  We propose a new method to calculate analytically higher-order perturbative
corrections and we apply it to the calculation of the two-loop virtual
corrections to Higgs pair production through gluon fusion. The method is based
on the expansion of the amplitudes in terms of a small Higgs transverse
momentum. This approach gives a very good approximation (better than per-mille)
of the partonic cross section in the center of mass energy region
$\sqrt{\hat{s}} \lesssim 750$ GeV, where $\sim95\%$ of the total hadronic cross
section is concentrated. The presented method is general and can be applied in
a straightforward way to the computation of virtual higher-order corrections to
other $2\to2$ processes, representing an improvement with respect to
calculations based on heavy mass expansions.
