LIFETIME OF COSMIC RAY MUONS Sara Lim & Elizabeth Ann Pollock*
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• Lorentz Transformations and Time Dilation: • 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 without relativity), with relativity, they travel ~2.2 µs • due to length contraction, muon travels ~632 m in its reference frame LIFETIME OF COSMIC RAY MUONS Sara Lim & Elizabeth Ann Pollock* Abstract : Introduction: Theory & Background Expectations & Experimental Set-up Results Cosmic Ray Muon Momentum Distribution at Sea Level *Cosmic Ray Muons and Particle Physics; Thomas K. Gaisser Expectations (via MATLAB simulation) • given the dimensions of the tank, and that the muon energy loss = 2 MeV/(g/cm 2 ), incident muons with energy less than or equal to 60 MeV will stop in the tank • number of muons/min passing through tank ~ 707 • muons stopped in the tank per minute ~ 3-5 muons • ~0.3827% of muons stopped per minute in the tank • Mass: 105.6 MeV/c 2 = 206.7*m e • Velocity: ~ 0.998 c • Lifetime: 2.2 μs (muon rest frame) • Flux of cosmic ray muons: j = 1 muon /cm 2 *min (sea level) • Muon distribution (see graph): 100-1000 MeV order • Muon Decay: Muons decay via the emission of an electron, i.e., via Beta Decay (and a muon neutrino and anti neutrino). Similarly, for antimiuons: , where Muons created in the upper atmosphere via cosmic ray showers travel at relativistic speeds, and thus experience time dilation. This time dilation is observed in the Muon Lifetime set up, where we found the lifetime of the muon to be 2.39 ± 0.5 μs, compared to the accepted value of 2.2 μs, giving a 8.63% percent error. Corrected data: Using a bin size of 0.5 μs and since data points for large times (t>16) are likely due to noise (the percentage of muons with decay time greater than 16 μs is less than 0.2%) , we subtract these data points from the rest of the data to obtain the corrected data below: Conclusions: From our data obtained in the lab, we calculated the average lifetime of the muon to be 2.39 ± 0.5 μs, a deviation from the accepted value of 2.2 μs by 8.63%. Errors: Errors in this lab are mostly a consequence of troubles obtaining useable data with the electronics. In addition, the bin size of 0.5 μs resulted in an error of ± 0.5 μs. Set-up • The start signal begins when a cosmic ray muon hits the scintillator, deposits its energy, and upon de-excitation emits a photon that travels to the Photo Multiplier Tube (PMT) which via the photoelectric effect multiplies and accelerates the signal in proportion to the incident energy. • The stopped antimuon then decays into a positron which annihilates with an electron, thus producing the stop signal. The stop signal occurs within a window of the ns range from the start signal (the incident muon). • After further amplification, the signal
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Transcript of LIFETIME OF COSMIC RAY MUONS Sara Lim & Elizabeth Ann Pollock*
• Lorentz Transformations and Time Dilation:
• 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 without relativity), with relativity, they travel ~2.2 µs• due to length contraction, muon travels ~632 m in its reference frame
LIFETIME OF COSMIC RAY MUONS
Sara Lim & Elizabeth Ann Pollock*Abstract:
Introduction:Theory &
Background
Expectations &Experimental Set-up
Results
Cosmic Ray Muon Momentum Distribution at Sea Level
*Cosmic Ray Muons and Particle Physics; Thomas K. Gaisser
Expectations (via MATLAB simulation)• given the dimensions of the tank, and that the muon energy loss = 2 MeV/(g/cm2), incident muons with energy less than or equal to 60 MeV will stop in the tank• number of muons/min passing through tank ~ 707• muons stopped in the tank per minute ~ 3-5 muons• ~0.3827% of muons stopped per minute in the tank
• Mass: 105.6 MeV/c2 = 206.7*me
• Velocity: ~ 0.998 c• Lifetime: 2.2 μs (muon rest frame)• Flux of cosmic ray muons: j = 1 muon /cm2*min (sea level)• Muon distribution (see graph): 100-1000 MeV order• Muon Decay: Muons decay via the emission of an electron, i.e., via Beta Decay (and a muon neutrino and anti neutrino). Similarly, for antimiuons:
,
where
Muons created in the upper atmosphere via cosmic ray showers travel at relativistic speeds, and thus experience time dilation. This time dilation is observed in the Muon Lifetime set up, where we found the lifetime of the muon to be 2.39 ± 0.5 μs, compared to the accepted value of 2.2 μs, giving a 8.63% percent error.
Corrected data: Using a bin size of 0.5 μs and since data points for large times (t>16) are likely due to noise (the percentage of muons with decay time greater than 16 μs is less than 0.2%) , we subtract these data points from the rest of the data to obtain the corrected data below:
Conclusions:
From our data obtained in the lab, we calculated the average lifetime of the muon to be 2.39 ± 0.5 μs, a deviation from the accepted value of 2.2 μs by 8.63%.
Errors:Errors in this lab are mostly a consequence of troubles obtaining useable data with the electronics. In addition, the bin size of 0.5 μs resulted in an error of ± 0.5 μs.
Set-up• The start signal begins when a cosmic ray muon hits the scintillator, deposits its energy, and upon de-excitation emits a photon that travels to the Photo Multiplier Tube (PMT) which via the photoelectric effect multiplies and accelerates the signal in proportion to the incident energy.• The stopped antimuon then decays into a positron which annihilates with an electron, thus producing the stop signal. The stop signal occurs within a window of the ns range from the start signal (the incident muon). • After further amplification, the signal is moderated via the threshold, which is set at 300 mV to reduce background noise.
