Determining the Muon Mass in an Instructional Laboratory

An instructional laboratory experiment to measure the muon mass is described. Using coincidence-anticoincidence detection, the decay of a cosmic-ray muon into an electron (or positron) is observed in a multiplate spark chamber, and recorded with a triggered CCD detector. The energy of the charged decay-product particle is then quantified by counting the number of spark gaps $n_S$ it traverses before being stopped by the chamber's aluminum plates. By running this apparatus under computer-control for several hours, the number of product-particles $N(n_S)$ with various $n_s$-values is obtained. The muon mass is obtained by a least-squares fit, which compares the experimentally observed $N(n_S)$ with simulation values predicted for this distribution by the Fermi description of muon decay via the weak interaction. We present the results for the muon mass we have obtained and discuss the simulation we developed to account for the observed skewing of $N(n_S)$ due to the various directions the spark-producing product particles move as well as the escape of some of the higher-energy particles from the chamber.