Scaling, Light-Cone Expansion, and the Van Hove Model

With certain assumptions on the coupling of two currents to particles of increasing spin, it is shown that the Van Hove model results in Bjerken scaling and Regge asymptotic be­ havior. The fields corresponding to these particles are related to the products appearing in the operator-product expansion near the light cone.

With certain assumptions on the coupling of two currents to particles of increasing spin, it is shown that the Van Hove model results in Bjerken scaling and Regge asymptotic be havior.The fields corresponding to these particles are related to the products appearing in the operator-product expansion near the light cone.
The Bjorken scaling limit 1 for deep-inelastic electron scattering, or more generally for the scattering of any current in the appropriate kinematic• region , may be accounted for by the behavior of products of currents close to each other's light cone. 2 -5 This scaling limit can be made consistent with Regge asymp totic 6 behavior; such a behavior may be suggested by the data on inelastic electron scattering.7 In this note we shall point out how these results may be achieved in the context of the Van Hove model. 8It may likewise shed some light on the nature of the bilocal operators appearing on the right side of the operator product expansions. 3It should be emphasized that none of the results will be derived; they will all be in serted into the model from the start.Our purpose is to show the consistency of these assumptions within a dynamical scheme, and as mentioned previously, to discuss their connection with the operator-product expansion.
For brevity we shall consider the scattering of a current by a spinless particle and study only the even charge-conjugation amplitude analogous to W2 of electroproduction.Let q1 and p 1 (q 2 and p 2 ) be the four momenta of the incoming (outgoing ) current and particle; the amplitude under discussion is with P=½(p1 +P2), Q=½ ( q1 +q2), -(P 2
We have found that the scaling and Regge limits may be made consistent with each other within a dynam- ical model, and comparing the coefficients of the (I/&()) terms in Eq.( 6) and Eq.(9), we find a direct interpretation of the fields 8"".. ."as the fields of particles of successively higher spins and masses whose ex- changes in the t channel sum up to a Regge-pole contribution.This analysis does not illuminate the diffractive or Pomeranchuk contribution to the Bjorken-Regge limits.If the vacuum trajectory is like all the other ones agd passes through particles, then a similar analysis to the one above may be applied to it.If, on the other hand, diffraction scattering is governed by a flat trajectory, a superposition of cuts, etc. , then the above discussion will be valid only for the ordinary exchanges.
PH YSICAL REVIEW D VOLUME 4, NUM BER 4 15 AUGUST 1971 Scaling, Light-Cone Expansion, and the Van Hove Model* Myron Bander Department of Physics, University of California at Irvine, Irvine, California 92664 (Received 5 May 1970)