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  1. In QED we have one vertex where one line is virtual and the other two are physical:

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But recently I came across the so-called Deeply Virtual Compton Scattering in which, after the interaction of an electron with a proton, a physical photon appears, as is possible in QED? Or another field theory is used here?

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  1. I also don't understand why this reaction is called DVCS. A photon is born real. (I would be grateful if you could advise me where to read about it in detail).
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  • $\begingroup$ It's deep virtual because a virtual photon is scattering off the protons constituent quarks. $\endgroup$
    – Triatticus
    Apr 4, 2023 at 23:13

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I am assuming you were looking at this paper, as it is using the same Feynman diagrams that you show.

Addressing the name of DVCS - Compton scattering is an inelastic scattering process where a photon interacts with a charged particle, resulting in altered momenta of both the photon and the charged particle. In DVCS case, the charged particle is a quark inside the proton. As Triatticus points out in the comments, it's virtual because the photon which scatters off the quark is virtual, and I assume that deeply comes from deep inelastic scattering and the Bjorken limit, i.e., the energy and momentum of the virtual photon going to infinity at the same rate.

As the diagrams show, the $e p \rightarrow e p \gamma$ gets contributions from two mechanisms, as one can't be sure how the photon was generated - the first one is the DVCS, and the other is Bethe-Heitler interaction (with the addition of an interference term). If the only interacting fermions were electrons, the process would be described by the theory of QED - unfortunately, the proton is a composite particle held together by the strong interaction. One can't know the kinematic properties of individual quarks inside the proton, but we can characterise the contents of the proton by parton distribution functions describing what fraction of the total momentum is carried by each parton (and is dependent on the energy at which the nucleon is probed). There are also nucleon form factors describing the electric and magnetic distributions inside a nucleon. The document says (in section 1.3.4.1) the B-H term is computed "using pure QED and can be expressed as a function of the elastic Form Factors", while the DVCS term is said to be parameterised by combinations of form factors.

So in conclusion, while only interactions between fermions and photons are present, you need information about the structure of the proton (a QCD bound state) to carry out the calculation. I would also argue that the photon-quark interaction is not described by QED, as the only fermions in QED are the electrons (you could probably argue muons and tau are included as well).

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