Asymptotic Sum Rules at Infinite Momentum

J. D. Bjorken
Phys. Rev. 179, 1547 – Published 25 March 1969
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Abstract

By combining the q0i 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 ν̃p cross sections is determined by the equal-time commutator of the Cabibbo current with its time derivative, taken between proton states at infinite momentum.

  • Received 30 September 1968

DOI:https://doi.org/10.1103/PhysRev.179.1547

©1969 American Physical Society

Authors & Affiliations

J. D. Bjorken

  • Stanford Linear Accelerator Center, Stanford University, Stanford, California

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Issue

Vol. 179, Iss. 5 — March 1969

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