EPJ

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EPJ C - Particles and Fields
Particles and Fields
Eur. Phys. J. C 28, 483-493 (2003)
DOI: 10.1140/epjc/s2003-01174-8

QCD saturation and $\gamma^{*}$- $\gamma^{*}$ scattering

M. Kozlov1 and E. Levin1, 2

1  HEP Department, School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University, Tel Aviv, 69978, Israel
2  DESY Theory Group, 22603, Hamburg, Germany


(Received: 22 November 2002 / Revised version: 27 January 2003 / Published online: 5 May 2003 )

Abstract
Two photon collisions at high energy have an important theoretical advantage: the simplicity of the initial state, which gives us a unique opportunity to calculate these processes for large virtualities of both photons in the perturbative QCD approach. In this paper we study QCD saturation in two photon collisions in the framework of the Glauber-Mueller approach. The Glauber-Mueller formula is derived emphasising the impact parameter dependence ( bt) of the dipole-dipole amplitude. It is shown that non-perturbative QCD contributions are needed to describe the large bt behaviour, and the way how to deal with them is suggested. Our approach can be viewed as the model for the saturation in which the entire impact parameter dependence is determined by the initial conditions. The unitarity bound for the total cross section, its energy dependence as well as predictions for future experiments are discussed. It is argued that the total cross section increases faster than any power of $ \ln(1/x)$ in a wide range of energy or x, namely $\sigma(\gamma^*-\gamma^*)\,\propto\,(1/Q^2) \,\exp(a \sqrt{\ln(1/x)})\,\leq\,1/m^2_{\pi}$, where $\exp(a \sqrt{\ln(1/x)})$ reflects the x dependence of the gluon density $xG\,\propto \,\exp(2 \,a \sqrt{\ln(1/x)})$ and $m_{\pi}$ is the pion mass.



© Società Italiana di Fisica, Springer-Verlag 2003

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