Power Corrections for N-Jettiness Subtractions at ${\cal O}(α_s)$

TL;DR

This work develops a complete framework for NLP power corrections to N-jettiness subtractions at NLO for color-singlet production, deriving master formulas within SCET$_{\text{I}}$, and delivering explicit kernels for all partonic channels in Drell-Yan and gluon-fusion Higgs production. By proving (and exploiting) universality in the soft and collinear limits and by treating Born measurements differentially in $Q$ and $Y$, the authors provide fully differential NLP results that align with existing numerical extractions and substantially improve subtraction efficiency. The results demonstrate that including NLL NLP terms dramatically reduces residual power corrections and enhances numerical stability across rapidity, with strong agreement against MCFM. The methodology sets the stage for extending NLP subtractions to higher orders and more complex processes, offering precise, differential control over subleading power effects crucial for high-precision collider phenomenology.

Abstract

We continue the study of power corrections for $N$-jettiness subtractions by analytically computing the complete next-to-leading power corrections at $\cal{O}(α_s)$ for color-singlet production. This includes all nonlogarithmic terms and all partonic channels for Drell-Yan and gluon-fusion Higgs production. These terms are important to further improve the numerical performance of the subtractions, and to better understand the structure of power corrections beyond their leading logarithms, in particular their universality. We emphasize the importance of computing the power corrections differential in both the invariant mass, $Q$, and rapidity, $Y$, of the color-singlet system, which is necessary to account for the rapidity dependence in the subtractions. This also clarifies apparent disagreements in the literature. Performing a detailed numerical study, we find excellent agreement of our analytic results with a previous numerical extraction.

Figures (11)

• Figure 1: Comparison of the $Y$-integrated LL power correction for hadronic $\mathcal{T}$ for $gg\to Hg$. The solid red and blue dashed curves show the LL results keeping only $\ln(\mathcal{T}/m_H)$. In the long-dashed orange and dotted light blue curves we keep all $\ln(\mathcal{T} e^{\pm Y}/m_H)$ or $\ln[\mathcal{T}/(\tilde{x}_{a,b} E_\mathrm{cm})]$ terms. In both cases, our result in eq. \ref{['eq:sigma_ggHg_had_LL_1']} and the result of ref. Boughezal:2018mvf in eq. \ref{['eq:sigma_ggHg_LL_had_lit']} agree. The small difference in the second case arises due to the fact that $e^{\pm Y}/m_H$ is not exactly the same as $\tilde{x}_{a,b} E_\mathrm{cm}$.
• Figure 2: The ${\mathcal{O}}(\alpha_s)$ nonsingular corrections for $Z$ production for the $q\bar{q}$ channel (top row) and the $qg+gq$ channel (bottom row). A fit to the nonsingular data is shown by the solid red curve. The LL and NLL results are shown by green dotted and blue dashed curves, respectively. In all cases, the NLL approximation provides an excellent approximation to the complete nonsingular cross section.
• Figure 3: The power corrections for the cumulative $\Delta\sigma(\tau_{\mathrm{cut}})$ at ${\mathcal{O}}(\alpha_s)$ for $Z$ production in the $q\bar{q}$ channel (top row) and $qg+gq$ channel (bottom row). In both cases, after the inclusion of the NLL power corrections, $\Delta\sigma(\tau_{\mathrm{cut}})$ is reduced by a factor of 100 or more for $\tau_{\mathrm{cut}} < 10^{-2}$.
• Figure 4: Same as fig. \ref{['fig:fitNLO']} for the hadronic $\mathcal{T}$ definition.
• Figure 5: Same as fig. \ref{['fig:cumulantNLO']} for the hadronic $\mathcal{T}$ definition.