We consider the production of pairs of Standard Model Higgs bosons via gluon fusion. Until recently the full dependence on the top quark mass $M_t$ was not known at next-to-leading order. For this reason we apply an approximation based on the expansion for large top quark masses up to $\mathcal{ O}(1/M_t^{ 12})$. At next-to-next-to-leading order we avoid the calculation of real corrections via the soft-virtual approximation and obtain top quark mass corrections up to $\mathcal{ O}(1/M_t^4)$. We use our results to estimate the residual uncertainty of the total cross section due to a finite top quark mass to be $\mathcal{ O}(10\%)$ at next-to-leading order and $\mathcal{ O}(5\%)$ at next-to-next-to-leading order.
Categories: hep-ph