γγ Cross-sections and γγ colliders

We summarize the predictions of different models for total cross-sections. The experimentaly observed rise of �γγ with √ sγγ, faster then that for �¯ pp, �γp is in agreement with the predictions of the Eikonalized Minijet Models as opposed to those of the Regge-Pomeron models. We then show that a measurement of �γγ with an accuracy of / 8 − 9%(6 − 7%) is necessary to distinguish among different Regge-Pomeron type models (among the different parametrisations of the EMM models) and a precision of / 20% is required to distinguish among the predictions of the EMMs and of those models which treat like ’photon like a proton’, for the energy range 300 < √ sγγ < 500 GeV. We further show that the difference in model predictions for �γγ of about a factor 2 at √ sγγ = 700 GeV reduces to ∼ 30% when folded with bremsstrahlung spectra to calculate �(e + e → e + e → e + e X). We point out then the special role that colliders can play in shedding light on this all-important issue of calculation of total hadronic cross-sections.