Double logarithmic contribution to Higgs pair production in the high-energy limit

We study the leading logarithmic QCD corrections to Higgs pair production in the high-energy limit, which originate from soft quark exchange in the Feynman diagram and are thus suppressed by the quark mass. It is found that triangle Feynman diagrams can be analyzed in the same way as single Higgs production mediated by bottom quarks [45-47], while for diagrams of box type we cannot get an all-order result due to the many more double logarithmic structures they own. In this paper we calculate the abelian corrections at three loops for the first time after obtaining the corresponding one- and two-loop leading logarithms, which are in total agreement with the analytical results in the literature.