Antimatter Annihilation Vertex Reconstruction with Deep Learning for ALPHA-g Radial Time Projection Chamber

TL;DR

This work addresses the challenge of reconstructing the vertical annihilation vertex of antihydrogen in the ALPHA-g rTPC by bypassing traditional track fitting and directly predicting the vertex along the $z$-axis from spacepoints using an ensemble of PointNet-based regression networks (PEAR). Trained on $2.7$ million simulated events with 800 spacepoints per event and optimized via the Huber loss, PEAR achieves tighter residuals and smaller bias than the conventional Helix Fit method, including in complex events where tracks are sparse or noisy. The central results show substantial improvements in the $z$-vertex resolution, with a lower $ ext{sigma}$ and $ ext{FWHM}$, and an ability to recover vertices in regions where the standard method fails, suggesting a significant potential impact on precision gravity measurements of antimatter. Future work will extend PEAR to predict full $(x,y,z)$ vertices, validate on real data, and explore uncertainty quantification and more advanced architectures to further enhance performance and applicability in ALPHA-g analyses.

Abstract

The ALPHA-g experiment at CERN aims to precisely measure the terrestrial gravitational acceleration of antihydrogen atoms. A radial Time Projection Chamber (rTPC), that surrounds the ALPHA-g magnetic trap, is employed to determine the annihilation location, called the vertex. The standard approach requires identifying the trajectories of the ionizing particles in the rTPC from the location of their interaction in the gas (spacepoints), and inferring the vertex positions by finding the point where those trajectories (helices) pass closest to one another. In this work, we present a novel approach to vertex reconstruction using an ensemble of models based on the PointNet deep learning architecture. The newly developed model, PointNet Ensemble for Annihilation Reconstruction (PEAR), directly learns the relation between the location of the vertices and the rTPC spacepoints, thus eliminating the need to identify and fit the particle tracks. PEAR shows strong performance in reconstructing vertical vertex positions from simulated data, that is superior to the standard approach for all metrics considered. Furthermore, the deep learning approach can reconstruct the vertical vertex position when the standard approach fails.

Figures (5)

• Figure 1: Conceptual schematics of the vertex reconstruction approach using our deep learning model (bottom), in contrast to the standard method that requires identification of particle tracks and fitting helix functions (top).
• Figure 2: Schematics of our modified PointNet architecture for the vertex reconstruction regression task, heavily based on Qi2017. The dimensions of hidden and output layers of the MLPs are indicated in parentheses. The architecture has been simplified by removing the initial input transform, and the final layer has been replaced with a linear layer to predict the $z$ position of the vertex. Unlike the original PointNet, which outputs classification scores, PEAR outputs a single prediction for each event, focused solely on $z$-vertex reconstruction. Three models are trained with this architecture, using three different random seeds, and their outputs are averaged to get the final $z$-vertex prediction.
• Figure 3: 2D histogram of predicted $z$ coordinate of the vertices by PEAR versus simulated (true) $z$ coordinate (left). Histogram of residuals for PEAR and Helix Fit with Gaussian fits (right). These plots use the test dataset.
• Figure 4: Box plot of residuals from PEAR and Helix Fit predictions (top). For this study, the line within the box denotes the median, the box extends from the lower to upper quartile, otherwise known as the interquartile range (IQR), and the whiskers extend to the furthest residuals within 1.5 times the IQR on either side of the distribution. Gaussian mean (used in ARA Eq. (\ref{['eq:overall_bias']}) to probe $z$-basis) (bottom). Each for 200 mm slices of the detector.
• Figure 5: Analysis of seven thousand events Helix Fit is unable to provide predictions for (previously excluded). Box plot (see Figure \ref{['figs:box_and_bias']} caption for general box plot description) of PEAR performance (top) and percentage of total events in each slice of the test set Helix Fit failed to predict (bottom), note that error bars on the percentages aren't visible due to their small magnitude.