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Using soft-collinear effective theory (SCET), we examine the 1/m b corrections to the factorization formulas for inclusive semi-leptonic B decays in the endpoint region, where the hadronic final state consists of a single jet. At tree level, we find a new contribution from four-quark operators that was previously assumed absent. Beyond tree level many sub-leading shape-functions are needed to correctly describe the decay process.

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We present the calculation of the full next-to-leading order (NLO) QCD corrections to Higgs boson pair production via gluon fusion at the LHC, including the exact top-mass dependence in the two-loop virtual and one-loop real corrections. This is the first independent cross-check of the NLO QCD corrections presented in the literature before. Our calculation relies on numerical integrations of Feynman integrals, stabilised with integration-by-parts and a Richardson extrapolation to the narrow width approximation. We present results for the total cross section as well as for the invariant Higgs-pair-mass distribution at the LHC, including for the first time a study of the uncertainty due to the scheme and scale choice for the top mass in the loops.