  In this paper, we present a dispersive analysis of the double-virtual
photon-photon scattering to two pions up to 1.5 GeV. Through unitarity, this
process is very sensitive to hadronic final state interaction. For the
$s$-wave, we use a coupled-channel $\pi\pi,\, K\bar{K}$ analysis which allows a
simultaneous description of both $f_0(500)$ and $f_{0}(980)$ resonances. For
higher energies, $f_2(1270)$ shows up as a dominant structure which we
approximate by a single channel $\pi\pi$ rescattering in the $d$-wave. In the
dispersive approach, the latter requires taking into account $t$- and
$u$-channel vector-meson exchange left-hand cuts which exhibit an
anomalous-like behavior for large space-like virtualities. In our paper, we
show how to readily incorporate such behavior using a contour deformation.
Besides, we devote special attention to kinematic constraints of helicity
amplitudes and show their correlations explicitly.
