# Lifetime of rho meson and Kaon

#### unscientific

1. The problem statement, all variables and given/known data

(a) What is a meson?
(b) State what these mesons are made up of and explain their quantum numbers and interactions.
(c) Find the lifetimes of rho meson and kaon.
(d) Find the dominant decay mode and explain why.
(e) Why is decay to 2 neutral pions forbidden?
(f) Explain how an a1 (1260) meson can be formed and a valid decay. 2. Relevant equations

3. The attempt at a solution

Part(a)

A meson is a composite hadron formed by a quark and an anti-quark. There are three generations of quarks - (u,d), (s,c) and (t,b).

Part(b)
Textbook problem.

Part (c)
How do I find the lifetime from these graphs? I can see that the graphs peak at 1300 decays/bin and 2500 decays/bin respectively. How do I convert that into lifetimes?

Part (d)
Dominant decay mode is in fact decay to 2 Kaons $K^+$ and $K^-$. The decay to 3 pions is OZI suppressed. We expect lifetime to be 1000 times longer than lifetime of kaons.

Part (e)
In short, because 2 neutral pions cannot have L = 1, otherwise they are anti-symmetric in exchange (which cannot be, since they are bosons that must be symmetric under exchange).

Part (f)
It is possible for L =S=J=1 through L-S coupling to give total J=1. They exist as a spin tripplet. A valid decay would be $a_1 \rightarrow K + \bar K$.

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#### BvU

Science Advisor
Homework Helper
(c) You don't. Instead, you use the uncertainty in the energy, so the width, not the height. Here or here

#### unscientific

(c) You don't. Instead, you use the uncertainty in the energy, so the width, not the height. Here or here
Thanks alot for the links, I'll read that up. Are my other parts to the question OK?

#### BvU

Science Advisor
Homework Helper
I like part (b) • unscientific

#### unscientific

(c) You don't. Instead, you use the uncertainty in the energy, so the width, not the height. Here or here
So since $\Delta E \delta t = \frac{\hbar}{2}$, I take that the lifetime is the uncertainty $\delta t$ so I simply estimate the half-width $\Delta E$ from the graphs to calculate $\Delta t$?

#### BvU

Science Advisor
Homework Helper
Yes. Nice, isn't it ?

• unscientific

#### unscientific

Yes. Nice, isn't it ?
These questions appear to be harder than they are..

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