  We investigate the resummation effects in the Standard Model Higgs boson pair
production through gluon-gluon fusion at the LHC with soft-collinear effective
theory. We calculate the total cross section and the invariant mass
distribution at Next-to-Next-to-Leading-Logarithmic level with $\pi^2$-enhanced
terms resummed, which are matched to the QCD Next-to-Leading Order results. In
the high order QCD predictions exact top quark mass effects are included in
full form factors. Our results show that the resummation effects increase the
Next-to-Leading Order results by about $20% \sim 30%$, and the scale
uncertainty is reduced to 8%, which lead to increased confidence on the
theoretical predictions. The PDF+$\as$ uncertainties are almost not changed
after including resummation effects. We also study the sensitivities of the
total cross section and the invariant mass distribution to the Higgs boson
self-coupling. We find that the total cross section and the invariant mass
distribution shape depend strongly on the Higgs boson self-coupling, and
therefore it is possible to extract Higgs boson self-coupling from the total
cross section and invariant mass distribution when the measurement precision
increases at the LHC.
