1. Sara Lim & Elizabeth Ann Pollock University of Rochester PHY 243: Advanced Lab Professor Regina Demina, Sergey Korjenevski, Dave Starling Muon Lifetime

2. Cosmic Ray Muons Mass: 105.6 MeV/c 2 = 206.7*m e Lifetime: 2.2 μs (Muon rest frame) Flux of cosmic ray muons: j = 1 muon /cm 2 *min (sea level) Lorentz Transformations Muon velocity ~ 0.998 c Therefore, muons are relativistic particles and experience length contraction time needed for muon to travel from upper atmosphere (10km) to lab~ 34.8 µs (in lab reference frame) (w/o relativity), with relativity, they travel ~2.2 µs in their rest frame due to length contraction, muon travels ~632 m in its reference frame

3. Muon Decay Weak Decay Fundamental Particle: Lepton - spin ½ (fermion) - experiences weak (W Boson decay), gravitational and electromagnetic forces Fermi Weak Interaction Constant: G F -Muons decay via the emission of an electron, or in other words, via Beta Decay (and a muon neutrino and anti neutrino). This form of decay has a characterstic coupling constant: G F - average lifetime of muon = 2.197 μs - mass of the muon = 105.6 MeV/ c 2 - we can calculate the Fermi constant The mean lifetime of the muon is given by: Therefore:

4. Experimental Set-up Voltage and Discriminator Settings * Voltage = +1500 V * Threshold = 300 mV

5. Statistical Expectations for Set-up Cosmic Ray Muon Momentum Distribution at Sea Level Given: * Flux: j = 1 muon /cm 2 *min (sea level) * Energy loss = 2 MeV/(g/cm^2) * Height = 32 cm * Diameter = 30 cm * muon distribution ~ 100 -1000 MeV order Expectations (via MATLAB) * number of muons/min passing through tank = 706.8583 * The number of muons that stop in the tank per minute is ~= 3.5 * Therefore, the percent of the number of muons stopped per minute in the tank is ~0.3827

6. Data Number of muons captured in scintillator : 21,607 Calculated mean lifetime of muon : 2.59 μs Percent error (compared to accepted value): 17.62% Bin Size: 0.5 μs

7. Corrected Data ·Correction performed by taking the data points at large times (t>16.0 μs) and subtracting it from the rest of the data. · These data points are likely to be due to noise because the percentage of muons with a decay time greater than 16.0 μs is less than 0.2%. Number of muons captured in scintillator : 20,829 Calculated mean lifetime of muon : 2.39 μs Bin Size: 0.5 μs Percent error (compared to accepted value) : 8.63% Correction resulted in a calculated mean lifetime that is 8.98% closer to the accepted value. N(t)=7279 e -t/2.39

8. Suggestions Voltage and Threshold levels are very sensitive to change threshold, use NI screw driver to measure threshold, use ground from CAMAC crate Oscilloscope, Channel B might not be working Useful Sites Gaisser, Thomas K. Cosmic Rays & Particle Physics. Cambridge University Press, 1990. Leo, W.R. Techniques for Nuclear and Particle Physics Experiments. Springer, 1987. Mellisinos, Adrian C, Napolitano, Jim. Experiments in Modern Physics.