Expanding Protons Seen by Hera

We show that the rising total photoproduction cross section recently observed at HERA is entirely consistant with the impact-picture in the theory of expanding protons which was proposed more than twenty years ago. More accurate data, which is expected to be forthcoming soon, will give this prediction a stringent test. Key-Words : Total photon cross section, impact-picture. Number of figures : 2 August 1994 CPT-94/P.3060 CERN-TH/7387/94 anonymous ftp or gopher: cpt.univ-mrs.fr ∗ Unité Propre de Recherche 7061 1 CERN Geneva, Switzerland and Gordon McKay Laboratory, Harvard University, Cambridge, MA 02138, U.S.A. 2 Work supported in part by the US Department of Energy under Grant N◦. DE-FG0284ER40158 and the Joint Service Electronics Program under Grant N00014-89-J-1023. Recently at HERA, theH1 and ZEUS detectors have measured the photoproduction total cross section at an average γp center of mass energy of 180 GeV . They confirm the previous and less accurate result of ZEUS and indicate that this total cross section is rising. This rise has caused a lot of excitement and vastly different rates of increase have been proposed which are based either on minijet contributions or on Regge type analyses. In this letter we will present a very simple approach to this increasing γp total cross section. Increases of hadron-hadron total cross sections have been theoreticaly predicted some years ago and these predictions have been accurately verified by experiment. The theoretical predictions were based on the multi-tower diagrams shown in fig.1a for pp and pp and fig.1b for πp elastic scattering. The multi-tower diagrams for γp are shown in fig.1c. The similarity of the diagrams in fig.1b and fig.1c implies that the γp total cross section can be related approximately to those of πp. The major differences between these two figures are i) The electromagnetic coupling e appears twice in fig.1c. ii) The photon is its own antiparticle. Because of those two differences it is natural to expect σtot(γp) = (const.)α ( σtot(π p) + σtot(π p) ) (1) where α is the fine structure constant. This eq.(1) should hold for all center of mass energies above about 10GeV . The constant is to be determined from 1 the low energy γp total cross section data. Note that the contribution from ρ-exchange is cancelled in the sum, as it should be. For σtot(π p) we have used the early impact picture predictions where a simple s dependence s was first given and later extensively used by various authors. Using these results it is found that the constant in eq.(1) is 1/3 and thus the predicted γp total cross section is shown in fig.2. The HERA data is surely going to improve rapidly and we are eager to see a much more accurate determination of the γp cross section. Thus we have encountered the expanding proton unambigously in two different experimental situations. In both cases, pp and γp, the next major increase in energy will come from LHC. In these cases the center of mass energy will reach 16 TeV for pp are more than 1 TeV for γp using electrons from LEP. Moreover using extracted π and π beams from LHC, the πp cross sections could be measured up to about √ s = 120 GeV . This will provide a most stringent test of the accuracy of our relation (1).