Abstract
In this article, we report how to use the "plus-type" subtraction scheme to deal with endpoint divergences in h\rightarrow\gamma\gammah→γγ or gg\rightarrow hgg→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_sαs. 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)ln3(−Mh2/mb2−i0) and resum to next-to-leading logarithm and beyond.
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