Jet Production at NNLO: Exploring a New Scheme

TL;DR

The paper introduces a novel non-local NNLO subtraction scheme for jet final states and applies it to dijet production in $e^+e^-$ annihilation and $H\to b\bar b$ decays, leveraging a $q_T$-like slicing variable $\mathfrak{q}$ with a cut $\mathfrak{q}_{\mathrm{cut}}$ to obtain fully differential cross sections. It provides a detailed perturbative framework including the hard, jet, and soft functions, a subtracted soft function computed with zero-bin subtractions, and a factorisation-breaking term that arises in certain recombination schemes; the NNLO corrections are assembled into the below-cut cross section with explicit coefficients in both $E$-scheme and WTA schemes, and validated against thrust-based results. Numerical results show excellent convergence to the known analytic coefficients and high precision, with the $H\to b\bar b$ channel achieving per-mille accuracy and the $e^+e^-\to 2$ jets channel around 2% due to cancellations among color structures. The work demonstrates the viability of non-local NNLO jet computations and lays groundwork for extending to more complex processes and resummation contexts.

Abstract

We consider dijet production in $e^+e^-$ collisions and in $H\to b{\bar b}$ decays at next-to-next-to-leading order (NNLO) in perturbative QCD. A new non-local subtraction scheme is applied, for the first time, to obtain the fully differential cross section for these benchmark processes. We discuss and explicitly evaluate the perturbative ingredients needed in the computation, and we compare the performance of different slicing variables to obtain the NNLO corrections.

Figures (2)

• Figure 1: NNLO correction in the various colour channels computed with different variables as a function of the slicing parameter. The exact result is shown in blue.
• Figure 2: As in Fig. \ref{['fig:Ajj']} but for ${H\to b{\bar{b}}}$.