"Solving the B0 Decay of Z0 to D+X

[kcirick]

I will put the question in exact wording that the prof gave us:

Homework Statement

A B+ - B- pair is produced in the decay of at Z0. The B then decays to D + X, where X represents some other particles, with a lifetime of 1.638 x 10^12 s. On average how far will the B0 travel before decaying? This is how the lifetime of the B was measured, by measuring the distance from the production vertex to a secondary vertex where it decayed. (M_B0 = 5.279Gev, M_Z0 = 91.188Gev).

Homework Equations

All I can think of that may help me (beside a clearer wording of the question) would be:

$$\tau = \frac{1}{\Gamma_{t}}$$
where $\tau$ is the lifetime of the particle and $\Gamma_{t}$ is the decay width.

The Attempt at a Solution

I just don't understand where the B0 comes from in this context? It just appears in the question. Is B0 a combination of B- and B+? How would the hint (at the end of the question, the masses of the particles) be any use if I use the formula in the 2nd part?

Any thoughts?

 

[Meir Achuz]

The B0 in the question must be a misprint. The PDG gives 1.53 as the B0 lifetime, not 1.638, so I don't think the B0 ever enters the problem.

 

[kcirick]

Yeah, I asked the prof, and it is a typo... I really don't like it when there is a typo in an assignment.

It was supposed to be $B^{0}$ and $\bar{B^{0}}$ as a decay process of $Z^{0}$.

Thanks for the help anyway!
-Rick