# Homework Help: Lifetimes of kaon and lambda baryon in a bubble chamber

1. Nov 13, 2012

### OGrowli

Lifetimes of kaon and lambda particles in a bubble chamber (updated)

Statement of the problem:

This isn't quite a homework problem. I'm just having trouble with the concepts of this lab. I'm working on a lab report dealing with analysis of bubble chamber photographs of the decay of a kaon and lambda particle. The lifetimes I calculated in the lab frame are much closer to the accepted mean lifetimes than the lifetimes I calculated for the rest frame. This could just be a coincidence, but I suspect that I've mixed up the lab frame and the particle's rest frame.

Attempt at a solution, and Relevent Equations:

A high energy $\pi^{-}$ decays into a neutral kaon and a neutral lambda particle, those in turn decay as:
$$\Lambda ^{0} \rightarrow p + \pi^{-}$$,
and
$$K^{0} \rightarrow \pi^{+} + \pi^{-}$$.

Taking the mass of the proton and pi meson to be given, the trajectories of the above charged particles and that of the original neutral particles can be used to find the momentum and then the rest mass of the kaon and lambda. I've found these already. The accepted values were within the error of my measurement.

Using the the energy and momentum found in the first part, we can find the velocity of the neutral particles in the lab frame:

$$v=\frac{pc^{2}}{E}$$

And then from the photograph we can measure the distance each particle traveled, dividing this by the velocity found in the last equation we should get the lifetime of each particle in the Lab frame:

$$t_{lab}=\frac{d}{v}$$

And from there we find the lifetime in the particle's rest frame using this equation:

$$t_{rest}=\frac{t_{lab}}{\gamma}$$,

where γ is the lorentz factor.

Here is what I calculated for the K0:

$$t_{lab}=8.07\pm 0.22 (10^{-11}s)$$
$$t_{rest}=5.52\pm 1.39 (10^{-11}s)$$

For the lambda0:
$$t_{lab}=2.80\pm 0.52 (10^{-10}s)$$
$$t_{rest}=1.82\pm 0.36 (10^{-10}s)$$

The fomula for t_lab deals with the velocity as measured in the lab frame, so that should be the lifetime of the lab frame. The fact that in both cases my t_lab is closer to the accepted rest mean lifetimes has me suspect. Is there anything wrong with my methodology here? Thank you for your replies.

Last edited: Nov 13, 2012