Determining the Lifetime of a Z Boson
08/12/2016
Abstract
Using data obtained from the CMS e-lab exploration, we attempted to determine the lifetime of a Z Boson. In order to need to use the Heisenberg Uncertainty Principle. We determined the time to be 1.84 x 10-25s.
Introduction
The Heisenberg Uncertainty Principle can be used to characterize short-lived particles produced in high energy collisions in accelarators (Nave). The Z boson is a neutral elementary particle, a partner to the charged W boson, and carries the Weak Force (CERN).
Procedures
To determine the lifetime (
) of the Z boson, Z --> 
data from the Large Hadron Collider was analyzed to find the width of the Z boson distribution. First, we ran a mass plot and explored different bandwidths to find a nice Breit-Wigner line shape as seen in Figure 1. A previous study used a bin width of 0.45, but we determined that a bin width of 0.6 gave us the best fit (Figure 2).
Next, the maximum number of events was determined to be 193, making half-maximum = 96.5. The maximum mass was determined to be 92.83 GeV and the minimum mass was 89.26. This results in a value of 3.57 GeV for 
.
The Uncertainty equation, 
E = 
/2 = h-hat/2
was solved for 
(lifetime). We used the given value for h-hat; 6.582 x 10-22 MeV.
Results
We determined the lifetime of the Z boson to be 1.84 x 10-25s. The accepted value is 3 x 10-25s, giving us 39% error. We also found the accepted value for 
to be 2.4952 GeV/c2 (Lawrence-Berkley).
Figures
Discussion and Conclusions
Our value was on the same order of magnitude as the accepted value. Our data looked at 2304 events, compared to millions of events that Lawrence-Berkley looked at. Future studies should include much more data. We would also like to look at dielectron, ditau, and hadron events.
Bibliography
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Nave, R. "The Uncertainty Principle." Particle Lifetimes from the Uncertainty Principle . HyperPhysics, n.d. Web. 12 Aug. 2016.
"CERN Accelerating Science." The Z Boson. CERN, n.d. Web. 12 Aug. 2016.
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