The (Speed and) Decay of Cosmic-Ray Muons

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

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? 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

Expected Results N(t) = N 0 e t/τ Counts Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 7 / 30

Expected Results But only if there s no noise! Counts Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 7 / 30

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, 2011 8 / 30

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, 2011 9 / 30

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, 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, Accidentals 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, Accidentals 72 000 72 000 72 000 72 000 72 000 72 000 72 000 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, Accidentals 70 000 60 000 50 000 40 000 30 000 20 000 10 000 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 12 / 30

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

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

Time Calibration t Μs 10 t 0.01 ± 0.03 Μs 0.0199 ± 0.0002 Μs Bin Χ Ν 2 0.0037 8 6 4 2 Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 21 / 30

Results Muon Decay Counts vs. Time Counts 50 Residuals 40 30 20 Counts 0.24 ± 0.05 39.9 ± 0.9 Χ Ν 2 0.65 t 1.99±0.04 Μs 10 5 10 15 Time Μs 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

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

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 10 5 cm 2 s 1 sr 1 at 10 km up Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 27 / 30

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

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

Thank You! Any questions? Jason Gross (8.13) Cosmic-Ray Muons November 4, 2011 30 / 30