Higgs pair production at next-to-next-to-leading logarithmic accuracy at the LHC

We perform the threshold resummation for Higgs pair production in the dominant gluon fusion channel to next-to-next-to-leading logarithmic (NNLL) accuracy. The calculation includes the matching to the next-to-next-to-leading order (NNLO) cross section obtained in the heavy top-quark limit, and results in an increase of the inclusive cross section up to 7% at the LHC with centre-of-mass energy E-cm = 14TeV, for the choice of factorization and renormalization scales mu(F) = mu(R) = Q, being Q the invariant mass of the Higgs pair system. After the resummation is implemented, we estimate the theoretical uncertainty from the perturbative expansion to be reduced to about +/- 5.5%, plus similar to 10% from finite top-mass effects. The resummed cross section turns out to be rather independent of the value chosen for the central factorization and renormalization scales in the usual range (Q/2, Q).