The (Speed and) Decay of Cosmic-Ray Muons Jason Gross MIT - - - PowerPoint PPT Presentation

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The (Speed and) Decay of Cosmic-Ray Muons Jason Gross MIT - - - PowerPoint PPT Presentation

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The (Speed and) Decay of Cosmic-Ray Muons Jason Gross MIT - Department of Physics Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 1 / 30 Goals test relativity (time dilation) determine the mean lifetime of muons Jason Gross (8.13)

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SLIDE 1

The (Speed and) Decay of Cosmic-Ray Muons

Jason Gross

MIT - Department of Physics

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 1 / 30

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SLIDE 2

Goals

test relativity (time dilation) determine the mean lifetime

  • f muons

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 2 / 30

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SLIDE 3

Goals

test relativity (time dilation) determine the mean lifetime

  • f muons

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 2 / 30

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SLIDE 4

Muons

elementary particle unit negative charge spin 1/2 unstable

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 3 / 30

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SLIDE 5

Why Muons?

unstable long mean lifetime (≈ 2.2 µs) naturally abundant penetrating

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 4 / 30

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SLIDE 6

Why Muons?

unstable long mean lifetime (≈ 2.2 µs) naturally abundant penetrating

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 4 / 30

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SLIDE 7

Why Muons?

unstable long mean lifetime (≈ 2.2 µs) naturally abundant penetrating

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 4 / 30

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SLIDE 8

Why Muons?

unstable long mean lifetime (≈ 2.2 µs) naturally abundant penetrating

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 4 / 30

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SLIDE 9

Why Muons?

contact point between theory and reality (we can predict mean lifetime from Fermi β-decay, if we know the mass)

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 5 / 30

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SLIDE 10

Experimental Outline

muons generated by cosmic-rays above 15 km capture muons in a block of plastic scintillator record arrival & decay events

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 6 / 30

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SLIDE 11

Experimental Outline

muons generated by cosmic-rays above 15 km capture muons in a block of plastic scintillator record arrival & decay events

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 6 / 30

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SLIDE 12

Experimental Outline

muons generated by cosmic-rays above 15 km capture muons in a block of plastic scintillator record arrival & decay events

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 6 / 30

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SLIDE 13

Expected Results

N(t) = N0e−t/τ

2 4 6 8 10 t Μs Counts

Expected Count Rate vs. Decay Time

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 7 / 30

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SLIDE 14

Expected Results

But only if there’s no noise!

2 4 6 8 10 t Μs Counts

Expected Count Rate vs. Decay Time

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 7 / 30

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SLIDE 15

Experimental Setup

High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit Delay Line Time to Amplitude Converter Multichannel Analyzer 11" Diameter x 12" High Plastic Scintillator PMT PMT Light Tight Box

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 8 / 30

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SLIDE 16

Muon Detection

High Voltage 11" Diameter x 12" High Plastic Scintillator PMT PMT

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 9 / 30

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SLIDE 17

Noise Removal

High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit 11" Diameter x 12" High Plastic Scintillator PMT PMT Light Tight Box

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 10 / 30

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SLIDE 18

Noise Removal

# Accidentals = Tn1n2∆t

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 11 / 30

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SLIDE 19

Noise Removal

If n1 = 104 s−1, n2 = 2 · 104 s−1, T = 1 hour, ∆t = 100 ns,

2 4 6 8 10 t Μs Accidentals

Accidental Count vs. Apparent Time

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 12 / 30

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SLIDE 20

Noise Removal

If n1 = 104 s−1, n2 = 2 · 104 s−1, T = 1 hour, ∆t = 100 ns,

2 4 6 8 10 t Μs 72 000 72 000 72 000 72 000 72 000 72 000 72 000 Accidentals

Accidental Count vs. Apparent Time

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 12 / 30

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SLIDE 21

Noise Removal

If n1 = 104 s−1, n2 = 2 · 104 s−1, T = 1 hour, ∆t = 100 ns,

2 4 6 8 10 t Μs 10 000 20 000 30 000 40 000 50 000 60 000 70 000 Accidentals

Accidental Count vs. Apparent Time

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 12 / 30

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SLIDE 22

Noise Removal

High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit 11" Diameter x 12" High Plastic Scintillator PMT PMT Light Tight Box

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 13 / 30

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SLIDE 23

Experimental Setup

High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit Delay Line Time to Amplitude Converter Multichannel Analyzer 11" Diameter x 12" High Plastic Scintillator PMT PMT Light Tight Box

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 14 / 30

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SLIDE 24

Experimental Setup

Start Stop Delay Measured by TAC Delay

Arrival times of pulses along the STOP input (red) and the START input (green) of the TAC.

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 15 / 30

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SLIDE 25

Experimental Setup

arrival interval ≈ decay time

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 16 / 30

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SLIDE 26

Experimental Setup

arrival interval ≈ 1

2 decay time

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 17 / 30

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SLIDE 27

Experimental Setup

arrival interval ≫ decay time

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 18 / 30

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SLIDE 28

Experimental Setup

Lifetime: ≈ 2.2 µs Arrival Rate: ≈ (0.2 ± 0.1) s−1

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 19 / 30

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SLIDE 29

Experimental Setup

High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit Delay Line Time to Amplitude Converter Multichannel Analyzer 11" Diameter x 12" High Plastic Scintillator PMT PMT Light Tight Box

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 20 / 30

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SLIDE 30

Time Calibration

t 0.01 0.03 Μs 0.0199 0.0002 Μs Bin ΧΝ

2 0.0037

100 200 300 400 500 Bin 2 4 6 8 10 t Μs

Time Calibration

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 21 / 30

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SLIDE 31

Results

Counts 0.24 0.05 39.9 0.9

  • t

1.990.04 Μs

ΧΝ

2 0.65

Residuals

5 10 15 Time Μs 10 20 30 40 50 Counts

Muon Decay Counts vs. Time

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 22 / 30

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SLIDE 32

Results

My Value: τ = (1.986 ± 0.042) µs Book Value: τ = 2.197 034(21) µs My Value: mµ = (107.96 ± 0.46) MeV/c2 Book Value: mµ = 105.658 366 68(38) MeV/c2

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 23 / 30

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SLIDE 33

Sources of Error

systematic: didn’t account for the delay in the cable, so all my times are shorter than they should be poor estimation of errors (least squares gives (2.30 ± 0.04) µs) not enough data to get an estimate of the accidentals (if I fit to ae−t/τ, I get (2.06 ± 0.04) µs)

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 24 / 30

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SLIDE 34

Sources of Error

systematic: didn’t account for the delay in the cable, so all my times are shorter than they should be poor estimation of errors (least squares gives (2.30 ± 0.04) µs) not enough data to get an estimate of the accidentals (if I fit to ae−t/τ, I get (2.06 ± 0.04) µs)

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 24 / 30

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SLIDE 35

Sources of Error

systematic: didn’t account for the delay in the cable, so all my times are shorter than they should be poor estimation of errors (least squares gives (2.30 ± 0.04) µs) not enough data to get an estimate of the accidentals (if I fit to ae−t/τ, I get (2.06 ± 0.04) µs)

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 24 / 30

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SLIDE 36

Testing Relativity: Muon Travel Time

generated 10-15 km above sea level

  • thers’ experiments suggest most likely

momentum is 1 GeV / c to go 10-15 km at this momentum (which corresponds to 0.994c) takes 30-50 µs (but if we throw away all of special relativity, then this momentum corresponds to 9.5c, and it only takes 5 µs)

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 25 / 30

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SLIDE 37

Testing Relativity: Muon Travel Time

generated 10-15 km above sea level

  • thers’ experiments suggest most likely

momentum is 1 GeV / c to go 10-15 km at this momentum (which corresponds to 0.994c) takes 30-50 µs (but if we throw away all of special relativity, then this momentum corresponds to 9.5c, and it only takes 5 µs)

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 25 / 30

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SLIDE 38

Testing Relativity: Muon Travel Time

generated 10-15 km above sea level

  • thers’ experiments suggest most likely

momentum is 1 GeV / c to go 10-15 km at this momentum (which corresponds to 0.994c) takes 30-50 µs (but if we throw away all of special relativity, then this momentum corresponds to 9.5c, and it only takes 5 µs)

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 25 / 30

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SLIDE 39

Testing Relativity

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 26 / 30

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SLIDE 40

Testing Relativity: Muon Intensity

about 10−2 cm−2 s−1 sr−1 (muons intensity at sea level) without time dilation, it takes at least 30 µs to get down to sea level if we take τ ≈ 2 µs, if there is no time dilation, we see 3 · 10−5% of muons corresponds to about 105 cm−2 s−1 sr−1 at 10 km up

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 27 / 30

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SLIDE 41

Testing Relativity: Muon Intensity

about 10−2 cm−2 s−1 sr−1 (muons intensity at sea level) without time dilation, it takes at least 30 µs to get down to sea level if we take τ ≈ 2 µs, if there is no time dilation, we see 3 · 10−5% of muons corresponds to about 105 cm−2 s−1 sr−1 at 10 km up

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 27 / 30

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SLIDE 42

Testing Relativity: Muon Intensity

about 10−2 cm−2 s−1 sr−1 (muons intensity at sea level) without time dilation, it takes at least 30 µs to get down to sea level if we take τ ≈ 2 µs, if there is no time dilation, we see 3 · 10−5% of muons corresponds to about 105 cm−2 s−1 sr−1 at 10 km up

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 27 / 30

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SLIDE 43

Testing Relativity: Muon Intensity

about 10−2 cm−2 s−1 sr−1 (muons intensity at sea level) without time dilation, it takes at least 30 µs to get down to sea level if we take τ ≈ 2 µs, if there is no time dilation, we see 3 · 10−5% of muons corresponds to about 105 cm−2 s−1 sr−1 at 10 km up

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 27 / 30

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SLIDE 44

Testing Relativity

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 28 / 30

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SLIDE 45

Testing Relativity

Relativity Wins!

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 29 / 30

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SLIDE 46

Thank You! Any questions?

Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 30 / 30