Structure of the Interaction

In our model, the and couplings are exactly equivalent, except that the latter has a cutoff energy. Thus we can apply the same arguments as those which lead to s-channel photon production in electromagnetic annihilation to the case of our direct electron-hadron coupling (DEHC). We begin by considering the Coulomb scattering of a state from an electron. This occurs via the familiar Feynman diagram containing the -channel exchange of a virtual photon. Similarly, the scattering of from an electron in the DEHC model proposed here involves the -channel exchange of a virtual hadron or . The vertex is simply a high-energy real electron emitting a virtual hadron, by hadron-gluon coupling and evaporation or boiling. This is a strong vertex and hence it will lead to a typical strong interaction energy dependence. Now, it is well known that we may rotate the Feynman diagram for Coulomb scattering through and replace the outgoing by an incoming to obtain the one-photon annihilation graph. Here the photon is in the s channel. Transforming the DEHC graph in the same manner, we arrive at a graph depicting a point strong interaction between the electron and positron, resulting in the production of an s-channel vector meson which then undergoes strong decay to other hadrons (see Fig. 2 above). Final-state interactions, which will have a very high cross section at the energies involved, will serve to increase the mean hadron multiplicity detected. This analysis is similar to that usually presented for interactions, in which we assume that the vertex is pointlike and its inner structure is not determined.

By stating that the and vertices are pointlike, we have evaded the problem of how lepton number is conserved. We consider the ultimate annihilation of the electron and positron in an collision as a superstrong process which can occur only when the particle cores are brought within the superstrong interaction radius by another interaction. The electron core is defined to be lepton-numbered, and the superstrong interaction is the only interaction which conserves `number'. Since the core-gluon coupling is superstrong, the gluons in electrons must also be lepton-numbered. Thus, in collisions, the final superstrong core annihilation may occur, producing a vacuum state. However, in interactions, for example, no final core interaction may take place, since the superstrong interaction conserves `number' and the gluons in nucleons are hadron-numbered.

If , then no charge will reside in the electron's gluon cloud (unlike the situation for the nucleon meson cloud) and hence all the charge must be concentrated in the central core. This distribution of charge would further diminish the contribution of the electron's internal structure both to and to the electric form factor. If , then the gluon cloud could contribute to the electron charge.

We might expect hadrons and leptons to have similar gluonic core structures, and this idea is upheld by experiment. In interactions, where the nucleon meson cloud is unimportant and the core is probed, there is a slight rise in the total cross section. This may be caused by gluons beginning to evaporate from the central region (this mass scale is also suggested by lepton size considerations). Furthermore, the relation derived from generalized vector dominance (GVD) connecting to at high energies (Minami and Terada 1974; Minami 1975) may owe its surprising accuracy to hadron boiling from the proton gluon core, since at the core is probably the most significant part of the nucleon (as indicated by eN scaling at this energy).

In the model described above, we can perform a naive calculation of the electron self mass. Since we predict that the electron has a radius , the range of the gluon interaction must be times that of the strong interaction, so that we have (superstrong) (strong). The electron has an effective super-strong interaction area times the effective strong interaction area of the nucleon, and hence we predict . , that is, , in excellent agreement with experiment. An interesting possibility is that the weak interaction arises simply because of gluon evaporation from lepton and hadron cores (this would favour ).

The existence of a meson cloud in hadrons but not in leptons may be accounted for in terms of the difference in gluon content between the two classes of particle. In leptons there is only one type of gluon, while in hadrons there are three, perhaps corresponding to the three colours of quarks. The interaction potential due to a single type of gluon would be attractive for , and would then become repulsive just outside this radius (this could be the repulsion felt by two close fermions) and soon fall to zero. The three types of hadronic gluons will have slightly different masses, so that the ranges of their interactions will differ. In leptons the repulsive part of the one-gluon potential will disperse any meson cloud, but in hadrons the three gluon potentials will interfere, creating regions of slight attraction in which mesons will collect. These can undergo strong interactions with other hadrons (they will boil at a very low temperature) and hence a meson cloud will be held around the nucleon.

[ Figure 2 ] DEHC contribution to the anomalous magnetic moment of the electron.

Naive hadronic electron models predict that the pseudoscalar meson decay should receive contributions from DEHC, and experimentally it is found that (Davies et al. 1974). However, in the model proposed here, -parity or isospin conservation forbid all DEHC diagrams contributing to the process.

reactions should receive DEHC contributions via the third-order triangle graph (see Fig. 3), given by

where is the second-order vertex function in QED, which behaves as for large . Thus the integral (3) is logarithmically divergent, so that the high energy domain will be comparatively unimportant.

Results for agree with QED to within up to about . This is to be expected, since the hadronic core radius in hadrons is that in electrons, so that electron production via DEHC in high energy interactions will be suppressed by a factor relative to hadron production.

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