# Homework Help: Neutral pion lifetime

1. Aug 17, 2007

### noospace

Hi all,

I'm having trouble understanding the short lifetime on the neutral pion. I understand that in the residual strong interaction between nucleons, the range of the virtual pion is limited by Heisenberg's uncertainty relation for energy, which thus limits its lifetime. I don't understand why this would be the case in other interactions such as $\pi^0 \to 2\gamma$ where the pion is not virtual.

Thanks

2. Aug 18, 2007

### malawi_glenn

Is this a homework problem?

The lifetime of the real neutral pion is greater then the life time of a virtual pion. The neutral pion decays since it consits of a quark-anti quark pair of the same pair. And eventually, they will anihilate. In contrast with the case of the virutal pions in the pion-exchange model of the strong force.

http://en.wikipedia.org/wiki/Pion

3. Aug 18, 2007

### noospace

Interesting. Why is a quark anti-quark pair belonging to the same pair more likely to decay than one belonging to different pairs?

4. Aug 19, 2007

### malawi_glenn

The neutral pion can decay through the electromagnetic force, the quarks and anti quarks from the same family can anihilate; and the electromagnetic force is stronger (more likley to occur) than the weak force.

The negative pion for instance, must decay through the weak force; via exchange of W-boson. As you can see in the Feynman diagrams for each process.

When particles decay, and react, certain quantities must be conserved. In our macroscopical world; we see that energy, linear and angular momentum must be conserved. In the microscopical world, things like "lepton number", "baryon number" etc must be conserved, and which quantities that must be conserved is also depented on which force that is acting. In electromagnetic, Isospin is not conserved, and in weak; Parity is not conserved. etc.