The Bjorken scaling limit in field-theory models

Abstract

The Bjorken scaling limit for deep inelastic electron-proton scattering is investigated in a field-theory model by methods previously used to discuss Regge properties and the Bjorken-Johnson-Low limit. In a cut-off theory the results are similar to those obtained by Drell, Levy and Yan in an analysis inspired by the parton picture, except that behaviour of the structure functions in the large-ω limit is identified with properties of Regge poles in thet-channel. A theory with a neutral gluon is favoured since it leads toR=0. A new sum rule is derived. If third spectral-function effects are neglected this sum rule reduces to one satisfied in the Veneziano model of Landshoff and Polkinghorne. In a theory without a cut-off, scale invariance is violated by logarithmic terms arising from the same mechanisms which lead to similar violation of the Bjorken-Johnson-Low limit. The leading-order terms from convergent diagrams are summed and agree with a similar expression calculated by Chang and Fishbane.