The inelastic electron-proton scattering cross section can be written as
$$\frac{d\sigma}{dE_2d\Omega}=\frac{\alpha^2}{4*E_1\sin^4{\frac{\theta}{2}}}(W_2\cos^2{{\frac{\theta}{2}}}+2W_1\sin^2{{\frac{\theta}{2}}})$$
where $W_1$ & $W_2$ are the proton's structure functions. We further define the following dimensionless functions:
$$F_1=MW_1$$
$$F_2=\nu W_2$$
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?
