The SMU Muon Observatory project utilizes a particle detector in the Fondren Science Building to detect the passage of short-lived subatomic particles known as “muons.” Muons are heavy cousins of the more familiar electron, which is found in every atom in the universe. Unlike the electron, which lives forever once it comes into existence, the life of a muon is fleeting. If you trap a muon, your victory will be brief: muons only live for an average of 2.2 millionths of a second, or 2.2 microseconds.
Muon Weather Conditions
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How do I understand the current conditions?
The rate at which muons pass through Fondren Science varies in cycles over the year, in many ways akin to the way seasons on Earth. We determine the historical average rate at which muons pass through the detector. We compare the current rate to that historical rate, and define the following scale to help you get a “quick feel” for how that compares to the historical average. Our measure of the “deviation” from that average is based on the standard deviation of historical data from the mean.
In the future, it would be interesting to take into account variations in the average over the year and make a distinction between “seasonal” variations and weather in the context of a seasonal average.
Muon Lifetime Measurement
The rate at which muons stop in the detector, and subsequently decay, is quite low. Only the lowest-energy muons raining down on the Earth can be stopped by such a compact instrument. The rate at which we observe events in the instrument suitable for lifetime measurement is just a few per hour. The above image automatically refreshes every 30 seconds, but don’t hold your breath while waiting for it to noticeably change!
The detector and its electronics were constructed by Professors Tom Coan and Jingbo Ye. The detector consists of a volume of scintillator optically connected to a photomultiplier tube (PMT). This is all sealed in a light-tight container. When electrically charged particles move through the scintillator, interacting with atoms in the material, this causes light to be emitted. The PMT received the light, converts it to electrical signals, and amplifies the signals. The electronics that readout the PMT take in electrical pulses from the PMT and signal process them. A pulse of sufficient quality initiates (“triggers”) a counter in the electronics; if a second pulse of sufficient quality is received by the electronics within 20,000 nanoseconds, this is stored as a “muon decay event”. Otherwise, the counter times out, records the event, and resets the trigger for the next pulse. These timeout events are useful for recording the raw rate at which muons pass through the scintillator but don’t get captured and decay; this is useful for assessing the local rate of cosmic ray radiation from outer space.
Learn more about the detector and the details of muon physics from Professors Tom Coan and Jingbo Ye and their “Muon Physics” handbook.
The data are retrieved by a small computer (currently a Raspberry Pi linux machine) using a serial port interface. This computer interface was established with expertise from SMU OIT’s Internet-of-Things Developer, Guillermo Vasquez. The data are pipelined from the detector electronics to the USB port on the computer. Software polls the USB port, loads the data buffered there, formats it, and saves it to disk. One file per day is stored; each line in the file represents a muon candidate (either a timeout event or a decay event). Each file is about 2.5 Megabytes in size, uncompressed.
The Physics of Muon Passage, Stopping, Capture, and Decay
The muons raining down on Fondren Science are created when cosmic rays strike molecules in the air above the campus. The collisions produce particles called “charged pions,” which decay in about 0.1 billionth of a second to muons. Two kinds of muons can be produced: positively charged and negatively charged.
The most common muons have kinetic energies of about 1 billion electron-Volts, or 1 GeV (for muons that come straight down from the sky to the earth). Such a muon is traveling at immense speed – 99.6% the speed of light. The detector, depicted above, is only about 1 foot high. At this speed, such a muon would punch through the detector, depositing 2 MeV/cm of material (for a total of 60 MeV of energy loss in material), slowing to just 99.5% the speed of light, and doing all of this in about 1 nanosecond.
Less common are the lower-energy muons. These can have kinetic energies of about 50 MeV; such a muon would slow in the detector, losing 2 MeV/cm of material traversed, and would lose all kinetic energy before leaving the detector. The detector will have stopped it. If this is all that happens, on average 2.2 microseconds later the stopped muon will decay.
How long does it take to stop a muon? This can happen in about 10 nanoseconds (billionths of a second), even taking into account that the muon slows as it loses energy.
However, negatively charged muons have a good chance of being captured by an atom in the detector when they slow down. Just like their cousin electrons, they can fall into orbit around a central nucleus… say, of a Carbon atom in the detector. Their orbits will be tighter than those of electrons – about 200 times tighter. Under these conditions, muons can interact with the nucleus before they decay, and the subsequent emission of energy can look a lot like muon decay. This process – atomic capture of muons and subsequent interaction (via the weak nuclear force) with the nucleus – shortens the time between pulses of energy in the detector from 2.196 microseconds to 2.043 microseconds, the typical timescale of this interaction with a Carbon nucleus.
The “Bohr Radius” of the muon orbit around the nucleus is a measure of how close it gets to the nucleus. For a typical atom in organic material, this is just 10 times the radius of the nucleus.
Since approximately half the muons reaching Fondren Science Building are positively charged, and half negatively charged , the observed decay time of the muon will be skewed low by the following degree: 0.5*2196ns + 0.5*2043ns = 2120 nanoseconds.
In the fit of a decay model to the data above, it’s impossible to discern between the two kinds of muon; therefore, we expect the observed lifetime of the muon to be observed to be shorter than the 2196 nanoseconds of the purely stopped, uncaptured muon.
The Data Analysis
The data for the lifetime determination are “unbinned,” meaning we begin with each and every detector event with a time between triggers less than 20 microseconds. In addition, we remove data with a trigger time lower than 1 microsecond, as the electronics has a known problem with short-duration triggers. A model of the data is constructed using the ZFit python library; the data are modeled using an exponentially decaying component (the muon decay) and a flat rate of random coincidences (e.g. two muons pass through the detector within 20 microseconds). The model’s parameters – the lifetime of the muon and the fraction of the data represented by the real muon decays – are determined by using the MINUIT algorithm to maximize the probability that the model, plus its parameter values, describe the observed data (minimize the negative-log-likelihood). The model is then displayed overlaid on the data, binned into specific time windows. Goodness-of-fit measures (p-value and chi-square) are reported, and the model is found to describe the data very well.
 O.C. Allkofer, W.D. Dau. “The muon charge ratio at sea level in the low momentum region.” Physics Letters B, Volume 38, Issue 6, 1972, Pages 439-440, ISSN 0370-2693, https://doi.org/10.1016/0370-2693(72)90177-3.