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. © 1969 The American Physical Society.