Paper

The Relationship between Resonance Width and Particle Lifetimes

Alex Olds

06/08/2016

Abstract

Introduction

This study was performed to explain how the resonance width of a given particle relates to said particle’s lifetime, if at all. Knowing this relation would allow to find one or the other by simply knowing either the resonance width or the lifetime. Although this relation is known, this study applied it to the z-boson to find how easy and accurate the relationship is from experimental data and comparing it to known values. This appears to reinforce currently accepted science, without creating any conflicts or gaps in knowledge.

 

The purpose of this study is to increase the knowledge of the interlacing characteristics of subatomic particles. Knowledge also may be gained on how these characteristics relate.

Procedures

Data was collected from publicly avaiable sources from the ATLAS detector at CERN, on Z -> μ μ events. This data was then plotted as invariant mass vs the Breit-Wigner probability density to form a curve (fig. 1). This curve was then labelled with  Γ  at  half-maximum. From this, the value of  Γ  can be found. Next, the Uncertainty Principle is taken in the form  ΔE = (Γ/2) =( ? /(2τ)) and Γ is substituted with it's value. This gives us a new equation of 1.25 = ( ? /(2τ)).

 

Results

For this data,  Γ= 2.5. We now substitute Γ for 2.5 in ΔE = (Γ/2) =( ħ /(2τ)). This gives us a new equation of 1.25 = ( ħ /(2τ)) and solve for  τ. In this case,  τ = 2.32847804x10-25 . For reference, the lifetime of the Z-Boson is believed to be roughly 3x10-25 by the particle physics community. 

Figures

Discussion and Conclusions

The Resulting lifetime estimation of 2.32847804x10-25 is remarkably accurate, not only is it on the same order of magnitude as the accepted 3x10-25 lifetime, it is far closer than expected, given that the original Γ measurement was an estimation. This result contributes further support for this method, as it does appear that there is, in fact, a definite relationship between the resonance width and the lifetime, as well as showing that this method is a reasonable estimation of that relationship.

Bibliography

 Ocariz, J. (2012, October 14). Probability and Statistics for Particle Physicists. KEK-Proceedings, 2013(8), 253-280. doi:10.5170/CERN-2014-001.253