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RE: Photon-photon scattering detected at LHC!
Well, they exist in the sense that they are disturbances of the underlying field. I am not claiming that they can be observed anywhere. In perturbation theory, one still integrates over the virtual particles' momentum to get the amplitudes.
That's a calculation trick. You seem to say,. in your post, that they materalize, but they don't. That's my only point. You could for instance use other techniques going beyond the Feynman diagram approach for taking care of the same calculation and get the same result.