Who can tell me what a real photon is? Or refer me to some kind of authoritative informative definition that is accepted and trusted by particle physicists? I say all this because I think it's of paramount importance. If we have no clear idea of what a photon actually is, we lack foundation...
How can we understand pair production if we don't understand what the photon is? Or the electron? Or the electromagnetic field? Or everything else? It all starts with the photon.
I think this is really a philosophical problem, not a physics problem. No answer will satisfy you, because you are asking a question which it is impossible to answer with finality : What is the essence of a thing?
Exactly the same problem exists with every concept of human thought, not only in science (What is energy? What is time? What is colour? What is consciousness?...) but also in the humanities (What is love? What is beauty? What is happiness?...). In each case the more we try to define something, the more elusive it becomes, the less we seem to really understand what the essence of it is. And when we think we have a grasp of it, some new property emerges to throw our understanding into disarray again.
I agree with AnoE (perhaps because I am a disciple of Richard Feynman) that things can only be understood as the sum of their properties, their inter-relations with other things.
In life, it is not necessary to know what love is in order to experience it, or to know what justice is in order to act justly or recognise injustice. The only definition we can give is to summarise our experience of a thing into one or more idealised "models" which isolate the features we consider to be "essential".
In the same way, it is not necessary to have an ultimate definition of a photon as a solid foundation before we can study light or develop powerful theories like QED. A working definition or model is adequate, one which allows us to identify and agree on the common experience and properties which we are investigating.
The history of science shows that the concepts we use are gradually refined over decades or centuries, in particular the question of "What is light?" This lack of ultimate definition has not prevented us from developing elaborate theories like QED and General Relativity which allow us to predict with astonishing accuracy and expand our understanding of how the universe works.
"Photon" and "electron" and "magnetic field" are only our models of things we find in the universe, to help us predict and find relationships between things. As Elias puts it, these models are, of necessity, approximate concepts. They are not what really exists. It is inevitable that they will change as we refine our approximations to try to fit new properties, new observations, into the framework of our understanding, our theories.