Observation of deviations from scaling in the structure functions for deep-inelastic inclusive lepton-hadron scattering may provide a test of the hypothesis that the strong interactions are described by an asymptotically free field theory. Tests not involving additional assumptions are obtained for the combinations of structure functions $F_2\mathrm{}\left(\mathrm{ep}\right)\mathrm{}-F_2\mathrm{}\left(\mathrm{en}\right)\mathrm{}$, $F_2\left(\nu \right)-F_2\left(\overline{\nu }\right)$, and $x{F}_3(\nu or \overline{\nu })$. Neutrino and electron scattering experiments are compared as possible tests of asymptotic freedom.

• Received 3 June 1974

DOI:https://doi.org/10.1103/PhysRevD.10.2141