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We obtain a simple analytic expression for the high energy $\gamma^*\gamma^*$ scattering cross section at the next-to-leading order in thelogarithms-of-energy power counting. To this end we employ the eigenfunctionsof the NLO BFKL equation constructed in our previous paper. We also constructthe eigenfunctions of the NNLO BFKL kernel and obtain a general form of thesolution for the NNLO BFKL equation, which confirms the ansatz proposed in ourprevious paper.

$\gamma^* \gamma^*$ Cross Section at NLO and Properties of the BFKL Evolution at Higher Orders