We perform the all orders resummation of threshold enhanced contributions for the Higgs boson pair production cross section via gluon fusion, including finite top quark mass (M t ) effects. We present results for the total cross section and Higgs pair invariant mass (M hh ) distribution. We obtain results at next-to-leading logarithmic accuracy (NLL) which retain the full M t dependence, and are matched to the full next-to-leading order (NLO) prediction. Our NLL+NLO results represent the most advanced prediction with full M t dependence for this process, and produce an increase of about 4% in the total cross section with respect to the NLO result for LHC energies, and for a central scale μ 0 = M hh /2. We also consistently combine the full NLL with the next-to-next-to-leading logarithmically (NNLL) accurate resummation computed in the Born-improved large-M t limit, and match it to the next-to-next-to-leading order approximation of ref. [1], so called NNLOFTa. We find that the resummation effects are very small at NNLL for μ 0 = M hh /2, in particular below 1% at 13 TeV, indicating that the perturbative expansion is under control. In all cases the resummation effects are found to be substantially larger for the central scale μ 0 = M hh , resulting in a more stable cross section with respect to scale variations than the fixed order calculation.
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