Electron-positron vs electron-proton scattering

[TravisThePhys]

Homework Statement

True/False: Because the potential between an electron and positron is identical to that of an electron and proton, if we compensate for the difference in mass, the differential scattering cross section in electron-proton scattering must be the same as for electron-positron scattering.

Same question, but now for proton-proton scattering and proton-positron scattering.

Homework Equations

The Attempt at a Solution

it seems like both of these statements have to be false. If electron-positron scattering were indistinguishable from electron-proton scattering with respect to their differential scattering cross section, how exactly do we experimentally probe things like the proton through electron-proton scattering experiments in order to discover the properties of the quarks? However, I don't know how to justify this intuition in a theoretical way. Does this have something to do with the difference between "equal mass scattering" vs "unequal mass scattering" that isn't accounted for when we say that we will account for the mass differences?

 

[andrien]

for electron positron scattering there are contributions from two photon annihilation, single quantum virtual annihilation(timelike) which is important when dealing with positronium hyperfine splitting of ground state.they correspond to non zero matrix element which will not be present in electron proton scattering.only the direct interaction corresponds to the potential which you are talking.but if we will take the case of proton having some internal structure then on the basis of lorentz invariance and gauge invariance the vertex factor where photon interacts with proton will be different involving some form factors which ultimately gives rosenbluth formula for electron proton scattering cross section which is different from electron positron scattering cross section.the next one you can judge by yourself.