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Production of Pure QED Atom

  1. May 17, 2015 #1
    Studying the production of the bound state of ##μ^+μ^- ## in the scattering experiments of ##e^+e^-## at electron positron colliders ##e^+e^-\toμ^+μ^- ## via ##e^+e^-\to 2γ\toμ^+μ^- ##. This bound state further can decay into ##e^+e^-## or ##2γ##.

    I am confused about the vertex ## 2γ\toμ^+μ^- ## in the Feynman diagram, how can I include it in decay amplitude? Of course it need some detail of bound state, wave-function etc., but how to deal with this stuff? Looking for some literature/QFT book which involves this type of vertex for production of positronium (##e^+e^-##) or muonium (##e^+μ^-##).
     
  2. jcsd
  3. May 19, 2015 #2

    nrqed

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    Is your question about what Feynman diagram contributes to this reaction?
    First, note that there is no vertex for two photons going directly to a mu+ and mu-. The diagram is a one-loop "box" diagram.
     
  4. May 23, 2015 #3
    Dear nrqed, I know the diagram, I am curious about how to add the details of the "box" in the amplitude?
     

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  5. May 26, 2015 #4

    nrqed

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    I am a bit confused why you initially mentioned e e+ going to two gammas, I don't see this in the diagram.

    For the box, it depends if the
    Hi,

    Ah ok. I am confused why you mentioned e- e+ going to two photons in your original post, this does not occur in your diagram.

    Well, it depends on whether the muon and antimuon are produced with a small relative speed or not. If it is large, you can just do the usual Feynman diagram expansion. But at small speeds, the muon and antimuon can interact for a long time, being essentially bound through the Coulomb interaction. In that case, one must sum up an infinite number of Coulomb photon exchanges between the two. This can be done. I don't know if my PhD thesis is available online easily (Patrick Labelle, Cornell University, 1994) but I do it there. Or look for old papers by Peter Lepage (on positronium) or my Toichiro Kinoshita (on muonium)
     
  6. May 26, 2015 #5

    nrqed

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    Now that I think of it, the easiest reference to find is a paper on pionium by Labelle and Buckley. It is on the archives. I am pretty sure we give the formula needed in that paper.
     
    Last edited: May 26, 2015
  7. May 26, 2015 #6
    Thanks dear P. Labelle, I acknowledge your help. Sorry for my poor understanding & language used in question. I found all of your papers on HEP-INSPIRE, I also found many of my answers there. The paper you mentioned (with Buckley), I just downloaded & reading now. I am not able to get your thesis, it is not available in PDF form online.
     
  8. May 27, 2015 #7

    nrqed

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    You are very welcome. And there is no reason to apologize for anything!

    If anything is unclear in my papers, please don't hesitate to ask!!

    Regards,

    Patrick
     
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