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Relative Flux of Positive and Negative Cosmic Ray Muons at the Surface of 

the Earth 

 Alan J. Gelman 

Glenbrook South High School    

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Table of Contents 

Abstract­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­1 

Safety Sheet­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­2 

Title Page­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­3 

Table of Contents­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­4 

Acknowledgements­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­5 

Purpose and Hypothesis­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­5 

Background Research­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­6 

Materials and Methods­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­7 

Results and Discussion­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­8 

Data­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­8 

Data Analysis and Discussion­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­10 

Error Analysis­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­11 

Conclusion­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­11 

References­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­13 

 

 

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Acknowledgements 

First and foremost, I would like to thank Ms. Mary Ann Ericksen, for supervising and                             

sponsoring this experiment, and for providing valuable help. I would also like to thank Mr.                             

Jeffrey Rylander for providing me with all the necessary equipment to make this experiment                           

possible, and the Glenbrook South Science Department for providing me a room in which to                             

perform this experiment. In addition, I would also like to thank my fellow members of the                               

Glenbrook South Particle Physics Research Group, Ann Isaacs, Keyur Patel, Dennis                     

Cherepanov, Matthew Moran, Nicholas Ermolov, and George Gikas for their input and                       

assistance with the experimental procedure. 

 

 

Purpose and Hypothesis 

The purpose of this experiment is to find whether or not positive muons or negative                             

muons are more abundant at the surface of the Earth, and to determine by how much they are                                   

more abundant. I hypothesized that positive muons will be the most abundant as other                           

experiments have shown that positive muons are more abundant in the Earth’s upper atmosphere,                           

and I expect these results to be consistent at the Earth’s surface. 

 

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Background Research 

Cosmic rays are beams of subatomic particles such as protons and neutrons that move                           

through the interstellar matrix. When a cosmic ray enters the Earth’s atmosphere, it collides with                             

molecules that exist in the upper atmosphere, and a shower of secondary subatomic particles is                             

created (Rylander 1996). One of these secondary particles is called a “muon.” While the majority                             

of the other subatomic particles, such as neutrinos, pass through the Earth’s surface undetectably,                           

muons are actually able to reach the Earth’s surface, and are detectable with the use of muon                                 

detectors. However, they might also further decay into an electron, a neutrino, and a muon                             

neutrino, none of which are detectable with a muon detector (Dorigo 2010). Because of the fact                               

that muons are charged particles, they are affected by the Earth’s magnetic field in the sense that                                 

their trajectories toward the Earth’s surface are bent by a certain amount. Positive muons tend to                               

be deflected from the east toward the west, and negative muons tend to be deflected from the                                 

west to the east. 

Studies have shown that in the Earth’s upper atmosphere, positive and negative muon                         

flux can vary, and such studies have also measured that at any point in the Earth’s upper                                 

atmosphere, positive muon flux is larger than negative muon flux (Relative Abundances of                         

Positive and Negative Muons in the Atmosphere n.d.). 

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Materials and Methods 

This experiment was performed in three stages. In the first stage, the control stage, a pair                               

of muon detectors were placed in stacked orientation facing directly upward. This was performed                           

as a control, and ideally, equal amounts of positive and negative muons would be detected. After                               

the detectors were placed in this configuration, flux data were recorded for a four day period,                               

from Tuesday to Friday, and saved onto a computer. For the first period of data collection, the                                 

detectors were angled eastward at 120 ± 1.50 (Fig. 1), with a meter of space in between them to                                     

ensure that data was collected accurately and with as few stray muons as possible. Flux data                               

were then recorded for another four day period. During the second period, the detectors were                             

angled westward at 120 ± 1.50 (Fig. 2) with the same meter of space between them, and flux data                                     

were recorded for yet another four day period. When all the data was collected and stored on the                                   

computer, flux graphs were made for each period based on the data. 

 

  

 

   

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Results and Discussion 

Data     

 

     Fig. 3 

 

        Fig. 4 

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        Fig. 5 

 

Period 1 (East) 

Day  Tuesday  Wednesday  Thursday  Friday 

Events  233  1,796  1,534  1,576  

Period 2 (West) 

Day  Tuesday  Wednesday  Thursday  Friday 

Events  12  100  146  93  

 

 

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Data Analysis and Discussion 

The results from the three periods of data collection are shown in figures 3, 4, and 5                                 

above, as well as the two tables above, labeled for the period of data collection that they                                 

represent. Figure 3 shows the results from the control trial, and figures 4 and 5 show the results                                   

from periods one and two of data collection, respectively. There is a significantly greater amount                             

of muon flux shown for period one of the study (fig. 4) than for period two (fig. 5). This shows                                       

that a significantly greater amount of positive muons exist at the surface of the Earth than                               

negative muons. The results of this experiment, that positive muons are much more abundant                           

than negative muons at the surface of the Earth, are consistent with the upper atmospheric muon                               

experiment (Relative Abundances of Positive and Negative Muons in the Atmosphere n.d.),                       

which concludes that at any point in Earth’s upper atmosphere, positive muons are more                           

abundant than negative muons. 

 

 

 

 

 

 

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Error Analysis 

The presence of some outliers for the second period of data collection (fig. 5) may be the                                 

result of noise, unwanted particles, being detected by the muon detectors. In addition, all the data                               

was captured in three single­trial, four day runs. Had a few more trials been performed and had                                 

each trial taken more days, then the final results would have probably been much more precise,                               

and with comparatively fewer outliers. 

Conclusion 

The data recorded in this experiment shows that at the surface of the Earth, positive                             

muons are significantly more abundant than negative muons, which proves my hypothesis due to                           

the overwhelmingly higher amount of flux of positive muons as opposed to negative muons. The                             

data in figures 4 and 5, as well as that in the tables for the two periods of data collection                                       

demonstrate this difference in showing that there is over than ten times as many positive muons                               

at the surface of the Earth than negative muons. One explanation for this phenomenon could be                               

that the cosmic rays from which these muons originate could be a subatomic particle which                             

decays into specifically positive muons, and that that subatomic particle is much more abundant                           

in the universe than its symmetric equivalent which decays into negative muons. Another                         

explanation could be that most negative muons might, for whatever reason, decay into electrons                           

and neutrinos more readily higher in the atmosphere than positive muons. These inferences may                           

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be explored in further experiments. Finally, the results that were obtained in this experiment are                             

validated by the fact that they coincide with the results collected by the upper atmospheric muon                               

flux experiment (Relative Abundances of Positive and Negative Muons in the Atmosphere n.d.),                         

which stated that positive muons are more abundant in any part of the upper atmosphere than                               

negative muons. 

 

 

   

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References 

 Relative Abundances of Positive and Negative Muons in the Atmosphere. (n.d.). Retrieved 

November 21, 2015. 

 Muon basics. (n.d.). Retrieved December 28, 2015, from 

http://www2.fisica.unlp.edu.ar/~veiga/experiments.html 

 Understanding Muon Decay. (2010, March 4). Retrieved December 28, 2015, from 

http://www.science20.com/quantum_diaries_survivor/understanding_muon_decay 

 Rylander, J. W. (1996). Muon mean lifetime measurement in a high school classroom 

(Unpublished master's thesis). 

   

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