Next-to-leading power corrections to $V+1$ jet production in $N$-jettiness subtraction

TL;DR

This paper derives next-to-leading-power (NLP) corrections to the N-jettiness factorization theorem for 1-jet processes, using vector boson plus jet production as a concrete example. By applying expansion by regions and a subleading soft theorem, the authors obtain analytic NLP-LL corrections that separate into universal phase-space factors and process-dependent matrix-element corrections, valid differentially in $Q^2$, $Y$, $p_T$, $\eta$, and $\mathcal{T}$. The work also outlines NLP-NLL contributions, demonstrates pole cancellation across soft, beam, and jet sectors (including non-hemisphere terms), and provides numerical validation against fitted coefficients, showing good agreement for inclusive and differential cross sections. Additionally, the paper discusses how choices of the $\rho_i$ parameters and frame definitions can influence the size of power corrections, suggesting strategies to reduce NLP effects and outlining directions for extending the analysis to NLP-NNLO. The results enhance the predictive power of the N-jettiness subtraction method by analytically capturing subleading power effects that become relevant at high-precision LHC data analyses.

Abstract

We discuss the subleading power corrections to one-jet production processes in $N$-jettiness subtraction using vector-boson plus jet production as an example. We analytically derive the next-to-leading power leading logarithmic corrections (NLP-LL) through ${\cal O}(α_S)$ in perturbative QCD, and outline the calculation of the next-to-leading logarithmic corrections (NLP-NLL). Our result is differential in the jet transverse momentum and rapidity, and in the vector boson momentum squared and rapidity. We present simple formulae that separate the NLP corrections into universal factors valid for any one-jet cross section and process-dependent matrix-element corrections. We discuss in detail features of the NLP corrections such as the process independence of the leading-logarithmic result that occurs due to the factorization of matrix elements in the subleading soft limit, the occurrence of poles in the non-hemisphere soft function at NLP and the cancellation of potential $\sqrt{\mathcal{T}_1/Q}$ corrections to the $N$-jettiness factorization theorem. We validate our analytic result by comparing them to numerically-fitted coefficients, finding good agreement for both the inclusive and the differential cross sections.

Figures (5)

• Figure 1: Behavior of the NLO cross section as a function of $\mathcal{T}_{\text{cut}}$. The red line represents the leading power result, while the blue line includes the NLP-LL power corrections. The difference between the top and the bottom insets is the jet algorithm choice for the leading power result. In the top plot, we use MCFM with an anti-$k_T$ pre-clustering jet algorithm. In the bottom plot, we use $N$-jettiness itself as a jet algorithm.
• Figure 2: Full nonsingular cross section as a function of $\mathcal{T}_{\text{cut}}$ as defined in Eq. \ref{['eq:fullnonsing']} for the inclusive case. The solid red line represents a fit of the form Eq. \ref{['eq:fullnonsingfit']}. The data refers to the numerical results from our code for $Z$+jet production. The solid green line indicates the analytic leading logarithmic power corrections, normalized to the LO cross section.
• Figure 3: On the left we show plots analogous to Fig. \ref{['fig:powcorrplot']}. On the right we show plots analogous to Figure \ref{['fig:nonsingularinclusive']} for the differential cross section at the values $\eta=2$ (top), $p_T=50$ GeV (middle) and $Y=2$ (bottom).
• Figure 4: Analogous to Figure \ref{['fig:diffplots']} but for the inclusive cross section in the $qg$ channel.
• Figure 5: $\mathcal{T}_{\text{cut}}$ dependence of the cross section according to three combination of the normalization factors: the hadronic definition ($\rho_a=\rho_b=\rho_J=1$), the boosted definition \ref{['eq:boosteddef']} and the minimal definition \ref{['eq:minimaldef']}.