Next-to-leading power SCET in Higgs amplitudes induced by light quarks

TL;DR

This paper develops a subtraction scheme within NLP SCET to handle endpoint divergences in Higgs production amplitudes induced by light quark loops, enabling precise calculations up to three loops and resummation of logarithms.

Contribution

It introduces a novel plus-type subtraction scheme with re-factorization conditions for endpoint divergences in Higgs amplitudes within NLP SCET, applicable to high-order loop calculations.

Findings

Successfully reproduces three-loop amplitudes with logarithmic accuracy.

Provides a systematic method for endpoint divergence subtraction in NLP SCET.

Enables resummation of logarithms beyond next-to-leading order.

Abstract

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.