Asymptotic Sum Rules at Infinite Momentum

Abstract

By combining the qO-im method for asymptotic sum rules with the P -CQ method of Fubini and Furlan, we relate the structure functions W2 and WI 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 . . vW2(v,q2)-f2 v 0 2 as v andq2 tendto 00. 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 up and Yp cross sections is determined by the equal-time commutator of Cabibbo-current with its time derivative, taken between proton states at infinite momentum.

Baryons as relativistic three-quark bound states

“…This contrasts sharply with the comprehension of QCD in the high-energy regime. QCD's property of asymptotic freedom is the reason for Bjorken scaling [145], and the logarithmic running of the coupling leads to scaling violations which have been verified over a huge range of kinematical variables. Referring to the picture in which at large momentum scales the observed approximate scale independence is accounted for by the presence of quasi-free and point-like constituents of hadrons, quarks and gluons provide the most effective language to describe hadronic processes.…”

Formulation of Bethe--Salpeter equation in e--p deep inelastic scattering

“…in the min integral representation of the amplitude, the scaling property of vW2 can be revived to the same form as that Bjorken who first derives, by a rather (3) general argument, a result that the structure functions MW1(v,q2) and VW2(v,q2) will respectively become Fl (w) and F2(w), which are functions of the ratio w = 2Mv/-q2 only, when the limit v,-q2 +co is approached with w being fixed. Since then, under the suggestion that a knowledge of the form of vW2 or MWl may serve as a tool to understand the structure of the nucleon, quite a few authors have been using practical physical processes and various models to study this problem.…”

Exclusive Production of Neutral Vector Mesons at the Electron-Proton Collider HERA

“…Much of the notation and choice of variables in this section is motivated by the investigations of deep inelastic electron-nucleon scattering performed at SLAC in the late 1960s which led to the discovery of Bjorken scaling [21] and the further development of the infinite momentum frame formalism [22,23]. For a detailed general treatment of particle kinematics, extending beyond that of deep inelastic scattering, we refer to the book by Byckling and Kajantie [24].…”