QCD factorizations in γ∗γ∗→ρL0ρL0

We calculate the lowest order QCD amplitude, i.e. the quark exchange contribution, to the forward production amplitude of a pair of longitudinally polarized ρ mesons in the scattering of two virtual photons γ∗(Q1)γ∗(Q2)→ρL0ρL0. We show that the scattering amplitude simultaneously factorizes in two quite different ways: the part with transverse photons is described by the QCD factorization formula involving the generalized distribution amplitude of two final ρ mesons, whereas the part with longitudinally polarized photons takes the QCD factorized form with the γL∗→ρL0 transition distribution amplitude. Perturbative expressions for these, in general, non-perturbative functions are obtained in terms of the ρ-meson distribution amplitude.