The (Speed and) Decay of Cosmic-Ray Muons
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1 The (Speed and) Decay of Cosmic-Ray Muons Jason Gross MIT - Department of Physics Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
2 Goals test relativity (time dilation) determine the mean lifetime of muons Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
3 Goals test relativity (time dilation) determine the mean lifetime of muons Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
4 Muons elementary particle unit negative charge spin 1/2 unstable Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
5 Why Muons? unstable long mean lifetime ( 2.2 µs) naturally abundant penetrating Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
6 Why Muons? unstable long mean lifetime ( 2.2 µs) naturally abundant penetrating Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
7 Why Muons? unstable long mean lifetime ( 2.2 µs) naturally abundant penetrating Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
8 Why Muons? unstable long mean lifetime ( 2.2 µs) naturally abundant penetrating Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
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, / 30
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, / 30
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, / 30
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, / 30
13 Expected Results N(t) = N 0 e t/τ Counts Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
14 Expected Results But only if there s no noise! Counts Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
15 Experimental Setup High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit Delay Line Time to Amplitude Converter PMT PMT Multichannel Analyzer 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
16 Muon Detection High Voltage Constant Fraction Discriminator Constant Fraction Discriminator PMT PMT 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
17 Noise Removal High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit PMT PMT 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
18 Noise Removal # Accidentals = Tn 1 n 2 t Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
19 Noise Removal If n 1 = 10 4 s 1, n 2 = s 1, T = 1 hour, t = 100 ns, Accidentals Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
20 Noise Removal If n 1 = 10 4 s 1, n 2 = s 1, T = 1 hour, t = 100 ns, Accidentals Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
21 Noise Removal If n 1 = 10 4 s 1, n 2 = s 1, T = 1 hour, t = 100 ns, Accidentals Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
22 Noise Removal High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit PMT PMT 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
23 Experimental Setup High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit Delay Line Time to Amplitude Converter PMT PMT Multichannel Analyzer 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
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, / 30
25 Experimental Setup arrival interval decay time Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
26 Experimental Setup arrival interval 1 2 decay time Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
27 Experimental Setup arrival interval decay time Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
28 Experimental Setup Lifetime: 2.2 µs Arrival Rate: (0.2 ± 0.1) s 1 Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
29 Experimental Setup High Voltage Constant Fraction Discriminator Constant Fraction Discriminator Coincidence Circuit Delay Line Time to Amplitude Converter PMT PMT Multichannel Analyzer 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
30 Time Calibration t Μs 10 t 0.01 ± 0.03 Μs ± Μs Bin Χ Ν Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
31 Results Muon Decay Counts vs. Time Counts 50 Residuals Counts 0.24 ± ± 0.9 Χ Ν t 1.99±0.04 Μs Time Μs Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
32 Results My Value: τ = (1.986 ± 0.042) µs Book Value: τ = (21) µs My Value: m µ = ( ± 0.46) MeV/c 2 Book Value: m µ = (38) MeV/c 2 Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
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, / 30
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, / 30
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, / 30
36 Testing Relativity: Muon Travel Time generated km above sea level others experiments suggest most likely momentum is 1 GeV / c to go km at this momentum (which corresponds to 0.994c) takes 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, / 30
37 Testing Relativity: Muon Travel Time generated km above sea level others experiments suggest most likely momentum is 1 GeV / c to go km at this momentum (which corresponds to 0.994c) takes 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, / 30
38 Testing Relativity: Muon Travel Time generated km above sea level others experiments suggest most likely momentum is 1 GeV / c to go km at this momentum (which corresponds to 0.994c) takes 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, / 30
39 Testing Relativity Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
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 % of muons corresponds to about 10 5 cm 2 s 1 sr 1 at 10 km up Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
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 % of muons corresponds to about 10 5 cm 2 s 1 sr 1 at 10 km up Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
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 % of muons corresponds to about 10 5 cm 2 s 1 sr 1 at 10 km up Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
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 % of muons corresponds to about 10 5 cm 2 s 1 sr 1 at 10 km up Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
44 Testing Relativity Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
45 Testing Relativity Relativity Wins! Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
46 Thank You! Any questions? Jason Gross (8.13) Cosmic-Ray Muons November 4, / 30
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