No Track left behind: Graph-based Vertexing for long-lived Particle Reconstruction

TL;DR

This paper tackles the challenge of reconstructing displaced vertices from long-lived particles in fast-simulation environments by introducing a graph-based vertex finder together with an initialization-free Gauss–Newton vertex fitter. The approach is implemented as a self-contained Delphes module, GraphDisplacedVertexFinder, and augmented with LLPReconstruction for kinematic analyses, enabling turn-key LLP studies in phenomenology. Validation in an IDEA-like FCC-ee detector with exotic Higgs decays to heavy neutral leptons demonstrates high vertexing efficiency, purity, and resolution across a broad lifetime range, while enabling model-independent projections for $\mathrm{BR}(h\to NN)$ down to the $\sim\!10^{-5}$ level. The work provides a practical, open-source tool bridging phenomenology and experiment, applicable to future lepton colliders and adaptable to hadron colliders, thereby strengthening realistic LLP sensitivity studies in fast-simulation frameworks.

Abstract

Reconstruction of displaced vertices is a cornerstone of both precision flavour physics and searches for long-lived particles (LLPs) at colliders. While existing vertexing algorithms are highly optimised for primary and short-lived secondary vertices, they face limitations when confronted with the large displacements and heterogeneous topologies characteristic of LLP decays. In this work we present a new approach to displaced vertex reconstruction combining an initialisation-free robust vertex fitter with a graph-based track clustering strategy. The algorithm is implemented as a self-contained Delphes module and can be straightforwardly integrated into existing detector cards, providing a turn-key tool for phenomenological studies. This plug-and-play functionality fills a gap left by public software frameworks, which either lack displaced-vertex capabilities or are not readily usable in fast-simulation environments. We validate our approach in an IDEA-like FCC-ee detector, using Higgs-strahlung $e^+e^- \to Zh$ with exotic $h\to NN$ decays as a benchmark process. We demonstrate excellent efficiency, resolution, and purity across a broad range of lifetimes, and derive model-independent projections for the FCC-ee sensitivity to exotic Higgs branching fractions.

Figures (14)

• Figure 1: Vertex reconstruction efficiencies of $N$ decays binned in the transverse displacement $L_{xy}$ of the true $N$ decay position. For the different panels we have assumed proper $N$ lifetimes $c\tau(N)\in[10,100,1000]\:\mathrm{mm}$ (as indicated).
• Figure 2: Vertex reconstruction efficiencies of $N$ decays binned in the transverse and longitudinal displacement $L_{xy}$ and $L_z$ of the true $N$ decay position. For the different panels we have assumed proper $N$ lifetimes $c\tau(N)\in[10,100,1000]\:\mathrm{mm}$ (as indicated).
• Figure 3: Left: Purity of the reconstructed vertices depending on the amount of tracks per reconstructed vertex. Right: Distribution of track multiplicities of the reconstructed vertices.
• Figure 4: Spatial vertexing resolution in the transverse direction (see text for details), exemplified by $x$, depending on the $N$ decay position $L_{xy}$. Data points with (binomial) error bars indicate the bootstrapped residual widths in each bin, while the orange line denotes the median of the post-fit vertex uncertainty. Vertical dashed lines denote the different barrel layers of the tracking system as indicated in the legends.
• Figure 5: Spatial vertexing resolution in the longitudinal direction (see text for details), depending on the $N$ decay position $L_{xy}$. Data points with (binomial) error bars indicate the bootstrapped residual widths in each bin, while the orange line denotes the median of the post-fit vertex uncertainty. Vertical dashed lines denote the different barrel layers as indicated in the legends.