College - Author 1

College of Science and Mathematics

Department - Author 1

Physics Department

Degree Name - Author 1

BS in Physics

Date

6-2026

Primary Advisor

Thomas Gutierrez, College of Science and Mathematics, Physics Department

Additional Advisors

Chad Miller, College of Science and Mathematics, Physics Department

Abstract/Summary

This senior project investigates the muon lifetime through three complementary approaches: theoretical calculation, laboratory measurement, and computational simulation. The theoretical component develops the necessary background from relativistic field theory to the effective weak interaction, culminating in the leading-order Fermi-theory prediction of τ ≈ 2.2 μs, which explains why the muon lifetime lies on the microsecond scale.

The experimental component measures the lifetime of stopped cosmic-ray muons using a plastic scintillator, photomultiplier tube, and analog timing electronics. A binned Poisson likelihood fit to the primary 15-day acquisition run τ = 2.17+0.03-0.09 μs, consistent with the accepted value within the extracted uncertainty. A secondary run taken after replacing the preamplifier yields a lower fitted lifetime and larger background, demonstrating the sensitivity of the measurement to the signal-conditioning electronics.

The computational component models the detector geometry and stopped muon event selection in Geant4. The full simulated sample gives τ = 2.199 ± 0.014 μs. Together, these results show that the same physical quantity can be understood from the formal structure of weak-interaction theory, extracted from real detector data, and recovered under controlled simulation conditions. The agreement between the theoretical expectation, the primary experimental measurement, and the idealized simulation provides a coherent cross-check of the muon lifetime across all three methods.

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