Abstract

In order to determine whether all muons travel, and thus enter the detctor, vertically, we conducted an experiment in which the angle of the panels was varied, so as to change the horizontal surface area. Based on the changes in average flux, we concluded to some muons are deflected to, or created in, non-vertical paths. 

Introduction

Research Questions:

-How does changing the angle of the detector panels (and thereby changing the horizontal surface area) affect the flux?

-If flux does not change proportionally to horizontal surface area, is the difference substantial enough to indicate that some of the muons are not entering the detector vertically?

Null Hypothesis: If horizontal surface area is decreased through change in the angle of the panels, then the amount of flux will decrease directly proportionally. 

Hypothesis: The data will indicate that some muons do not enter the detectors vertically.

Procedures

Procedure:

-Stack the panels in sets of two and set the detector to two-fold coincidence.

-Collect data using both sets of panels at horizontal orientation. Then repeat the test with one set of panels tilted at 30, 45, 60, and 90 degrees from the horizontal, while the other set remains horizontal as a control test. Run each test to collect 240 data points (by running each test for 4 hours with a bin width of 60 seconds).

-Calculate the horizontal surface area of the panels at the given angles.

-Plot surface area v. flux and run data analysis to approximate a line of best fit.

-Determine whether surface area and flux are directly proportional (as would be expected if all the muons were entering the detector vertically) or not.

-If the two are not proportional, determine if the deviation is statistically significant (using the chi-squared test).

-Based on the deviation, determine approximately how many muons do not enter the panels vertically.

Adjustment of Data:

-Set a baseline for the control test (in this case the average of all the control tests, or 11,900).

-Calculate percent difference between observed control tests and the baseline.

-Adjust test data by same percent difference with the appropriate sign.

Analysis:

-During the test in which both sets of panels were horizontal the flux varied widely between panels 0 and 1, and panels 2 and 3, at values of 14,800 and 9,800 respectively. Since the majority of the control flux values were at about 12,000-13,000, we decided that there might have been some issue with the data. In order to account for this issue while still having a horizontal data point, we changed both our test value and control value to 12,150, the average of the two.

-The observed data was plotted and fit to a linear regression.

-The predicted line was determined by calculating the average horizontal surface area during the tests and the average flux to create a linear relationship with the expected slope.

-The data conclusively shows that there is a linear relationship (through the R^2 value of 0.99) between the flux and the horizontal surface area. However, it also shows that the slope of this relationship is less than expected.

-By comparing the observed flux at 90 degrees and the predicted flux at 90 degrees, the flux that is due to non-vertical muons can be obtained. By further multiplying this flux by the time and area, the amount of muons that enter non0vertically can be calculated. The percentage of non-vertical muons is found by comparing this calculated number of non-vertical events at 90 degrees to the total number of events at 0 degrees.

Results

Sources of systematic error:

-slightly off-set calibration of panels

 -difference in time it takes the muon signal to travel through different panels, photomultiplier tubes,      and wiring to reach the DAQ, which may record less events of coincidence

-two-fold coincidence between panels which were not stacked

-obstacles permanently above location of muon detectors

-flaw in use of averages to derive predicted line

Sources of random error:

-transient obstacles

-weather (temperature, barometric pressure, could cover, humidity, etc.)

-slight movement in panels

-variation in room temperature-error in precision of angle measurement

Discussions & Conclusions

The difference between the predicted change in flux and the observed change in flux appears significant (given that the slope of the observed line is more ~2.5 times smaller than that of the predicted line), and thus invalidates the null hypothesis.

The data indicates that the flux is being affected by another variable.

We cannot fully conclude whether this variable is muons entering the detector at an angle or some other factor such as barometric pressure, temperature, obstacles to the muons, etc.

Given however, that the data was adjusted accordingly to the variation in the control panel during the same time period, we have relative confidence in the accuracy of the results.

As expected if muons were entering the detector at an angle, the result when the panels were tilted at 90 degrees is much higher than expected, while the results at lower angles are less than expected.  Given that the predicted line was derived from the average surface area and the average flux, when the angles are low, if muons enter the panels non-vertically, the values should be lower than those of the predicted line, and vice-versa.

Our results support the idea that some muons are deflected from their vertical path, or are created with a non-vertical velocity component.

Approximately 720,000 muons in four hours enter the detector non-vertically, therefore about 33% of muons are not travelling vertically.

Future Studies:

-Cross reference data with weather (temperature, barometric pressure, cloud cover, humidity, etc.).

-Repeat study but with panels tilted individually and one-fold coincidence.

-Repeat study with all four panels stacked.

-Conduct study in a temperature controlled environment.

-Conduct study outdoors so as to limit obstruction. 

-Conduct multiple trials, switching the panels and the DAQs.

Bibliography