Is it possible for a pion to decay into a proton and a photon?

[Kenai]

Hey guys,
I was wondering if this reactions is possible:

$$\pi^{+} + n \rightarrow p + \gamma$$

(Assuming there is enough energy in the initial state to make the reaction go)

If not, what law is violated?

Lepton and baryon numbers are ok... also angular momentum, so I guess it's possible, but still... I can't figure out how to draw the feynman diagram, since there is a total of 5 quarks in the initial state ($$u,\bar{d}... d,d,u$$) and there is just 3 in the final state (u,u,d and gamma).

At first, I was thinking in merging d and $$\bar{d}$$ into a photon , but just 1 photon would violate the momentum conservation law...

Any ideas?

Thanks

 

[daschaich]

I can't figure out how to draw the feynman diagram

I would attach gluon(s) to the quark lines, and have a quark radiate a photon.

 

[Kenai]

I would attach gluon(s) to the quark lines, and have a quark radiate a photon.

Ok, a gluon can be attached into $$d, \bar{d}$$

But then I would have an excited system with:

$$d \bar{d} \rightarrow \it{g}$$

Which is the problem, since I would already have the $$u u d$$ configuration necessary for the proton in the final state, and the gamma can come from radiation from a quark as you said.

I'm using now the W boson to interact with one of the down quarks producing an up quark, I guest that would be possible. What do you guys think?

 

[daschaich]

All of your hadrons are bound states, and have tons of glue floating around inside them. I'm coming from a lattice QCD perspective, where we don't even bother drawing the gluons; we just use "quark-line diagrams" (and compute the path integral nonperturbatively...).

At any rate, two quick comments:

1) Your diagram basically has pi^+ converting into a W^+. This is going to be way off mass-shell, and also introduces two weak vertexes. I suspect it is negligible.

2) Isn't this process just pion photo-production "in reverse"? There should be lots of relevant literature about gamma-p interactions. They may invoke some "hadronization" for the pion and nucleon final states, in lieu of dealing with the glue.

 

[Kenai]

i got it! =)

I just turned d dbar into a gluon and made it interact with another quark, producing a photon as in the Compton Scattering pointed here:
http://www-e706.fnal.gov/gifs/feynman-dp-color.jpeg

$$q \it{g} \rightarrow q \gamma$$

:)

 

[Parlyne]

1) Your diagram basically has pi^+ converting into a W^+. This is going to be way off mass-shell, and also introduces two weak vertexes. I suspect it is negligible.

I would guess that the helicity problem with that is worse than the mass shell suppression.