Unified Treatment of Hadronic Processes Involving High-Mass Virtual Photons

Abstract

A unified treatment of the three processes (I) lepton+proton \ensuremath{\rightarrow} lepton+hadrons, (II) proton+proton \ensuremath{\rightarrow} lepton pair+hadrons, and (III) lepton pair \ensuremath{\rightarrow} hadrons is presented. Our dynamical model is an off-mass-shell bootstrap theory of the hadrons. We show that the model predicts slow ${q}^{2}$ (photon mass squared) variation of the differential cross sections for processes I and II in spite of the fact that the model requires the elastic and quasi-elastic hadronic form factors to decrease faster than any power in ${q}^{2}$. The cross section for process III, however, is predicted to decrease rapidly in ${q}^{2}$ and to violate the scaling law observed for process I. More detailed predictions of multiplicities and angular distributions of the final states are made, as well as the surprising predictions that for large ${q}^{2}$, the ratio $\frac{(\frac{d\ensuremath{\sigma}}{d{q}^{2}})(pp\ensuremath{\rightarrow}pp+\mathrm{lepton}\mathrm{pair})}{(\frac{d\ensuremath{\sigma}}{d{q}^{2}})(pp\ensuremath{\rightarrow}\mathrm{pp}\ensuremath{\pi}+\mathrm{lepton}\mathrm{pair})}$ for process II and the ratio $\frac{\ensuremath{\sigma}(\mathrm{lepton}\mathrm{pair}\ensuremath{\rightarrow}\overline{p}p)}{\ensuremath{\sigma}(\mathrm{lepton}\mathrm{pair}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+\mathrm{real}\mathrm{photon})}$ for process III should both approach zero. The latter ratio should be comparable to 1 for ${q}^{2}\ensuremath{\simeq}6$ Be${\mathrm{V}}^{2}$.