Compton Scattering and Fixed Poles in Parton Field-Theoretic Models

We extend a class of parton models to a fully gauge invariant theory for the full Compton amplitude. The existence of local electromagnetic interactions is shown to always give rise to a constant real part in the high energy behavior of the amplitude TI(v ,q’). In the language of Reggeisation this is interpreted as a fixed pole at J = 0 in Tl and v T2, with residue polynomial in the photon mass squared. (Submitted to Phys. Rev. Letters) TWork supported in part by the U. S. Atomic Energy Commission. *NATO fellow 1970-1972. Recent inelastic electroproduction experiments (which essentially measure the imaginary part of the forward off-shell Compton amplitude) hint at a composite nature for the nucleon. This has been represented by parton models involving point-like (possibly field theoretic) constituents, but up to the present time these concepts have only been applied to the scaling, incoherent impulse approximation, region. Gauge invariance and the low energy theorem place further restrictions upon such theories, and in this letter we report the extension of parton-field theoretic ideas to a discussion of the full Compton amplitude. In particular we shall see that such models always give rise to a real part at high energies additional to that expected from the Regge behavior of the imaginary part. This extra real part should be identified with the “fixed pole”’ of conventional Regge analysis. Evidence for such a fixed pole for on-shell photons has been found phenomenologically from dispersion relations. 2 In addition we find that the “fixed n pole” appears as a constant real part, C , in Tl independent of q’ , and appears in v T2 in the form -Cq2/y. 3 If the proton were as simple as the nucleus, then the high energy behavior of the Compton amplitude would follow directly from the coherent impulse approximation. At v = 0 the Compton amplitude on a nucleus is given by the Thomson limit4 fl(0) = (Z2 o/M nucleus) whereas at energies high compared to the binding energy, but below threshold for photoproduction of mesons, the forward amplitude Z is given by the coherent sum of the individual nucleon amplitudes, fl( v ) = -c $ i=l 1 (0. 1 = mi). In fact, for the case of a composite proton the analogous high energy behavior would be given by the coherent sum of t’seagullt’ terms for the individual proton constituents (quarks, bare hadrons) and the formulae (7), (11) we give later correspond to this picture. Field theory gives us the clearest example of a fully covariant , gauge invariant, Compton amplitude which can also incorporate the composite nature of the nucleon.