Measurement of Muon Lifetime
Alex Povilus
Physics 441- Fall 2003
September 16, 2003
Abstract
The lifetime of the muon particle is found by statistically analyzing the time distribution of
muon decays within a scintillator. The proper lifetime, τ , was found to be 2.159±0.015(stat) ±
0.004(sys)µsec for 175003 muon decays recorded over a period of 96 hours.
The decay of the muon has revolutionized the foundations of particle physics since the mid-1930’s
by directly demonstrating the existence of a new fundamental charge, one which is associated with the
”weak” force. By analyzing the statistics of such decays, we are able to learn about the nature of this
weak force and its relative strength to other forces.
I. Apparatus
The apparatus, at its core, is simply a scintillator which is sensitive to muons passing through it and
electrons produced by the decay of muons. When a muon passes through the fluid of the scintillator, it
excites small energy changes in electrons of carbon rings within it. The energy is eventually transferred
from the carbon rings to light-producing compounds via dipole interactions, allowing for the detection of
muons. The light produced is faint, but can nonetheless be detected by photomultiplier tubes (PMTs)
which convert the photon into a current of electrons.
When obtaining a signal from the PMTs, it is important to be able to immediately interpret the
signal through hardware so that software is not bogged down with recording and discriminating data.
In fact, this element of the experiment is key to finding data for most experiments in particle physics,
since often there is more data than what needs to or even can be recorded. One can configure hardware
discrimination by means of a discriminator circuit and a time-to-amplitude conversion circuit (TAC). The
discriminator circuit filters out background noise and weaker signals not caused by muons. Once this
signal was calibrated, the rate of events detected by the chamber was ∼ 60/sec which correlates well with
the accepted rate of about 100 muons/m2 s with a resolution between muons of 0.30µsec, all points before this were removed from
consideration. The exponential least-squares curve fit to this data set was found to be,
P (∆t) = 5.63 + (476 ± 2)e∆t/(2.159±0.015(stat)±0.004(sys)µsec) (3)
with χ2 = 1.038 for 906 degrees of freedom. This value correlates well, within 2σ, with the accepted
υ
value of τ = 2.1970µsec.1
III. Conclusion
The lifetime of the muon was found to be 2.159 ± 0.015(stat) ± 0.004(sys), which correlates well with
accepted values. This experiment demonstrated how instrumentation ”events” can be interpreted in a
statistical manner to observe phenomena in particle physics. Possible improvements to this experiment
include longer observation times and reduction of the oscillation in the discriminator signal.
References
1. Giovanetti, Dey, et altera, Phys. Rev. D 29, 343-348 (1984)
2