Getting to Higgs
Reviewing Particle Lifetimes
The lifetimes of elementary particles are statistical in nature. In a given sample, one particle might decay
immediately, another in 1 nanosecond, yet another after 10 milliseconds,
and still another in 50 years. What we call the lifetime is the time it
takes for a sample to decay so 1/e (~30%) of the sample is left; after 2
lifetimes, 1/e
2 of the sample is left, and so on.
Take, for example, a sample of cosmic ray muons produced in the upper
atmosphere. These muons, when observed at (relative) rest in the
laboratory, have a mean lifetime T. Now, since particle decay is
statistical in nature, the number of undecayed particles after a given
time is a negative exponential function:
N(t) = No
e-t/T
where N(t) is the number of muons at time t, N
o is the initial
number of muons, t is time, and T is the muon lifetime. We can take
N
o to be the number of muons at some time;
then N(t) can be measured at later times.
This equation allows us to to understand particle decays. If one can measure enough information the equation can tell the rest of the story.