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

TL;DR

This work analyzes N-jettiness subtractions for $gg\to H$ at subleading power, focusing on 0-jettiness and using SCET to derive leading-logarithmic NLP corrections at NLO and NNLO across partonic channels. It couples analytic results with a detailed numerical study against full $H+1$ jet NLO results to quantify the impact of NLP terms on subtraction efficiency and to explore rapidity and observable-definition effects. The findings show that including LL NLP corrections substantially reduces missing power corrections, especially in the dominant $gg$ channel, and highlight a substantial dependence on the $\mathcal{T}_0$ definition, favoring the leptonic definition for stable, nearly rapidity-independent behavior. The work also draws connections to Drell-Yan universality and lays groundwork for computing NLL terms and extending the approach to more complex processes in the pursuit of efficient, accurate NNLO calculations for LHC Run 2 and beyond.

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 $τ=\mathcal{T}_N/Q$, 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 $α_s τ\lnτ$ and $α_s^2 τ\ln^3τ$ (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 $α_sτ$ and $α_s^2 τ\ln^2τ$ 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.

Figures (12)

• Figure 1: An estimate of the missing power corrections $\Delta \sigma(\tau_{\mathrm{cut}})$ based on their functional form at NLO (green), NNLO (blue), and N$^3$LO (orange). The solid (dashed) lines correspond to the (N)LL power corrections, showing the possible improvement by removing the LL corrections. On the left, the estimate is normalized to the full N$^n$LO contribution, while on the right it is normalized to the LO cross section (assuming a 30% correction of each perturbative order relative to the previous order). In both cases, the bands around the LL estimate illustrates a factor of $3$ variation.
• Figure 2: Representative NLO diagrams for Category 1. In (a) a gluon becomes soft, and in (b) two gluons become collinear. Collinear particles are shown in light blue, soft particles in orange. The power counting of the hard-scattering operators and Lagrangian insertions is explicitly indicated.
• Figure 3: Representative NLO diagrams for Category 2. In (a) a quark becomes soft, and in (b) a quark and a gluon become collinear. The power counting of the hard-scattering operators and Lagrangian insertions is explicitly indicated.
• Figure 4: Two-loop hard-collinear contributions, which are used to compute the LL divergence at subleading power. The grey circle represents a one-loop hard virtual correction. (a) shows the contributions to category 1, when two gluons become collinear, and (b) shows the contributions to category 2 (b), when a quark and a gluon become collinear.
• Figure 5: Representative diagrams contributing to $\sigma_{gq}$, where either a soft quark crosses the cut (a), or a collinear quark crosses the cut (b). One-loop corrections to these diagrams give rise to the $C_F(C_F+C_A) \ln^3\tau$ structure at NNLO.