ep - p h / 99 03 43 8 v 2 1 6 Ju n 19 99 Impact - picture predictions for the γγ total cross section at LEP

We show that the rising total cross section σ(γγ → hadrons) recently observed by the L3 and OPAL Collaborations at LEP are fully consistent with the impact-picture for high-energy scattering. The impact picture is then used to predict this total cross section at higher energies. These experimental results confirm once more the success of the theoretical approach, which predicted for the first time, nearly thirty years ago, the universal increase of total cross sections at high energies. Key-Words : Photon-photon total cross section, impact-picture approach. Number of figures : 1 March 1999 CPT-99/P.3793 CERN-TH/99-76 anonymous ftp: ftp.cpt.univ-mrs.fr Web address: www.cpt.univ-mrs.fr Unité Propre de Recherche 7061 Recently at LEP the L3 and OPAL Collaborations have produced new results on the total cross section σ(ee → eehadrons) for several values of the ee center of mass energy, up to √ s = 183GeV [1-3]. The analysis of these data allows to isolate the two-photon cross section σ(γγ → hadrons), which has been obtained in the range 5 ≤ Wγγ ≤ 145GeV . The lowest energy data [1], which corresponds to 5 ≤ Wγγ ≤ 75GeV , has revealed experimentally for the first time a rise for the twophoton cross section. This increasing energy dependence has been confirmed on the full energy range, as seen on Fig. 1, showing that the photon behaves pretty much like a hadron. Increasing total cross sections were first predicted nearly thirty years ago [4] entirely on theoretical grounds based on quantum field theory. Indeed, one of the starting point of that theoretical work was γγ scattering; see for example [5] and [6]. One of the results of this theory, sometimes referred to as the impact picture, is that there is a universal increase of all total cross sections at very high energies [4, 7]; see Eq.(1) below. It is the purpose of this letter to return to the root of the theory and apply it [8, 9] for comparison with the experimental data on γγ total cross section σ tot. In view of the recent experimental results [1-3], several theoretical attempts have been made to explain the behavior of σ tot. This energy behavior can be described by a Regge-type parametrization based on the exchange of Regge trajectories and Pomeron in the t-channel, which was used for all hadron total cross sections [10]. In early impact-picture predictions [8], a simple s dependence s was first obtained and later extensively used by several authors i.e. Ref.[10, 11]. However, a best fit to the LEP data by the L3 collaboration gives a higher power value [2]. The Dual Parton Model with unitarization constraint [12] gives a faster rise of the cross section, also the model of γγ scattering [13] where the total cross section receives contributions from three event classes, VDM processes, direct and anomalous processes. In the framework of eikonalized amplitudes, a model of mini-jet [14] explains the increase of the cross section through the rise of jet cross sections, while a model [15] using the vector dominance and an eikonalized form of the quarks and gluons interactions, reproduces the energy dependence of the total cross sections for pp, p̄p, γp and γγ. Returning to the impact picture, which is the basis of the present consideration, we have learned that the effective interaction strength increases with energy in the form [4, 7] s (ln s)c′ , (1) a simple expression in terms of two key parameters c and c. It should be emphasized that these two parameters are independent of the scattering process under consideration, i.e., the increase in the total cross section for example is universal. The scattering amplitude from the impact picture is given by