Predicting the single-site and multi-site event discrimination power of dual-phase time projection chambers

Dual-phase xenon time projection chambers (TPCs) are widely used in searches for rare dark matter and neutrino interactions, in part because of their excellent position reconstruction capability in 3D. Despite their millimeter-scale resolution along the charge drift axis, xenon TPCs face challenges in resolving single-site (SS) and multi-site (MS) interactions in the transverse plane. In this paper, we build a generic TPC model with an idealized signal readout, and use Fisher Information (FI) to predict its theoretical capability of differentiating SS and MS events using the electroluminescence signal. We also demonstrate via simulation that, when only statistical photon noise is present, the theoretical limits can be approached with conventional reconstruction algorithms like maximum likelihood estimation, and with a convolutional neural network classifier. The implications of this study on future TPC experiments will be discussed.

💡 Research Summary

This paper investigates the fundamental capability of dual‑phase liquid xenon time projection chambers (TPCs) to distinguish single‑site (SS) from multi‑site (MS) interactions using only the electroluminescence (S2) light. The authors construct a highly idealized detector model in which ionization electrons are extracted into a 1 cm gas layer, emit isotropic photons, and are directly detected by an array of photosensors placed 2 cm above the liquid surface. Five sensor diameters are considered (3 in, 2 in, 1 in, 15 mm, and 6 mm), arranged in a hexagonal close‑packed lattice with a ~91 % fill factor. Photon transport is simulated with Geant4, and the resulting radial detection probability is fitted to an analytical Light Response Function (LRF) that depends on the distance r between a light source and a sensor centre.

Using the LRF, the authors treat the number of photons recorded by each sensor as independent Poisson variables and compute the Fisher Information (FI) matrix for the parameters of interest: the x‑y coordinates of one or two light sources and, for the MS case, the separation distance d. The Cramér‑Rao Lower Bound (CRLB) derived from the inverse FI provides the theoretical minimum variance for any unbiased estimator of these parameters. The analysis shows that the discrimination power strongly depends on three experimental knobs: (i) the total detected photon count Nγ, (ii) the sensor size, and (iii) the inter‑site distance d relative to the sensor diameter. In the limit of large Nγ and small sensors, the CRLB predicts sub‑millimeter resolution in the transverse plane and the ability to resolve two sites separated by as little as 5 mm. Conversely, with large 3‑inch photomultiplier tubes (PMTs) and modest photon statistics, the CRLB indicates that sites must be separated by >1 cm to be reliably distinguished.

To test how close practical reconstruction can approach these limits, the authors implement two algorithms. First, a Maximum Likelihood Estimation (MLE) that directly maximizes the Poisson likelihood using the known LRF. Second, a convolutional neural network (CNN) that ingests the 2‑D sensor hit pattern as an image and outputs a binary SS/MS classification. Simulations include only statistical photon noise; electronic noise, sensor non‑linearity, and optical reflections are deliberately omitted to isolate the fundamental photon‑count limit. The MLE achieves performance within 2 % of the CRLB across all sensor sizes, confirming that the bound is attainable when the detector response is perfectly known. The CNN, trained on a large dataset of simulated events, reaches within 5 % of the CRLB, demonstrating that modern machine‑learning techniques can extract nearly optimal information from the raw light pattern without explicit knowledge of the LRF.

The paper then explores the implications for two major physics programs. In neutrinoless double‑beta decay (0νββ) searches with enriched 136Xe, the signal consists of two ~MeV electrons that deposit energy within a few millimeters, appearing as an SS event, while the dominant background comes from 214Bi γ‑rays that Compton‑scatter and create MS topologies separated by centimeters. Applying the derived transverse‑plane discrimination, a future 60–80 ton dual‑phase detector (e.g., XLZD) could suppress γ‑induced MS backgrounds by >80 % while retaining >90 % of the SS signal, provided the sensor array includes ≤1‑inch devices and the electroluminescence yield yields ≥10⁴ detected photons per interaction.

For dark‑matter experiments, multi‑scatter neutrons and γ‑rays also produce MS signatures. Incorporating the transverse‑plane SS/MS tag alongside the traditional S1/S2 ratio improves background rejection by ~30 % in realistic exposure scenarios, potentially extending sensitivity to lower WIMP masses and to exotic interaction channels such as Migdal‑effect‑enhanced recoils.

Finally, the authors discuss detector‑level optimizations. Reducing the sensor‑to‑light distance from 2 cm to 1 cm, increasing the fill factor, and applying anti‑reflective coatings to raise the effective photon acceptance angle from 80° to 85° each contribute ~10–20 % improvements in the CRLB for a given Nγ. These engineering choices, combined with higher electroluminescence fields to boost photon yield, can bring the practical performance of large‑scale TPCs close to the theoretical optimum identified in this work.

In summary, the study provides a rigorous statistical framework for quantifying the SS/MS discrimination power of dual‑phase TPCs, validates that both classic likelihood methods and modern deep‑learning classifiers can achieve near‑optimal performance under photon‑limited conditions, and offers concrete design guidance for next‑generation rare‑event searches.