Theory of Deep-Inelastic Lepton-Nucleon Scattering and Lepton-Pair Annihilation Processes. I

however, the same problem done with hard-pion techniques did require a cutoff. " One possible physical explanation for the cutoff is given in the vector-dominance model, which says that the strong-interaction vertex (of the vector meson connecting to the hadron line) has an unknown form factor associated with it. Even though the concept of a cutoff (or effective cutoff A) is accepted, any derivation of its value from 6rst principles is lacking. The empirical "double-pole" form of the nucleon form factors would suggest an effective cutoff in the range of the vectormeson masses (i.e. , 0.7—0.8 BeV) for that case. Since this is smaller than the hadronic mass to which it connects, it has also been suggested that a cutoff in the neighborhood of the hadronic mass is reasonable. The above discussion would suggest that, for E mesons, a reasonable cutoff would be in the range 0.5— 0.8 BeV. However, previous calculations of the kaon electromagnetic mass difference have typically required "M. B. Halpern and G. Segre, Phys. Rev. I.etters 19, 611 (1967). cutoffs in the range of 20 BeV and higher. "Therefore, the present calculation shows a signiicant improvement since the cutoff has been reduced to 3.0—3.5 BeV. One might wonder if the inclusion of other s-channel trajectories such as the ones on which the E*or E~ mesons lie would further decrease this value. Since the present calculation has a change of sign of the mass difference for a cutoff of about 1.5 BeV, it seems doubtful that the inclusion of these other trajectories would reduce the required cutoff to a "reasonable" value.