N-Jettiness Subtractions for $gg\to H$ at Subleading Power

Abstract

$N$-jettiness subtractions provide a general approach for performing fully-differential next-to-next-to-leading order (NNLO) calculations. Since they are based on the physical resolution variable $N$-jettiness, ${\mathcal{T}}_N$, subleading power corrections in $\tau ={\mathcal{T}}_N/Q$, with $Q$ a hard interaction scale, can also be systematically computed. We study the structure of power corrections for $0$-jettiness, ${\mathcal{T}}_0$, for the $gg\to H$ process. Using the soft-collinear effective theory we analytically compute the leading power corrections ${\alpha }_s\tau \ln \tau$ and ${\alpha }_s^2\tau {\ln }^3\tau$ (finding partial agreement with a previous result in the literature), and perform a detailed numerical study of the power corrections in the $gg$, $gq$, and $q\bar{q}$ channels. This includes a numerical extraction of the ${\alpha }_s\tau$ and ${\alpha }_s^2\tau {\ln }^2\tau$ corrections, and a study of the dependence on the ${\mathcal{T}}_0$ definition. Including such power suppressed logarithms significantly reduces the size of missing power corrections, and hence improves the numerical efficiency of the subtraction method. Having a more detailed understanding of the power corrections for both $q\bar{q}$ and $gg$ initiated processes also provides insight into their universality, and hence their behavior in more complicated processes where they have not yet been analytically calculated.

16 pages, 12 figures

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