Results

Both the zenithal and azimuthal distributions were significantly different from what would be expected from the theoretical arguments. The likely primary factor in this discrepancy is shielding from the building (Tate Labs), in the basement of which the apparatus was located.

Zenithal Distribution

The zenithal distribution was measured by pointing the apparatus so it would receive muons from the west, then varying the horizontal distances d of the lower detectors (see Apparatus) to collect flux rates for several angles at once.

The measured distribution had a different shape than was expected, as indicated below. In the figure, the results were fit to expected distributions generated by the Monte Carlo simulation for various powers of k in the distribution; the curves do not actually correspond to

curves.

(Summary of the measured zenithal muon-flux distribution)

For smaller angles (theta<30), the best fit was to with a chi squared = 8.5 for the 7 upper data points (p=0.20). For the rest of the distribution, however, the best-fit distribution was with , albeit with a chi squared = 94 for 5 data points. Overall, these results do not agree well with a

distribution with a constant ; they could be explained with an exponent that varies with zenith angle. Most likely, this effect is due to the variable amount of shielding in different directions provided by Tate Labs, which were directly overhead (see below).

Azimuthal Distribution

The distribution was measured in azimuthal slices as well by keeping the lower detectors the same distances from the top detector and rotating the entire apparatus in 45° increments. Three different slices were taken, one for each lower detector.

The azimuthal-slice results were equally surprising. As shown below, the effect observed was exactly the opposite of what was expected: There was a consistently higher muon flux from the east than from the west, a result again most likely attributable to shielding from the building.

(Summary of the measured azimuthal muon-flux distribution)

Shielding Hypothesis

It is plausible that the concrete in the surrounding building modified the shape of the observed distribution. Although muons normally pass through solid rock and other materials easily, they do lose a certain amount of energy, and the lowest-energy ones eventually lose all their energy and "range out." Cosmic-ray muons already lose 2 !GeV to the atmosphere; those remaining have an average energy of 4 !GeV. According to information in (Particle Data Group 2012), the range of 1 !GeV muons in concrete is 65.5 cm, which is easily the amount of concrete that muons might experience going through the bulk of the building to reach our apparatus. Thus, it is expected that the building significantly affects the lower-energy portion of the measured spectrum, possibly having large effects on the

The aerial photo below depicts the shape of Tate Labs and how it might affect the measured zenithal distribution, with the apparatus's approximate location circled in red. As the image shows, there is much more building mass to the west of the apparatus than to the east, which would explain the inverted east-west effect. The image can be compared with the measured azimuthal distribution. Most of the peaks and dips make sense, except for the one of the inner detector in the northwest direction; this could indicate some high-mass or well-shielding experimental equipment above the detector in this direction.

(Aerial view of Tate Labs, possibly explaining the observed shielding profile; image courtesy of Google Earth)

The zenithal distribution could also be affected by shielding, although the way in which it is affected is more subtle since only the lower-energy muons are being cut off. However, the anisotropic nature of the zenithal shielding profile does explain why the exponent <latex>k</latex> is seen to vary with zenithal angle.

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