Muon Speed measurement

Ezra Hart, Weston Norris,/br> University of Minnesota - School of Physics and Astronomy

Minneapolis, MN 55455

Abstract:

The velocities of high energy atmospheric muons from particle cascades caused by cosmic ray collisions were measured by the use of multiple scintillator panels, and timing differences were determined between events in each plate. The results were (3.077±0.186)x10^8 m/s, which is ≈0.5σ away from the expected value of approximately 99.4% of light speed.[1]

Introduction

Earth’s upper atmosphere is constantly bombarded with high energy particles (cosmic rays) which create showers of new particles. Charged particles known as muons are created by these collision events, and travel at speeds around 99.4% of light.[1] This experiment used scintillating panels with photomultiplier tubes to detect the muons’ passing, and used the PMTs’ signal outputs from the panels to calculate their velocity.

Theory

Muons have a relatively high mass of 106 MeV and a long lifetime of ~2.2µs, which combined with time dilation effects due to their relativistic speeds, allow them to reach ground level – unlike other charged particles created in an atmospheric shower.[2] Anti-muons are also able to do this, but are identical to muons other than charge sign. As such, the inability to distinguish between them did not adversely affect results. Panels made of scintillating plastic, which emits a photon when charged particles move through it, were used to detect passing muons. Photomultiplier tubes were employed to amplify the photon signal from the panels into an electrical signal.

Cosmic rays collide with the atmosphere with a uniform angle distribution, but the flux of the muons created which reach the Earth’s surface decrease proportionally to cos2(theta), where theta is measured from azimuth.[3] Therefore, to increase muon count and decrease flight-path length uncertainty, the experiment sought to detect muons which traveled close to vertically. Flight times for a large number of muons were measured over multiple distances, so that a histogram resembling a Gaussian probability distriubution was obtained. After correcting for timing delays, these distances were plotted vs. the calculated time of flight to find an average velocity for atmospheric muons. Expected results were 0.994c.

Experimental Set-Up:

In order to ignore any muons that were traveling through the panels but not through the corridor, it was made that in order for a data point to count, there had to be signals from panels 1, 2, 4, and 5 all within a 25ns time window – a situation only likely to occur if a muon really did travel through all four panels in the corridor. Background rate measurements put the number of muon counts through an 18cm by 18cm square at ~4000 counts per day. It would be possible for two different muons to trigger our apparatus and have it look like one, giving an out of line data point. But at the ~4000 counts per 18cm squared per day rate, and the 100ns scale at which things happened in the machine, there was approximately a 1 in 100,000,000 chance that any particular data point would be caused by two muons arriving together – essentially an ignorable phenomenon.

Results

The equipment was set up to collect muon data for 1 to 2 days at each of the seven height positions for panel three. At each of these height settings, a histogram of the time measurements was recorded and logged by a multichannel analyzer and computer. Some of the histograms possessed minor secondary spikes, or single data points too far from the histogram center to be considered reasonable to include. By changing the Discriminator's thresholds, we were able to get rid of some of these. The units on the histograms were counts on the y-axis, and bins on the x-axis. To convert the bins to nanoseconds, a calibration curve was made by giving the multichannel analyzer known time differences with a delay machine.

After final thresholds and signal widths were determined, each rung of the ladder had the central panel set to its height for 2-3 days. This was enough time to obtain enough data that the set from each rung could be reasonably fitted to a Gaussian curve. The peaks and the error on their positions were found and plotted against each other to obtain a linear graph whose slope was the velocity. Unknown offsets that were equal for all points made values of time negative, but that didn't affect the slope.

Conclusion

The final result’s error is about 7% of the calculated velocity. The calculated velocity, though at first glance suggests a super-luminal speed for atmospheric muons, could well have been within more realistic limits with only a slight shift in the slope, even as a factor of less than 0.5σ. To get a better result, it would need to have been established sooner in the experiment what settings on the electronics to use to collect reasonable data, so that the central panel could have been left at each rung height for longer periods of time.

Acknowledgements

Kurt Wick for motivation and prodding

Greg Pawloski for guidance

Clem Pryke for some coding advice in MatLab

References

[1] Film, Time Dilation{An Experiment with ¹-Mesons}

D. H. Frisch and J. H. Smith, Education Development Center, Newton, Mass., 1963(As referenced in) Speed and Decay of Cosmic Ray Muons

Nichols A. Romero and Mukund T. Vengalattore MIT, Cambridge, Massachusetts 02139

[2] The Compact Cosmic Ray Telescope aboard the Kuiper Airborne Observatory.

Steve Kliewer, Endeavour Academy, Paso Robles, CA 93447. In collaboration with Stanford Linear Accelerator Center and NASA Ames Research Center

[3] Cosmic Rays

Revised October 2013 by J.J. Beatty, et. al.

http://pdg.lbl.gov/2013/reviews/rpp2013-rev-cosmic-rays.pdf

Others not specifically referenced in the above text:

Muon Basics.National University of LaPlata, Argentina: http://www2.fisica.unlp.edu.ar/~veiga/experiments.html

Flux Variation of Cosmic Muons

N. Ramesh, M. Hawron, C. Martin, A. Bachri

Southern Arkansas University, Magnolia, AR 71754