Rigorous bounds on massive lepton pair production and tests of parton models

Using Lagrange inequality multipliers, we derive rigorous upper bounds on cross sections for the process $\mathrm{pN}\to l^{+}{l}^{-}+X$, in the context of the parton model. For definiteness, we work with a colored-quark version of the parton model, but our results are easily generalizable to other versions. The constraints we impose are given by our knowledge of $\nu W_2$ for protons and neutrons. Then, in a separate problem we add further constraints derived from considerations of the recent neutrino and antineutrino data from Gargamelle. Our upper bounds fall below the Brookhaven data. We conclude, therefore, that at least one of the following statements is true: (1) The experimentally observed cross section is not the scaling limit for the process. (2) The Drell-Yan formula for $\mathrm{pN}\to l^{+}{l}^{-}+X$ must be modified. (3) The colored-quark parton model is wrong.