The inelastic electron-proton scattering cross section can be written as
where $W_1$ & $W_2$ are the proton's structure functions. We further define the following dimensionless functions:
Assuming that the proton's constituents are point like and that electron collide elastically with these constituents, one can derive the Bjorken scaling: $F_1$ & $F_2$ do not depend on the momentum transfer. Also, we can show the Callan-Gross relation: $F_2=2xF_1$.
However, it is known that Bjorken scaling is broken when considering higher orders in perturbative calculation.
My question concern the validity of the Callan-Gross relation: does the braking of the Bjorken scaling violates the Callan-Gross relation?