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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?

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That's not exactly what you asked, but it may be relevant pointing out that the Callan-Gross relation is deduced assuming a parton model for your proton with only spin 1/2 particles as partons. But, among the partons you should consider also the particles from the "sea" (gluons...). This can make a difference, and should be the cause of Callan-Gross 'problems' near x=0:

Callan-Gross experimental test

So, the relation is not 'correct' even neglecting higher orders terms. I don't know what differences would this corrections bring, but I wonder if it's worthy to bother with them without correcting the parton choise first (not saying it isn't, I have no idea).

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