Inelastic-Compton-Scattering Inequalities in the Quark-Parton Model

On the assumption that partons are quarks, we derive several constraint relations (in the form of inequalities) for the structure functions of inelastic Compton scattering. Bounds on the structure functions of the inelastic Compton scattering with respect to those of inelastic electron-proton scattering are also discussed. All these inequalities must be true for any quark-parton model and, thus, furnish us with some means of testing the hypothesis of individual quark-parton identification. These are also very useful for obtaining information about the parton distribution function $P\left(N\right)\mathrm{}$ and about the minimum number of partons $N_0$ in a nucleon. The constraint relations that we have derived here can be made much stronger if one uses a detailed quark-parton model. Assuming $〈\frac{1}{N}〉=0.1\mathrm{}$, which is consistent with the presently available data on both inelastic electron and inelastic neutrino scattering, we make a quantitative analysis of the structure functions.