ASYMPTOTIC PROPERTIES OF VIRTUAL COMPTON AMPLITUDES IN LADDER MODEL

We study the asymptotic properties of the virtual Compton scattering amplitude for a spacelike spin-1 photon off a scalar target, in the limit k2, k2= fixed. This is accomplished by means of a perturbative model based on the ladder-diagram series. The absorptive parts of these amplitudes in the forward direction are related, as is well known, to the structure functions W1 and W2 that in turn describe inelastic electron scattering off the same target. In terms of W1 and W2 (using a 3 model for the hadron dynamics), we find that W1(1k2)ln(k2m2)F1() and W2(1k2)F2(). Notice that in this model W1 does not approach a constant limit. We also find, for large, that F1()1(0) and F2 2(0)-2, where (t) is the same Regge trajectory that dominates at high energy. To understand these results better, we also study the Bjorken limit for ik0, both for spin-0 and spin-1 currents. In the first case, we find that the expansion in inverse powers of ik0 is valid for the first few terms, while in the second case, one of the invariant amplitudes shows a term (ik0)-2ln(ik0). The similar behavior of W1 for k2 is presumably related to that logarithmic term. © 1969 The American Physical Society.