LIFETIME OF COSMIC RAY MUONS Sara Lim

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LIFETIME OF COSMIC RAY MUONSSara Lim
Elizabeth Ann Pollock
Abstract
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.
Introduction Theory Background
Expectations Experimental Set-up
Results
Corrected data Using a bin size of 0.5 µs and
since data points for large times (tgt16) 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

• 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 206.7me
• Velocity 0.998 c
• Lifetime 2.2 µs
• (muon rest frame)
• Flux of cosmic ray muons
• j 1 muon /cm2min
• (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

Cosmic Ray Muon Momentum Distribution at Sea
Level Cosmic Ray Muons and Particle Physics
Thomas K. Gaisser
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.

• 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

• 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.

where
,
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.
Errors