INELASTIC ELECTRON SCATTERING AND THE MULTI - REGGE MODEL t

We investigate the multi-Regge model in the kinematic region where the four momentum of one initial particle is large and spacelike. These kinematics occur in inelastic electron scattering through single virtual photon exchange. We predict a rapid fall off in the cross section as the virtual particle becomes more spacelike, contradicting present data. (Submitted to Phys . Rev. ) t Supported by the U. S. Atomic Energy Commission. * National Science Foundation Graduate Fellow. 2After radiative corrections, inelastic electron scattering measures the total cross sectionfor virtual photons as a function of the photon mass as well as its energy. This freedom of varying a particle mass is a new feature not yet available in other reactions; therefore, this process has recently attracted much theoretical interest. (1) (2) Denote the total cross sections for transverse and longitudinal virtual photons incident on spin averaged protons by (T T and u L respectively. Let v be the photon lab energy and let p: be the square of the photon four momentum. Bjorken (1) has shown that, as v and pf became V large with the ratio 2 p1 constant, it is likely that va T and v (T % have finite, as opposed to infinite, limits of value dependent on this ratio 2. Current (6) p1 data seem to indicate that this limit is nonvanishing . Most of the recent interest in the subject concerns the behavior of this limit as a function of + p1 * The multi-Regge model (MRM) has drawn interest as a possible description for highly inelastic hadronic collisions (3). We wish to relate the MRM to inelastic electron scattering by discussing the behavior of the MRM as the four momentum pl of an initial particle becomes large and spacelike. In this way we hope to gain some insight into the behavior of Bjorken’s limit functions. In particular, we ask if the above discussed behavior for v (T L and v c T is consistent with the simple MRM. Our calculation essentially follows the work of Halliday and Saunders (4) , except we allow one initial mass to be variable. For simplicity we treat all particles as spinless. Figure 1. shows our kinematics. A virtual particle of momentum pl collides with a particle of momentum p2 and unit mass (pi = 1). The f’ ma1 state consists of n identical particles labeled with momenta qi’ i=l, l l l n, and all of unit mass (qf = 1). Define invariants