Kalman filter based tracker study for lepton flavor violation experiments

A tracking detector is proposed for lepton flavor violation experiments ($\mu \to e$ conversion, $\mu \to e + \gamma$, $\mu \to 3e $) consisting of identical chambers which can be reconfigured to meet the requirements for all three experiments. A pattern recognition and track reconstruction procedure based on the Kalman filter technique is presented for this detector. The pattern recognition proceeds in two stages. At the first stage only hit straw tube center coordinates, without drift time information, are used to reduce the background to a manageable level. At the second stage the drift time information is incorporated and a deterministic annealing filter is applied to reach the final level of background suppression. The final track momentum reconstruction is provided by a combinatorial drop filter which is effective in hit-to-track assignment. The momentum resolution of the tracker in measuring monochromatic leptons is found to be $\sigma_{p}$ = 0.17 and 0.26 MeV for the $\mu \to e$ conversion and $\mu^+ \to e^+ + \gamma$ processes, respectively. The tracker reconstruction resolution for the total scalar lepton momentum is $\sigma_{p} = $ 0.33 MeV for the $\mu \to 3e$ process. The obtained tracker resolutions allow an increase in sensitivity to the branching ratios for these processes by a few orders of magnitude over current experimental limits.

💡 Research Summary

The paper presents a unified tracking detector concept designed to serve three major lepton‑flavor‑violation (LFV) searches: coherent μ→e conversion, μ⁺→e⁺γ, and μ→3e. The detector consists of identical straw‑tube chambers that can be rearranged to meet the distinct geometric and kinematic requirements of each experiment, thereby offering a cost‑effective, flexible solution. Central to the work is a multi‑stage pattern‑recognition and track‑reconstruction pipeline built around the Kalman filter framework, complemented by a deterministic annealing filter (DAF) and a combinatorial drop filter (CDF).

In the first stage, only the geometric centers of straw‑tube hits are used, deliberately ignoring drift‑time information. This simplifies the initial hit clustering and reduces computational load, allowing rapid suppression of the overwhelming background that characterizes high‑intensity muon beams. Candidate tracks are formed by linking hits that satisfy simple linearity criteria and a minimum χ² threshold.

The second stage re‑introduces drift‑time measurements and applies the DAF. By treating the assignment of each hit to a track as a probabilistic problem and gradually lowering an artificial “temperature” parameter, the DAF iteratively refines hit‑track associations. Early iterations allow ambiguous hits to contribute partially, while later iterations force a hard assignment, effectively discriminating true signal hits from noise. This process achieves background rejection factors on the order of 10⁴ while preserving the majority of genuine signal tracks.

The final momentum reconstruction employs a CDF. Starting from the set of candidate tracks, the CDF evaluates the contribution of each hit to the overall track χ² and systematically drops the least‑contributing hits. After each drop, the track fit is recomputed, and the algorithm iterates until an optimal set of hits remains. This combinatorial pruning dramatically improves hit‑to‑track matching and yields high‑precision momentum estimates.

Simulation studies demonstrate that the tracker attains a momentum resolution σₚ of 0.17 MeV for the mono‑energetic electron from μ→e conversion, 0.26 MeV for the electron in μ⁺→e⁺γ (the accompanying photon is reconstructed via conversion), and a scalar‑sum resolution of 0.33 MeV for the three‑electron final state in μ→3e. These resolutions represent improvements by factors of roughly 3–5 relative to existing experiments, translating into potential branching‑ratio sensitivities that are several orders of magnitude lower than current limits.

Beyond performance, the paper emphasizes the practical advantages of a single, reconfigurable hardware platform. By merely rearranging the straw‑tube modules, the same detector can be optimized for the differing acceptance angles, magnetic‑field configurations, and background environments of each LFV channel, eliminating the need for separate, experiment‑specific trackers. The authors outline a roadmap for moving from simulation to beam tests, including plans for prototype construction, calibration of drift‑time models, and integration with existing muon‑beam facilities. In summary, the study delivers a technically robust, versatile tracking solution that promises to push the frontiers of LFV searches by delivering unprecedented momentum precision while maintaining operational flexibility and cost efficiency.