FFTJet: A Package for Multiresolution Particle Jet Reconstruction in the Fourier Domain

This article describes the FFTJet software package designed to perform jet reconstruction in the analysis of high energy physics experimental data. A two-stage approach is adopted in which pattern recognition is performed first, utilizing multiresolution filtering techniques in the frequency domain. Jet energy reconstruction follows, conditional upon the choice of signal topology. The method is efficient, global, collinear and infrared safe, and allows the user to identify and avoid the event topology bifurcation points when energy reconstruction is performed.

💡 Research Summary

The FFTJet software package introduces a novel two‑stage framework for reconstructing particle jets in high‑energy physics experiments. Unlike traditional seed‑based clustering algorithms, FFTJet first transforms the event’s transverse energy distribution into the frequency domain using a two‑dimensional Fast Fourier Transform (FFT) on an η–φ grid. In this domain, multiresolution filters—such as Gaussian, Laplacian, or wavelet kernels—are applied at a series of scales. Each filter selectively amplifies structures of a particular size: high‑frequency components highlight fine sub‑jets, while low‑frequency components capture the overall jet shape. After filtering, an inverse FFT returns a set of scale‑specific energy density maps in real space. Local maxima in these maps are identified as candidate jet axes, providing a global, seed‑independent pattern‑recognition step that is intrinsically infrared (IR) and collinear safe because the filtering operation is linear.

The second stage performs conditional energy reconstruction. For each candidate axis the user specifies a signal topology (e.g., a cone, anti‑kt‑like distance measure, or a custom shape). A window function, whose radius is tied to the resolution scale of the first stage, is centered on the axis and used to sum the transverse momentum of particles (or grid cells) inside the window. This yields a jet four‑momentum estimate that respects the chosen topology. Crucially, the algorithm monitors “bifurcation points”: when two or more local maxima become sufficiently close that they would merge into a single energy plateau at a coarser scale, FFTJet flags the event and either halts reconstruction at that scale or switches to a different scale according to user‑defined rules. By avoiding reconstruction at ambiguous scales, the method prevents the over‑ or under‑estimation of jet energy that can occur when jets split or merge.

From a computational standpoint, FFTJet leverages the FFTW library to achieve O(N log N) performance for the Fourier transforms, where N is the number of grid cells. The subsequent filtering and peak‑finding steps are linear in N, making the whole pipeline scalable to events with millions of particles. Periodic boundary effects are mitigated by padding the η–φ grid, and the software provides a plug‑in architecture for custom filters and window functions, allowing analysts to tailor the algorithm to specific physics goals such as boosted‑object tagging or pile‑up mitigation.

Safety properties are built‑in: the linear filtering guarantees IR and collinear safety, and the deterministic, global nature of the peak search eliminates seed bias. Comparative studies reported in the paper show that FFTJet matches or exceeds the energy resolution and angular accuracy of widely used algorithms like anti‑kt and Cambridge/Aachen, especially in high pile‑up environments where its global frequency‑domain filtering naturally suppresses diffuse background. Moreover, the multiresolution approach yields a natural hierarchy of sub‑jets, facilitating substructure analyses without additional grooming steps.

In summary, FFTJet offers a powerful, efficient, and theoretically robust alternative to conventional jet reconstruction techniques. By performing pattern recognition in the Fourier domain, employing scale‑dependent filters, and incorporating explicit handling of topology bifurcations, it delivers global, seed‑free jet finding that is both infrared/collinear safe and adaptable to a wide range of experimental conditions. This makes it a valuable tool for current and future collider experiments that demand high precision, fast execution, and flexibility in jet definition.