The scaling functions for purely electromagnetic interactions

If we now compare scattering on proton and neutron targets, and if we temporarily attach a label to the distributions to signify the hadron involved, then on the grounds of isospin invariance we expect 

reverting to the convention that no label refers to distributions in the proton, we have 

We would naturally expect the structure of a hadron to be dominated by its valence quarks—u and d for a nucleon. So we might expect the contribution from the sea to be small. But this cannot be true for all x as we saw from the discussion of B x) in Section 16.2. And QCD arguments indicate that the sea should become increasingly important for small x. 

With this in mind consider the ratio of scaling functions obtained from ep and en reactions  

Since the distribution functions are positive one obtains the Nachtmann inequality  

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