Mean Lifetimes & Branching Raitos

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In summary, the F particle has a mean lifetime of 1.66*10^-2 seconds and the branching ratios for its three decay modes are 0.7999, 7.999*10^-5, and 0.19998.
  • #1
genloz
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Homework Statement


1. In a theory a charged particle called F- (charge=-1) exists. This particle has three decay modes that will be observed at the LHC. The mean time between F- particle creation and each kind of decay is found to be:
Mode Mean lifetime
Mode 1 5 microsec
Mode 2 50 millisecond
Mode 3 20 microsec
What is the mean lifetime of the F particle, and what are the branching ratios for each of the three modes?

Homework Equations


None given, but my thoughts were that these were relevant:
[tex]\Gamma_{overall} = \frac{1}{\tau}[/tex]
[tex]Branching Ratio= \frac{\Gamma_{partial}}{\Gamma_{overall}}[/tex]

The Attempt at a Solution


Mean Lifetime:
[tex]\tau = ((5*10^{-6})+(50*10^{-3})+(20*10^{-6}))/3[/tex]
[tex]\tau = 1.66*10^{-2}[/tex]

[tex]\Gamma_{overall} = \frac{1}{\tau}[/tex]
[tex]\Gamma_{overall} = 60.24[/tex]

Branching Ratio for Mode 1:
[tex]\Gamma_{partial} = \frac{1}{\tau}[/tex]
[tex]\Gamma_{partial} = \frac{1}{(5*10^{-6})}[/tex]
[tex]\Gamma_{partial} = 200000[/tex]
[tex]Branching Ratio= \frac{\Gamma_{partial}}{\Gamma_{overall}}[/tex]
[tex]Branching Ratio= \frac{200000}{60.24} = 3320[/tex]

But then that didn't look much like a ratio so I started to wonder if I'd made a mistake or units were incorrect or something?
 
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  • #2
Okay, I had a bit of a think and came to this conclusion...
[tex]\Gamma_{overall}=\frac{1}{\tau_{1}}+\frac{1}{\tau_{2}}+\frac{1}{\tau_{3}}[/tex]

Therefore,

Mode 1
[tex]\Gamma_{partial1}=\frac{1}{5*10^{-6}}[/tex]
[tex]\Gamma_{partial1}=200000[/tex]

Mode 2
[tex]\Gamma_{partial2}=\frac{1}{50*10^{-3}}[/tex]
[tex]\Gamma_{partial2}=20[/tex]

Mode 3
[tex]\Gamma_{partial3}=\frac{1}{20*10^{-6}}[/tex]
[tex]\Gamma_{partial3}=50000[/tex]


So,
[tex]\Gamma_{overall}=250020[/tex]

So the branching ratios are:
Mode 1
[tex]\frac{\Gamma_{partial1}}{\Gamma_{overall}}=\frac{200000}{250020}[/tex]
[tex]=0.7999[/tex]

Mode 2
[tex]\frac{\Gamma_{partial2}}{\Gamma_{overall}}=\frac{20}{250020}[/tex]
[tex]=7.999*10^{-5}[/tex]

Mode 3
[tex]\frac{\Gamma_{partial3}}{\Gamma_{overall}}=\frac{50000}{250020}[/tex]
[tex]=0.19998[/tex]

Does that sound about right?
 
  • #3
I guess the width should be hbar/meanlife but I don't think that matters in this instance...
 

What is the concept of mean lifetime in scientific research?

The mean lifetime is a statistical measure that represents the average time it takes for a group of particles or systems to decay or undergo a certain process. It is calculated by taking the sum of the time intervals for each individual decay or process and dividing it by the total number of events.

How is mean lifetime related to the concept of half-life?

The half-life is the time it takes for half of the particles or systems in a given sample to decay or undergo a certain process. It is related to the mean lifetime through the formula: mean lifetime = (ln2)/half-life.

What are branching ratios in particle physics?

Branching ratios, also known as branching fractions, are the ratios of the number of particles that undergo a specific decay or process to the total number of particles in a given sample. They are used to describe the probability of a specific decay or process occurring.

How are branching ratios determined experimentally?

In particle physics experiments, branching ratios are determined by counting the number of particles produced from a specific decay or process and comparing it to the total number of particles produced in the experiment. This allows researchers to calculate the branching ratio as a percentage or fraction.

Why are mean lifetimes and branching ratios important in scientific research?

Mean lifetimes and branching ratios provide valuable information about the fundamental properties of particles and systems. They can be used to test theories and models, and help scientists understand the underlying processes and interactions in the natural world.

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