Production of Pure QED Atom

1. May 17, 2015

Naeem Anwar

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. May 19, 2015

nrqed

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.

3. May 23, 2015

Naeem Anwar

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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4. May 26, 2015

nrqed

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)

5. May 26, 2015

nrqed

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
6. May 26, 2015

Naeem Anwar

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.

7. May 27, 2015

nrqed

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