Factorization at Next-to-Leading Power and Endpoint Divergences in $gg\to h$ Production

We derive a factorization theorem for the Higgs-boson production amplitude in gluon-gluon fusion induced by a light-quark loop, working at next-to-leading power in soft-collinear effective theory. The factorization is structurally similar to that obtained for the h → γγ decay amplitude induced by a light-quark loop, but additional complications arise because of external color charges. We show how the refactorization-based subtraction scheme developed in previous work leads to a factorization theorem free of endpoint divergences. We use renormalization-group techniques to predict the logarithmically enhanced terms in the three-loop gg → h form factor of order $ {\alpha}_s^3{\ln}^k\left(-{M}_h^2/{m}_b^2\right) $ with k = 6, 5, 4, 3. We also resum the first three towers of leading logarithms, $ {\alpha}_s^n{\ln}^{2n-k}\left(-{M}_h^2/{m}_b^2\right) $ with k = 0, 1, 2, to all orders of perturbation theory.