Paper

Relationship of half-life and decay widths

Kevin Warren and Kate Baugher

07/13/2017

Abstract

It was proposed that there is a relationship between the rate of decay and the profile width of a collision event.  When considering the Heisenberg Uncertainty Principle, the width of the graphic profile (decay width) for J/psi, upsilon, and Z boson particles were measured.  These measurements were compared to the half-life of each of the same particles. It was concluded that the J/psi and upsilon particles, which have a slower half-life had a narrower decay width.  The Z boson particle, which has a faster half-life, had a wider decay width.  

Introduction

The Heisenberg Uncertainty Principle suggests that particles with a longer half-life, will have a smaller uncertainty variance. To determine if such a relationship exists, the decay width on graphs will be measured for J/psi, upsilon, and Z boson particles.  The decay widths will be compared with the known half-life of these particles.  Relationships will be determined.

Procedures

Event/mass graphs of J/psi, upsilon, and Z boson particles were studied and marked for decay width.  The half-life of these same particles were ascertained through internet searches.  The data were charted and compared, to determine if a relationship exists between decay rate and decay width for these particles.

Results

The half-life and decay width of J/psi, upsilon, and Z boson particles were determined and charted (chart 1). The J/psi particle has a half-life of 7.2 x 10-21 and upsilon particle has a half-life of 1.21 x 10-20. The half-life of J/Psi and Upsilon are approximatetly 10,000 times slower than the half-life of the Z boson which has a half-life of 3 x 10-25 s. The J/psi particle has a decay width of 0.2 and the upsilon particle has a decay width of 0.3 which are smaller decay widths than the Z boson, with a decay width of 7.0. 

Figures

Discussion and Conclusions

The decay width and the half-life of J/psi, upsilon, and Z boson particles were compared. The results of this comparison indicated there was an indirect relationship between half-life and decay width.  The slower the decay rate of a particle and the smaller the decay width, the faster the decay rate of a particle and the larger the decay width.   The conclusion infers that this could be used as a quick and reasonable estimation method to determine a particle's decay rate.  Future study should include the collection of more data to further support the conclusion that there is an indirect relationship between decay rate and decay width and to more precisely define decay width for each particle.  Studies should also research other methods of decay such as dielectron events.

Bibliography

https://i2u2.org/elab/cms/viewplots

https://i.stack.imgur.com/8UcVJ.png

https://www.physicsforums.com/threads/decay-rate-and-lifetime-of-z-boson.673999/

http://www.marsd.org/cms/lib7/NJ01000603/Centricity/Domain/245/QuarkNetJ_psi0713.pdf

https://en.wikipedia.org/wiki/Upsilon_meson