Hadronic cross-sections in $\gamma \gamma$ processes and the next Linear Collider

Abstract. In this note we address the issue of theoretical estimates of the hadronic cross-sections for $\gamma\gamma$ processes. We compare the predictions of the mini-jet model with data as well as other models, highlighting the band of uncertainties in the theoretical predictions, as well as those in the final values of the $\sigma (\gamma \gamma \rightarrow{\mathrm{hadrons}}) $ extracted from the data. We find that the rise of $\sigma_{\gamma \gamma}^{\mathrm{tot}}$ with energy shown in the latest $\gamma \gamma$ data is in tune with the faster rise expected in the eikonal mini-jet models (EMM). We present an estimate of the accuracy with which this cross-section needs to be measured, in order to distinguish between the different theoretical models which try to “explain” the rise of total cross-sections with energy. We find that the precision of measurement required to distinguish the EMM-type models from the proton-like models, for $ 300 < s^{1/2}_{\gamma \gamma} < 500 $ GeV, is $\lesssim 20% $, whereas to distinguish between various proton-like models or among the different parametrisations of the EMM, a precision of $\lesssim 8$–9% or $\lesssim 6$–7%, respectively, is required. We also comment briefly on the implications of these predictions for hadronic backgrounds at the next linear collider (NLC) to be run in the $\gamma \gamma$ mode or $e^+e^-$ mode.