A new suite of Lund-tree observables to resolve jets

TL;DR

Lund-Tree Shapes (LTS) define a unified, declustering-based set of observables from the Lund jet plane that probe the geometry and hierarchy of QCD radiation in multi-jet final states. They provide both differential, global event-shape–like variables and integrated jet-rate–like observables that apply to any number of jets and to groomed jets, across $ee$, $pp$, and $ep$ collisions. The authors develop an all-order NNLL resummation framework, show the absence of non-global logarithms, and achieve NNLL+NNLO predictions for the LHC with detailed phenomenological studies of hadronisation and multi-parton interactions, demonstrating a robust tool for precision QCD and jet-veto analyses. The work establishes LTS as a versatile, theoretically clean approach to characterise multi-jet final states and to benchmark parton showers in diverse collider environments.

Abstract

We introduce a class of collider observables, named Lund-Tree Shapes (LTS), defined from declustering trees originating from the Lund jet plane representation of the QCD radiation pattern in multi-jet scattering processes. At the differential level, they are continuous global variables akin classical event shapes and $n\to n+1$ jet-resolution parameters, which probe the geometry and hierarchical structure of the radiation in an event. At the integrated, cumulative level, they naturally define $n$ jet rates, providing a jet-multiplicity-based characterisation of multi-jet final states. Their definition applies to scattering processes with any number of resolved jets in the final state, as well as to groomed jets. They are thus usable as resolution variables in the context of higher-order calculations via phase-space slicing, matching fixed-order calculations to parton showers, and testing the logarithmic accuracy of shower algorithms. From a theoretical viewpoint, such observables feature a simple all-order structure and are free of non-global logarithmic corrections. As an initial application, we derive next-to-next-to-leading-logarithmic accurate predictions for processes with two QCD legs at $e e$, $pp$ and $e p$ colliders, and matched predictions to next-to-next-to-leading order for the LHC, discussing aspects of collider phenomenology.

Figures (15)

• Figure 1: An illustration of LTS for two $Z$+jet events: $(a)$ In this event there are no primary declusterings from the beam, while the jet contains a primary declustering resulting from the recombination of emissions $g_2$ and $g_3$; $(b)$ In this event the jet contains no primary declusterings, while there are two primary declusterings from the beam corresponding to the (primary) emissions $g_2$ and $g_3$. The two-sided arrows indicate the Lund measures that enter the definition of the LTS.
• Figure 2: Location of NNLL corrections to the transfer function in the Lund plane of the Born $q\bar{q}$ system.
• Figure 3: Location of NNLL corrections in the Lund plane when computing $b$-dependent LTS for $pp$ events with rapidity defined in the event frame (purple) or in the frame where the colour singlet has zero rapidity (blue).
• Figure 4: Difference between the fixed-order and resummed-expanded differential cross sections, normalised to the Born cross section, c.f. Eq. \ref{['eq:deltaFFO']}, for DY (blue) and gluon fusion Higgs (red) production. We consider three values of $b$, $b=0$ (left), $b=1/2$ (middle) $b=1$ (right). The top panel shows the NLO comparison for $S_{b}^{(0)}$/$M_{b}^{(0)}$. The middle (bottom) panel shows the NNLO comparison for $M_{b}^{(0)}$ ($S_{b}^{(0)}$). The bands show the statistical uncertainty.
• Figure 5: Differential distribution for $M_{b}^{(0)}$ with $b=0$ (left), $b=1/2$ (middle) and $b=1$ (right) as a function of $\bar{v} = v\,Q$. The black dotted curve represents the NNLO result, the yellow dashed curve the NLO+NLL result, the blue (red) solid curve the NNLL+NNLO result with $p=2$ ($p=4$) in Eq. \ref{['eq:muLtilde']}. The green curve shows the NNLL+NNLO result with $p=2$ and $v_M = 0.8$. Scale uncertainties (computed as explained in the text) are indicated via the opaque bands. The middle panel shows the ratio of the NLO+NLL and NNLO results with respect to the NNLL+NNLO with $p=2$ ($v_M = 1$) result. The bottom panel shows the ratio of the NNLO+NNLO result with $p=4$ and that with $p=2$ and $v_M = 0.8$ to the $p=2$, $v_M = 1$ result.