1. Nov 30, 2009

### venomxx

Reading on pions the book glanced over this idea:

Aloud:
Neutral pion --> photon and photon

Not aloud:
Neutral pion --> photon

the book says its due to energy momentum conservation? but if photons are massless how does this work?

Cheers

2. Nov 30, 2009

### ansgar

You can try this by just putting up the equations of momentum- and energy conservation.. it is really simple.

3. Nov 30, 2009

### venomxx

cheers for the reply, but if the photon is massless how does it have any momentum to carry away?

4. Nov 30, 2009

### Bob S

If you apply the relativistic rest mass, momentum, total energy equation to photons:

E2 = (βγ m0c2)2 + (m0c2)2 to photons, we get

E = pc, or p = E/c

So massless photons of energy E have momentum E/c.

Bob S

5. Nov 30, 2009

### arivero

Still, to understand the complete problem we need other question: can a Z0 meson decay to two photons?

6. Nov 30, 2009

### venomxx

So, using p=E/c for the photon and using the energy and momentum of neutral pion, you can determine that it needs two photons to carry away the momentum as one would not be sufficient. Would i be correct in saying that?

arivero: i believe a Z0 is able decay into two photons with no problems....at least from what iv just looked up!

7. Nov 30, 2009

### Bob S

Consider a pi zero from the proton capture of a pi minus at rest going to a neutron plus pi zero. The pi zero momentum is miniscule. How could it decay to a single 135 MeV photon?

The Z0 branching ratio to two photons is less than ~5 x 10-5.
Bob S

8. Nov 30, 2009

### ansgar

no Z0 BOSON does not have couplings to the photon (at tree level), they are orthogonal states..

9. Nov 30, 2009

### ansgar

z0 meson?

10. Nov 30, 2009

### ansgar

No, the correct answer is that energy and momentum conservation can not be simoultatneously fulfilled in the case of pi0 decaying into one photon.

11. Nov 30, 2009

### arivero

12. Nov 30, 2009

### arivero

Some textbooks propose, to deep in the understanding of the "triangle", to compare the decay where the spin 0 pion goes to quark antiquark and then to two photons with other two triangles: the one with an spin 1 meson (pho, sigma, J/Psi, etc) decaying to the same mechanism, and the one with the Z0 decaying to any of their particle/antiparticle couplings and then to two photons.

The point I want to make is that, while the kinematic answer is enough for the Original Post goal, the OP has unfortunately chosen the most famously complicated example of electromagnetic decay.

Last edited: Nov 30, 2009
13. Dec 1, 2009

### Holychikenz

Consider this senario. The pion is initially at rest in its frame. The pion has a certain amount of rest energy mc^2 and when it decays into photons all of this energy is converted into the momentum of the photon E=pc. In order to uphold conservation of momentum, if the pion with initial momentum of zero were to decay into one photon, then that photon would necessarily be at rest. Well we know that this can't be the case because the photon must have velocity c and some energy corresponding to its energy (from the pion rest mass).
From that simple argument its straight forward to see that the number of photons must be greater than one (and using the quantum charge operator, must be even number of photons).

Hope this helps.

14. Dec 2, 2009

### venomxx

That helps alot, cheers for the great replys!! its so simple when you think about it....:)