03671 Sigma 0.11 ± 10.35

Results for 10k electron events Fit for X,Y and Z direction 0.5 to 10.0 MeV Energy Random position in the detector σx,y,z = ±14.34 cm

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SLIDE 11

Results MeV range

Time reconstruction results

Figure : Event time reconstruction results in MeV range

Only results within 20 cm of true vertex From fit σt ±0.33 ns Gaussian distribution around 0 ns expected Shift and excess due to underestimated TOFs

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SLIDE 12

Results GeV range

Reconstruction of a GeV muon

[cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 [cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 200 400 600 800 1000

YZ-projection

[cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 [cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 100 200 300 400 500 600 700

XZ-projection

[cm] 1000 − 500 − 500 1000 [cm] 1000 − 500 − 500 1000 200 400 600 800 1000

XY-projection

Figure : Example muon event

5.8 GeV Simulated event energy

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SLIDE 13

Results GeV range

GeV positional reconstruction results

Entries 2073 Std Dev 20.33 Underflow 253 Overflow 283 / ndf

2

χ 98.34 / 80 Prob 0.08022 Constant 2.65 ± 79.02 Mean 0.3846 ± 0.3173 Sigma 0.30 ± 14.54 Distance of RecoX from TrueX [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 10 20 30 40 50 60 70 80 90 Entries 2073 Std Dev 20.33 Underflow 253 Overflow 283 / ndf

2

χ 98.34 / 80 Prob 0.08022 Constant 2.65 ± 79.02 Mean 0.3846 ± 0.3173 Sigma 0.30 ± 14.54 Entries 2073 Std Dev 21.08 Underflow 289 Overflow 256 / ndf

2

χ 116.6 / 82 Prob 0.00722 Constant 2.72 ± 78.27 Mean 0.3847 ± 0.5295 Sigma 0.32 ± 14.39 Distance of RecoY from TrueY [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 10 20 30 40 50 60 70 80 Entries 2073 Std Dev 21.08 Underflow 289 Overflow 256 / ndf

2

χ 116.6 / 82 Prob 0.00722 Constant 2.72 ± 78.27 Mean 0.3847 ± 0.5295 Sigma 0.32 ± 14.39

Entries 2073 Std Dev 42.78 Underflow 346 Overflow 296

Distance of RecoZ from TrueZ [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 10 20 30 40 50 60 70 80

Entries 2073 Std Dev 42.78 Underflow 346 Overflow 296

Results for 2500 muon events Fit for X,Y and Z direction 5.0 to 10.0 GeV Energy Random position in the detector

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SLIDE 14

Results GeV range

GeV positional reconstruction near track

Entries 2500 Std Dev 20.97 Underflow 13 Overflow 14 / ndf

2

χ 104 / 73 Prob 0.009956 Constant 2.49 ± 94.99 Mean 0.4131 ± 0.2498 − Sigma 0.33 ± 19.93 Distance of RecoX from TrackX [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 20 40 60 80 100 120 140 Entries 2500 Std Dev 20.97 Underflow 13 Overflow 14 / ndf

2

χ 104 / 73 Prob 0.009956 Constant 2.49 ± 94.99 Mean 0.4131 ± 0.2498 − Sigma 0.33 ± 19.93 Entries 2500 Std Dev 21.08 Underflow 14 Overflow 12 / ndf

2

χ 123.6 / 73 Prob 0.0001992 Constant 2.50 ± 94.18 Mean 0.4158 ± 0.4333 − Sigma 0.34 ± 19.94 Distance of RecoY from TrackY [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 20 40 60 80 100 120 Entries 2500 Std Dev 21.08 Underflow 14 Overflow 12 / ndf

2

χ 123.6 / 73 Prob 0.0001992 Constant 2.50 ± 94.18 Mean 0.4158 ± 0.4333 − Sigma 0.34 ± 19.94 Entries 2500 Std Dev 16.11 Underflow 2 Overflow / ndf

2

χ 120.7 / 54 Prob 07 − 5.186e Constant 3.2 ± 123.8 Mean 0.31748 ± 0.04114 Sigma 0.24 ± 15.34 Distance of RecoZ from TrackZ [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 20 40 60 80 100 120 140 160 180 Entries 2500 Std Dev 16.11 Underflow 2 Overflow / ndf

2

χ 120.7 / 54 Prob 07 − 5.186e Constant 3.2 ± 123.8 Mean 0.31748 ± 0.04114 Sigma 0.24 ± 15.34

Distance to true track Point near track is enough for Novel track reconstruction Fit for X,Y and Z direction σx,y,z = ±34.56 cm

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SLIDE 15

Results GeV range

GeV time reconstruction

Figure : Event time reconstruction results in GeV range

Only results within 20 cm of true vertex From fit σt ±0.27 ns Gaussian distribution around 0 ns expected Shift due to underestimated TOFs and shift of reconstructed vertex along track

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SLIDE 16

Results GeV range

Summary & Outlook

Conclusion: Determination of time and position is achieved Applicable for a energy range of a few MeV to GeV MeV range: position: σx,y,z = ±14.34 cm, time σt ±0.33 ns GeV range: position: σx,y,z = ±34.56 cm, time σt ±0.27 ns Direction determination 99.2% with in 25◦ Build on Novel track reconstruction software foundation:

Results can be provided to the Novel track reconstruction Simple integration is possible

Parallelization & Fast algorithm (a few seconds for GeV events) Outlook: Implementation of a energy reconstruction Consideration of time delay effects Full adaptation for JUNO detector

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SLIDE 17

Results GeV range

Thank you for your attention.

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SLIDE 18

Sources

Literature

Juno collaboration. Neutrino physics with juno. http://arxiv.org/pdf/1507.05613v2.pdf.

S. Lorenz.

Topological Track Reconstruction in Liquid Scintillator and LENA as a Far-Detector in an LBNO Experiment. Dissertation, Physik-Department, der Universität Hamburg, Dezember 2016.

T. Stempfle.

Reconstruction of spatially extended events in borexino.

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SLIDE 19

Backup

For single energy at 3 MeV

Entries 936 Std Dev 6.653 Underflow 1 Overflow / ndf

2

χ 21.39 / 22 Prob 0.4967 Constant 6.0 ± 141 Mean 0.1737 ± 0.9251 − Sigma 0.140 ± 5.178 Distance of RecoX from TrueX [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 20 40 60 80 100 120 140 160 Entries 936 Std Dev 6.653 Underflow 1 Overflow / ndf

2

χ 21.39 / 22 Prob 0.4967 Constant 6.0 ± 141 Mean 0.1737 ± 0.9251 − Sigma 0.140 ± 5.178 Entries 936 Std Dev 5.099 Underflow Overflow / ndf

2

χ 16.79 / 19 Prob 0.6043 Constant 6.5 ± 154 Mean 0.15717 ± 0.06815 Sigma 0.124 ± 4.763 Distance of RecoY from TrueY [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 20 40 60 80 100 120 140 160 Entries 936 Std Dev 5.099 Underflow Overflow / ndf

2

χ 16.79 / 19 Prob 0.6043 Constant 6.5 ± 154 Mean 0.15717 ± 0.06815 Sigma 0.124 ± 4.763 Entries 936 Std Dev 11.92 Underflow Overflow / ndf

2

χ 29.52 / 34 Prob 0.6871 Constant 2.66 ± 62.52 Mean 0.39155 ± 0.08822 − Sigma 0.32 ± 11.61 Distance of RecoZ from TrueZ [cm] 100 − 80 − 60 − 40 − 20 − 20 40 60 80 100 Entries 10 20 30 40 50 60 70 Entries 936 Std Dev 11.92 Underflow Overflow / ndf

2

χ 29.52 / 34 Prob 0.6871 Constant 2.66 ± 62.52 Mean 0.39155 ± 0.08822 − Sigma 0.32 ± 11.61

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SLIDE 20

Backup

Approx resolution of [cm]

5 10 15 20 25 30

Energy [MeV]

1 2 3 4 5 6 7 8 9 10

Entries 10000 Mean x 9.335 Mean y 5.206 Std Dev x 4.092 Std Dev y 2.732 0 10000 0

10 20 30 40 50 60

Entries 10000 Mean x 9.335 Mean y 5.206 Std Dev x 4.092 Std Dev y 2.732 0 10000 0 20 40 60 80 100 120 140 160 180 200

Approx resolution per energy Figure

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SLIDE 21

Backup

Shift along track

Entries 2073 Mean 30.4 Std Dev 11.38 Underflow Overflow 639 Distance of TrueVertex to closest point on track from RecoVertex [cm]

20 − 20 40 60 80 100

Entries

10 20 30 40 50 60 70

Entries 2073 Mean 30.4 Std Dev 11.38 Underflow Overflow 639

Figure

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SLIDE 22

Backup

Reconstruction close to the track

[cm] 20 − 10 − 10 20 30 40 50 60 [cm] 1890 1900 1910 1920 1930 1940 1950 1960 1970 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 5200 5400

YZ-projection

[cm] 20 − 10 − 10 20 30 40 50 60 [cm] 1890 1900 1910 1920 1930 1940 1950 1960 1970 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 5200 5400

XZ-projection

[cm] 20 − 10 − 10 20 30 40 50 60 [cm] 20 − 10 − 10 20 30 40 50 60 3000 3500 4000 4500 5000 5500

XY-projection

Figure : Example for a reconstructed vertex near the track.

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SLIDE 23

Backup

Distance of MCVertex to RecoVertex [cm]

50 100 150 200 250

Energy [MeV]

5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000

Entries 2073 Mean x 33.34 Mean y 7325 Std Dev x 23.06 Std Dev y 1409 0 2059 14

2 4 6 8 10 12 14 16

Entries 2073 Mean x 33.34 Mean y 7325 Std Dev x 23.06 Std Dev y 1409 0 2059 14

Distance of MCVertex to RecoVertex per Energy

Figure

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SLIDE 24

Backup

Example reconstruction in the JUNO detector

[cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 [cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 1000 2000 3000 4000 5000 6000

YZ-projection

[cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 [cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 1000 2000 3000 4000 5000 6000

XZ-projection

[cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 [cm] 2000 − 1500 − 1000 − 500 − 500 1000 1500 2000 1000 2000 3000 4000 5000 6000

XY-projection

Figure : Example for a reconstructed vertex inside the JUNO detector.

True vertex simulated at the center No adjustments for acrylic or water Symmetry effects enable correct reconstruction

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SLIDE 25

Backup

Reconstruction of a MeV electron

[cm]

70
60
50
40
30
20
10

10 [cm] 1100 1110 1120 1130 1140 1150 1160 1170 1180 260 280 300 320 340 360 380 400

YZ-projection

[cm] 250 260 270 280 290 300 310 320 330 [cm] 1100 1110 1120 1130 1140 1150 1160 1170 1180 260 280 300 320 340 360 380 400

XZ-projection

[cm] 250 260 270 280 290 300 310 320 330 [cm]

70
60
50
40
30
20
10

10 220 240 260 280 300 320 340 360 380 400 420

XY-projection

Figure : Example electron event. 6.70 MeV Simulated event energy

5.32 cm Distance true (white) to reconstructed vertex (black) 5.46 cm Approximated statistical resolution ∼9 cm for BOREXINO ∼3 cm for JUNO (simulated in center)

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SLIDE 26

Backup

Direction determination

[ns] 60 − 40 − 20 − 20 40 60 [Entries] 200 400 600 800 1000 1200 1400

A Entries 14806 Mean 6.231 Std Dev 10.26

(a)

[ns] 60 − 40 − 20 − 20 40 60 [Entries] 20 40 60 80 100 120 140 160 180 200

B Entries 15214 Mean 16.75 − Std Dev 18.78

(b)

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SLIDE 27

Backup

Direction reconstruction

Angle difference [deg]

5 10 15 20 25 30 35 40 45

Energy [MeV]

5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000

Entries 2500 Mean x 6.427 Mean y 7165 Std Dev x 5.934 Std Dev y 1413 0 2479 21

10 20 30 40 50 60 70 80 90

Entries 2500 Mean x 6.427 Mean y 7165 Std Dev x 5.934 Std Dev y 1413 0 2479 21

Difference of angle from true direction to reconstructed direction

Figure : Direction determination for event GeV range

For 99.2% the direction was determined within 25◦ For 75.7% the direction was determined within 7◦

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SLIDE 28

Backup

Charge barycenter

Pbc(pmt) =

PMT

pmt=1

ppmt·Hitpmt PMT

pmt=1 Hitpmt 11 / 17

SLIDE 29

Backup

Survival probability

d [m] 20 40 60 80 100 (d)

surv

P 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure : Photon survival probability. Psp(s) = exp(− s

AL )

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SLIDE 30

Backup

Hit probability

Phit =

r 2

pmt·(

VpmtNormal·( Vvertex− Vpmt)) 4·| Vvertex− Vpmt|

3

d [m] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 [rad] α 0.2 0.4 0.6 0.8 1 1.2 1.4 (d)

hit

P 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Figure : Hit probability.

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SLIDE 31

Neutrino oscillation

Homestake Experiment => Solar neutrino problem Solution: Neutrino oscillation Pontecorvo–Maki–Nakagawa–Sakata matrix

UPMNS =   1 c23 s23 −s23 c23     c13 s13 e−iδ 1 −s13 eiδ c13     c12 s12 −s12 c12 1  

cij ˆ = cos(Θij) sij ˆ = sin(Θij) Θij ˆ = mixing angle δ ˆ = CP-violating phase

Transition probability

P(α → β; t) =

i

|UαiU∗

βi|2 + 2Re

j>i

UαiU∗

αjU∗ βiUβj exp

−i

∆m2

ij

2 L E

L ˆ

= travel distance E ˆ = energy ∆m2

ij = m2 i − m2 j 14 / 17

SLIDE 32

Neutrino oscillation

Neutrino Mass Ordering

Parameters that have been determined are: Θ12, Θ13, Θ23, ∆m2

21 and |∆m2 31|

Sign of ∆m2

31 is unknown:

Figure : Neutrino Mass Ordering [2]

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SLIDE 33

Neutrino oscillation

Determining the Neutrino Mass Ordering

Figure : Reactor antineutrino flux [1]

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SLIDE 34

Large liquid scintillator detectors

Jiangmen Underground Neutrino Observatory

Is being built in China Antineutrino experiment IBD: νe + p → e+ + n Muon rate ∼3 Hz

Figure : Outline of the JUNO detector [1]

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