  In this article, we report how to use the "plus-type" subtraction scheme to
deal with endpoint divergences in $h\rightarrow\gamma\gamma$ or $gg\rightarrow
h$ amplitudes induced by light quark loop, which can be formulated by
next-to-leading power (NLP) SCET. This subtraction is ensured by two
re-factorization conditions, which have been proven to all orders in
$\alpha_s$. Based on these conditions, cutoffs emerge naturally after some
re-arrangements to handle endpoint divergences and renormalization is
compatible with that. Our formalism can analytically reproduce three-loop
amplitudes up to $\ln^3(-M_h^2/m_b^2-i0)$ and resum to next-to-leading
logarithm and beyond.
