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(pi+)(n)-> (p)(gamma)

  1. Sep 21, 2010 #1
    Hey guys,
    I was wondering if this reactions is possible:

    [tex]\pi^{+} + n \rightarrow p + \gamma[/tex]

    (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 ([tex] u,\bar{d}... d,d,u [/tex]) and there is just 3 in the final state (u,u,d and gamma).

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

    Any ideas?

    Last edited: Sep 22, 2010
  2. jcsd
  3. Sep 21, 2010 #2
    Re: (pi+)(n)->(p)(gamma)

    I would attach gluon(s) to the quark lines, and have a quark radiate a photon.
  4. Sep 22, 2010 #3
    Re: (pi+)(n)->(p)(gamma)

    Ok, a gluon can be attached into [tex] d, \bar{d} [/tex]

    But then I would have an excited system with:

    [tex] d \bar{d} \rightarrow \it{g} [/tex]

    Which is the problem, since I would already have the [tex] u u d [/tex] 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?

  5. Sep 22, 2010 #4
    Re: (pi+)(n)->(p)(gamma)

    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.
  6. Sep 22, 2010 #5
    Re: (pi+)(n)->(p)(gamma)

    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:

    [tex]q \it{g} \rightarrow q \gamma [/tex]

  7. Sep 23, 2010 #6
    Re: (pi+)(n)->(p)(gamma)

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