# Incoherent assumption of the parton model

Consider the scattering process $ep\rightarrow eX$, in the frame of an ultra-relativistic electron, the partons inside the proton are "frozen," and since the time scale of strong interaction is much larger, the partons are non-interacting.

It is also true that the electron will only hit one parton each time, and so this seems identical to a multi-slit interference experiment and one expects interference terms in the scattering cross section.

However, it is assumed that the electron-parton scattering is incoherent. And so the cross section is proportional to the sum of probabilities $\sum_i |{\cal M}_i|^2$ instead of amplitude squared $|\sum_i {\cal M}_i|^2$. Moreover, we also treat parton distribution functions as real-valued probability distributions instead of complex wavefunctions.

I'm confused at the point that the partons are treated like "classical" point particles, i.e. the incoherent assumption.

• The final justification is the same as always: it works pretty well. Glauber style models are predictive. – dmckee Nov 9 '14 at 3:02