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) Cosmic-Ray Muons November 4, 2011 2 / 30
Goals test relativity (time dilation) determine the mean lifetime of muons Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 2 / 30
Muons elementary particle unit negative charge spin 1 / 2 unstable Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 3 / 30
Why Muons? unstable long mean lifetime ( ≈ 2 . 2 µs) naturally abundant penetrating Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 4 / 30
Why Muons? unstable long mean lifetime ( ≈ 2 . 2 µs) naturally abundant penetrating Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 4 / 30
Why Muons? unstable long mean lifetime ( ≈ 2 . 2 µs) naturally abundant penetrating Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 4 / 30
Why Muons? unstable long mean lifetime ( ≈ 2 . 2 µs) naturally abundant penetrating Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 4 / 30
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
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
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
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
Expected Results N ( t ) = N 0 e − t /τ Expected Count Rate vs. Decay Time Counts t � Μ s � 2 4 6 8 10 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 7 / 30
Expected Results But only if there’s no noise! Expected Count Rate vs. Decay Time Counts t � Μ s � 2 4 6 8 10 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 7 / 30
Experimental Setup Constant Delay Line Fraction Time to Discriminator Coincidence High Amplitude Circuit Voltage Constant Converter Fraction Discriminator PMT PMT Multichannel Analyzer 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 8 / 30
Muon Detection High Voltage PMT PMT 11" Diameter x 12" High Plastic Scintillator Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 9 / 30
Noise Removal Constant Fraction Discriminator Coincidence High Circuit Voltage Constant Fraction Discriminator PMT PMT 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 10 / 30
Noise Removal # Accidentals = Tn 1 n 2 ∆ t Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 11 / 30
Noise Removal If n 1 = 10 4 s − 1 , n 2 = 2 · 10 4 s − 1 , T = 1 hour, ∆ t = 100 ns, Accidental Count vs. Apparent Time Accidentals t � Μ s � 2 4 6 8 10 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 12 / 30
Noise Removal If n 1 = 10 4 s − 1 , n 2 = 2 · 10 4 s − 1 , T = 1 hour, ∆ t = 100 ns, Accidental Count vs. Apparent Time Accidentals 72 000 72 000 72 000 72 000 72 000 72 000 72 000 t � Μ s � 2 4 6 8 10 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 12 / 30
Noise Removal If n 1 = 10 4 s − 1 , n 2 = 2 · 10 4 s − 1 , T = 1 hour, ∆ t = 100 ns, Accidental Count vs. Apparent Time Accidentals 70 000 60 000 50 000 40 000 30 000 20 000 10 000 t � Μ s � 0 2 4 6 8 10 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 12 / 30
Noise Removal Constant Fraction Discriminator Coincidence High Circuit Voltage Constant Fraction Discriminator PMT PMT 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 13 / 30
Experimental Setup Constant Delay Line Fraction Time to Discriminator Coincidence High Amplitude Circuit Voltage Constant Converter Fraction Discriminator PMT PMT Multichannel Analyzer 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 14 / 30
Experimental Setup Measured by TAC Delay Delay Start Stop 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
Experimental Setup arrival interval ≈ decay time Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 16 / 30
Experimental Setup arrival interval ≈ 1 2 decay time Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 17 / 30
Experimental Setup arrival interval ≫ decay time Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 18 / 30
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
Experimental Setup Constant Delay Line Fraction Time to Discriminator Coincidence High Amplitude Circuit Voltage Constant Converter Fraction Discriminator PMT PMT Multichannel Analyzer 11" Diameter x 12" High Plastic Scintillator Light Tight Box Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 20 / 30
Time Calibration Time Calibration t � Μ s � t � � � 0.01 � 0.03 � Μ s � �� 0.0199 � 0.0002 � Μ s � � Bin � � 10 2 � 0.0037 Χ Ν 8 6 4 2 Bin � 100 200 300 400 500 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 21 / 30
Results Muon Decay � Counts vs. Time � Counts 50 Residuals 40 30 t � Counts � � 0.24 � 0.05 � � � 39.9 � 0.9 � � � 1.99 � 0.04 � Μ s 2 � 0.65 Χ Ν 20 10 Time � Μ s � 5 10 15 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 22 / 30
Results My Value: τ = ( 1 . 986 ± 0 . 042 ) µs Book Value: τ = 2 . 197 034 ( 21 ) µs My Value: m µ = ( 107 . 96 ± 0 . 46 ) MeV / c 2 Book Value: m µ = 105 . 658 366 68 ( 38 ) MeV / c 2 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 23 / 30
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
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
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
Testing Relativity: Muon Travel Time generated 10-15 km above sea level others’ 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
Testing Relativity: Muon Travel Time generated 10-15 km above sea level others’ 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
Testing Relativity: Muon Travel Time generated 10-15 km above sea level others’ 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
Testing Relativity Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 26 / 30
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