- #1
genloz
- 76
- 1
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?