Muon, Pion and Kaon Lifetime Measurements
L. Villaseñor
Instituto de Física y Matemáticas, University of Michoacan, Morelia Mich., 58040, México
Abstract. We describe a simple experimental setup that can be used to measure the lifetimes of
muons, pions and kaons from the secondary cosmic-ray radiation. It uses a sealed container
filled with 35 l of liquid scintillator and simple data acquisition hardware. The detector uses a 2"
photomultiplier (PMT) that collects the scintillation light produced by charged particles crossing
the detector volume. The electronics used consists of 4 NIM modules, a digital oscilloscope and
a PC. This equipment is multipurpose and can be conventionally found in any modern physics
laboratory. The results obtained by fitting data to the muon, pion and kaon lifetimes are the
following:  =2.208  0.027 s, =24.6  3 ns and= 12.5  2 ns. The measured plus-tominus charge ratio of cosmic ray muons for a latitude of 20 o North is 1.28  0.06. These values
are in good agreement with the literature.
INTRODUCTION
The measurement of the muon, pion and kaon lifetimes is one of the simplest
experiments that can be used to illustrate the basic elements of modern high energy
physics experiments. Primary cosmic rays are composed of protons (85%), alpha
particles (12%), electrons (2%) and heavier nuclei (1%). The primary cosmic rays that
reach the earth atmosphere collide with nuclei of nitrogen and oxygen of the
stratosphere to produce numerous secondary particles collectively called extensive air
showers. The four components of extensive air showers are [1]: 1) The hadronic
component including hadrons such as protons, neutrons, pions and kaons; this
component is very attenuated at sea level. 2) The electromagnetic component
originating either from primary cosmic rays or from the decay photons of neutral pions;
it is composed of electrons, positrons and photons and it reaches its maximum at
around 13 km a.s.l. 3) The muon component is composed of the decay muons of pions
and kaons; at sea level 80% of all charged particles are muons and 20% are electrons.
The muon lifetime at rest is 2.19 s; the fact that muons produced at heights of tens of
kilometers reach the ground before decaying is a consequence of the relativistic time
dilation. 4) The neutrino component is made up of neutrinos coming from decays of
pions, kaons and muons; this is the non-interacting component of extensive air
showers.
The muons used for this experiment are cosmic ray muons which come from the
decay in flight of secondary pions and kaons, the latter result from collisions of primary
cosmic rays with nuclei high in the earth atmosphere. At sea level the muon flux is
about 180 m2/s and it corresponds to approximately 75% of the flux of charged cosmic
rays.
FIGURE 1. Liquid scintillation detector.
FIGURE 2. Electronics and data acquisition system.
The muon flux has a mean energy of 2 GeV and a differential spectrum falling as
E up to a few TeV [2]. The pion flux at sea level is around 1000 times smaller than
the muon flux, however, pions and kaons can also be produced by the interaction of
secondary hadrons with the concrete ceiling of the laboratory, this production
mechanism can eventually dominate the flux of pions and kaons reaching the detector.
This experiment demonstrates the use of the following techniques: scintillation
detectors; discrimination, generation of pulses with variable width, logic pulse
coincidence and timing by means of NIM electronics; on-line data acquisition with a
digital oscilloscope connected to the GPIB port of a PC and off-line data analysis.
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EXPERIMENTAL SETUP
The detector, see Figure 1, consists of a cylindrical aluminum container of 26 cm
of diameter and 36 cm of height filled with 35 l of liquid scintillator which is a mineral
oil made up of carbon and hydrogen, for example Bicron BC-517H. The sealed
container has a 2" photomultiplier tube (PMT) looking downwards from the top of the
liquid. The PMT is inside the container, care was exercised to avoid any light leaks to
the interior of the detector. The inner surface of the detector which is in contact with
the liquid is the same aluminum surface of the container. Figure 2 shows the
electronics and data acquisition system used to operate the detector; the NIM modules
and the digital oscilloscope can be connected according to the specific type of cosmic
ray properties to be measured.
The operating point of the PMT is around -1700 V. A 50  resistor must terminate
the PMT output to match the impedance of the RG58 coaxial cable used. Standard
NIM modules are used to discriminate the PMT signals with a fixed threshold of -30
mV and to generate a time window within which a coincidence with a second pulse is
performed on a coincidence NIM module. The time window is set to 25 s for the
measurement of the muon lifetime and 300 ns for the case of the pion and kaon
lifetime measurements. A PC running under LabView is used as the basis of the data
acquisition system. The traces from the two-channel oscilloscope (Tektronix, model
TDS220) are read out into the PC through a GPIB port and are analyzed on-line on the
PC to obtain the time interval between the data acquisition system is set to trigger on
double pulses.
The use of the digital oscilloscope is essential in this setup although it may be
optional in other setups which use dedicated time-to-digital convertors such as the one
described in [3] where a simple clock-counter digital system is interfaced to a PC
through its parallel port. The advantage of using a digital oscilloscope is that the
charge of the first and second PMT pulses can be measured on-line or off-line to infer
the amount of scintillation light produced by the two particles, i.e. the stopping muon
and the decay electron for the case of two pulses being caused by a muon decay.
EXPERIMENTAL PROCEDURE
Step 1. First of all it is necessary to determine the 'voltage plateau'. This is the
operating point for the PMT high voltage. The use of a voltage lower than optimal
causes detector inefficiency; on the other hand, if the voltage is too high, there will be
an excess of background noise due to electronic noise in the PMT.
FIGURE 3. Raw data for the muon lifetime measurement. The solid curve is a fit to the data using the
function P1 + P2 exp(-t/P3). The measured background noise is 156.8 events/0.025 s and  = 2.109
 0.003 s.  is smaller than 2.19 ms because negative muons may suffer inverse beta decay in
addition to normal beta decay .
It is important that small changes in the high voltage do not lead to great changes
in the pulse rate; for this reason it is convenient to select an stable operating point at
the voltage plateau. The operating point can be found by selecting a fixed threshold on
the NIM discriminator of -30 mV and by taking measurements of the pulse rate as a
function of the PMT high voltage. Do not exceed -1800 V as the PMT may be
damaged. You may use steps of 20 V and use the NIM scaler to measure the single
pulse rate using appropriate time intervals leading to an statistical errors in the pulse
rate lower than 5 % [4]. Once the operating point is set, make a rough estimate of the
muon flux: divide the pulse rate by the effective area of the detector. You should get of
the order of 400 m-2s-1.
FIGURE 4. Comparison of the muon experimental data with two exponentials of different decay time.
Both exponentials have the same amplitude and the same asymtotic value equal to the background noise
of 156.8 events/0.025 s.
Step 2. Connect the electronics in the following way: the PMT signal goes through
CH1 of the digital oscilloscope to channel 1 of the NIM discriminator module with a
threshold of -30 mV. One of the NIM outputs of this module goes to the input of CH1
of the gate generator module with a time window set to 25 s for muon decay and 300
ns for pion and kaon decays. The output of the gate generator and a second output of
the discriminator go to the logic coincidence NIM module used in double coincidence
mode. The output of the coincidence NIM unit goes to the external trigger input of the
oscilloscope.
FIGURE 5. Raw muon data with a fit superimposed. The solid curve is a fit to the data using the
function P1[(exp(-t/P2) + P3exp(-t/P4)] + 156.8. The 1 340 845 events shown correspond to a data
taking time period of 2 572 h with a 35 l detector. The muon lifetime from this fit is 
=2.208  0.027 s and the measured plus to minus charge ratio of cosmic rays muons is 1.28  0.06.
Step 3. Use the LabView program provided (ICFA.vi) which reads out the
waveform of the digital oscilloscope into the PC and does the necessary on-line
analysis to measure the time interval between the two pulses and the charges and
heights of these pulses. This program writes a file on the PC hard disk with a line for
each event. These data can be analyzed off-line to extract the measurements for the
muon, pion and kaon lifetimes.
In addition, you can also write on-line analysis subroutines to integrate the areas under
each of the two pulses. You can also use the peak positions in these charge
distributions to calibrate the detector and to monitor the PMT gain [5,6].
Time Interval Between Double Pulses (ns)
Time Interval Between Double Pulses (ns)
FIGURE 6. Raw data for pion and kaon lifetime measurements. The solid curve is a fit to the data
using the function P1 + P2 exp(-t/P3). The upper fit from 107 to 278 ns gives  =24.6  3 ns and
the lower one from 50-75 ns gives  = 12.5  2 ns, in good agreement with the literature.
Step 4. After you collect a reasonably large number of events (at least one full day
of data taking), you can start analyzing the data [7]. Write a subroutine to fit an
exponential plus a constant to the raw data. The decay time of the exponential gives
you directly the lifetime and the constant gives you the background noise. In the case
of the muon lifetime measurement with a time window of 25 s, the background noise
consists of random coincidences of PMT pulses dominated by two muons crossing the
detector within the 25 s time window. In the case of the pion and kaon lifetime
measurement with a time window of 300 ns the noise is dominated by muon decays.
The rate of noise due to random coincidences of double pulses (number of noise
events per bin) can be calculated by the formula f2T, where f is the single pulse rate
and T is the integrated time of data collection. Explain this formula. The PAW
(Physics Analysis Workstation) [8] macros used to obtain Figures 3 and 4 can be
found in [3].
The muon lifetime obtained this way is smaller than 2.19 s because negative
muons that stop inside the liquid scintillator fall into K orbitals around the carbon and
hydrogen nuclei and can be absorbed through inverse beta decay, namely, a proton and
a negative muon interact through the weak force to produce a neutron and a neutrino.
Positive muons, on the other hand, are not absorbed by neutrons because they never
cross the nuclei due to their electrostatic repulsive force. As a first correction, you can
assume that the ratio of negative to positive muons reaching the detector is equal to 1.0
and use the known lifetime of the muons in vacuum (2.19 s) to estimate the rate of
capture of negative muons by carbon nuclei in the detector. The size of this effect is
depicted in Figure 4, where two exponentials are compared to experimental data, one
corresponding to negative muons (the one with smaller decay time) and the other to
positive ones. Note that the statistical error bars on the data points are smaller than the
gap between the two curves; this is a necessary condition to obtain a direct
measurement of the negative-muon capture effect.
Step 5. After several days of data taking for the muon case you can put together all
the muon data sets and attempt to measure directly the charge ratio of cosmic ray
muons and the capture probability per unit time of negative muons by carbon nuclei
[9]. A simple PAW macro used to obtain the results shown in Figure 5 is in [3].
Step 6. The fit to the pion and kaon data sets is done in a similar way: a fit to an
exponential plus a constant in the range of 50-75 ns to obtain the lifetime of kaons and
a fit in the range of 107-278 ns to obtain the lifetime of pions, see Figure 6. These
ranges are selected to minimize 2/dof.
Step 7. Write and hand in a detailed report of all the work you did related to this
laboratory course.
CONCLUSION
The detector described was used to detect double-pulse events by means of a
double-pulse trigger. The two pulses are required to be within a time window of 300
ns for the case of the decays of pions and kaons, and 25 s for the case of muons. The
ratio of positive to negative muons can also be measured provided the statistics is
sufficiently high [10]. The distributions of the time intervals between the two pulses
are in good agreement with the lifetimes of muons, pions and kaons. The results
obtained for the muon, pion and kaon lifetimes are the following:  =2.208  0.027
s,  =24.6  3 ns y  = 12.5  2 ns, in good agreement with the literature [2]. The
measured plus to minus charge ratio of cosmic rays muons at a latitude of 20o North is
1.28  0.06, also in good agreement with the literature.
ACKNOWLEDGMENTS
This work was partially supported by CIC-UMSNH and CONACyT (G32739-E and
G38706-E). I thank E.H. Payaye for providing assistance during the lab sessions.
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