QuarkNet Muon Lifetime Explorer

Analyzes cosmic muon data from a QuarkNet muon hodoscope to measure the lifetime of stopping muons.

Positively and negatively charged muons created in the Earth's atmosphere in cosmic ray showers arrive at sea level predominantly downwards directed with a constant flux of roughly 1 per square meter per second per sterradian and mean energy of order 1 GeV. Those with energy of a fraction of GeV can be brought to rest by ionization energy loss (a few MeV/cm) plastic scintillator paddle a few cm thick. Visible prompt scintillation light resulting from the energy deposition can be detected by a photomultiplier tube (PMT) as an electronic pulse and the time determined to nanosecond precision.

A muon decays to an electron and two neutrinos, and , in vacuum with a rest frame characteristic lifetime . The decay electron has an energy ranging from zero to about 50 MeV and will likely produce a later pulse in the same paddle and possibly in any nearby paddle. The time difference between a muon arrival signal and the decay electron signal follows an exponential distribution for both positive and negative muons. A positive muon stopped in scintillator typically rapidly forms a muonium atom while a negative muon displaces an electron creating a muonic atom. In either case, the "stopped" muon is actually in motion with a speed but relativistic time dilation of the lifetime is negligible. A stopped negative muon is subject to capture by an atomic nucleus, reducing its lifetime.

This script illustrates analysis of cosmic ray scintillator data samples in the public repository maintained by Quarknet. The data files are text files, each line providing a channel number, pulse leading edge time, and pulse width. The script explores several MATLAB methods for filtering the data and fitting the lifetime distribution.

Accomanying this script is a file describing how to access QuarkNet muon lifetime data interactively and by using MATLAB. Included is a folder containing sample data files. The Fermilab Test Array data used here constitutes signals from a single paddle with phototubes at both ends. Simultaneous signals for scintillation light are required, heavily discriminating against electronic noise pulses generated in the PMTs. The text data file was downloaded from the Quarknet site having there selected data files requiring blessing/quality assurance and filtered for a minimal twofold signal coincidence. The file is assumed to be in the MATLAB path.

Many other data files are available for muon lifetime studies, including files which derive from stacks for four paddles each with one PMT. A concidence of simultaeous signals in two paddles indicates an ionising particle like a muon passed through the topmost paddle and into another paddle, again discriminating against PMT noise. The coincidence triggers storage of the initial times and times of subsequent signals. A signal a few microsceconds later in either of the initial paddles is an indication of a likely muon decay event.