Cross section

Because the photon does not carry electric charge ?

 

Well, the proton carries electric charge, and the electron carries electric charge as well, so they interact by exchanging a virtual photon (say for instance in the lowest order appriximation). I guess you are asking about a real photon. How a real photon interacts with a proton depends on the energy of course. At energies around the proton mass and/or QCD scale (which I guess is your question, since ultra-high energy photons can not be produced easily) you can effectively describe the proton-photon interaction by the photon hadronic content, wich fluctuates say in a vector meson (or such hadronic configuration with the right quantum numbers). This is Regge calculus. So you need you photon to fluctuate into something else before interaction. You expect that this is going to considerably reduce your cross section.

 

Err, I think you're over complicating this... The most elementary scattering cross-section calculations for photon-electron and photon-proton is the Thompson scattering cross-section. That formula has an inverse mass dependence. Classically, the reason is that the heavier particle does not move as much --- it doesn't polarise as easily.

 

It might help to know what energy scale we're considering here. At low photon energies, genneth's explanation could be on the right track, while if the photon has enough energy that we could consider it interacting with a particular quark, we would automatically reduce the coupling by a factor of 1/3 to 2/3.