Production of Pure QED Atom

In summary, the conversation discusses the production and decay of the bound state of mu+mu- in scattering experiments at electron positron colliders. The participants also discuss the inclusion of a "box" diagram in the amplitude and the importance of considering the Coulomb interaction between the muon and antimuon in certain scenarios. They mention various papers and resources that provide further information on this topic.
  • #1
Naeem Anwar
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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^-##).
 
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  • #2
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.
 
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  • #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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  • #4
Naeem Anwar said:
Dear nrqed, I know the diagram, I am curious about how to add the details of the "box" in the amplitude?

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
Naeem Anwar said:
Dear nrqed, I know the diagram, I am curious about how to add the details of the "box" in the amplitude?
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)
 
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  • #5
nrqed said:
I am a bit confused why you initially mentioned e e+ going to two gammas, I don't see this in the diagram.

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)
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.
 
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  • #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.
 
  • #7
Naeem Anwar said:
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.
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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1. What is a QED atom and how is it different from a regular atom?

A QED (Quantum Electrodynamics) atom is a theoretical type of atom that is made up of a single electron and a single positron (anti-electron). It is different from a regular atom in that regular atoms contain multiple electrons and protons, while a QED atom only contains one electron and one positron.

2. How is a pure QED atom produced in a laboratory setting?

In a laboratory setting, a pure QED atom can be produced through the process of pair production, where a high-energy photon is converted into an electron and a positron. The electron and positron can then be confined in a small space, forming a QED atom.

3. What are the potential applications of pure QED atoms?

Pure QED atoms have potential applications in quantum computing and precision measurements. They have also been proposed as a means of studying the fundamental laws of physics and testing theories such as quantum electrodynamics.

4. How stable are QED atoms and how long do they last?

QED atoms are highly unstable and have a very short lifespan. Due to the interaction of the electron and positron, the atom quickly annihilates and releases energy in the form of gamma rays. Their lifespan is on the order of 10^-21 seconds.

5. Are there any challenges in producing and studying pure QED atoms?

Yes, there are several challenges in producing and studying pure QED atoms. One major challenge is the short lifespan of the atoms, which makes it difficult to observe and study their properties. Additionally, the production of pure QED atoms requires extremely high-energy photons, which can be technically challenging to produce in a laboratory setting.

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