Asymptotic Sum Rules at Infinite Momentum

By combining the q₀→i∞ method for asymptotic sum rules with the P→∞ method of Fubini and Furlan, we relate the structure functions W₂ and W₁ in inelastic lepton-nucleon scattering to matrix elements of commutators of currents at almost equal times at infinite momentum. We argue that the infinite-momentum limit for these commutators does not diverge, but may vanish. If the limit is nonvanishing, we predict νW₂(ν, q²)→f₂(νq²) and W₁(ν, q²)→f₁(νq²) as ν and q² tend to ∞. From a similar analysis for neutrino processes, we conclude that at high energies the total neutrino-nucleon cross sections rise linearly with neutrino laboratory energy until nonlocality of the weak current-current coupling sets in. The sum of νp and ̃ \~νp cross sections is determined by the equal-time commutator of the Cabibbo current with its time derivative, taken between proton states at infinite momentum.