Suppression of $^{14}\mathrm{C}$ photon hits in large liquid scintillator detectors via spatiotemporal deep learning

Junle Li; Zhaoxiang Wu; Guanda Gong; Zhaohan Li; Wuming Luo; Jiahui Wei; Wenxing Fang; Hehe Fan

physics.ins-detMar 29, 2026

Suppression of $^{14}\mathrm{C}$ photon hits in large liquid scintillator detectors via spatiotemporal deep learning

Authors: Junle Li, Zhaoxiang Wu, Guanda Gong, Zhaohan Li, Wuming Luo, Jiahui Wei, Wenxing Fang, Hehe Fan

Organizations: School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China · Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China · School of Physical Sciences, University of Chinese Academy of Science, Beijing 100049, China · College of Computer Science and Technology, Zhejiang University, Hangzhou 310027, China

Abstract

Liquid scintillator detectors are widely used in neutrino experiments due to their low energy threshold and high energy resolution. Despite the tiny abundance of $^{14}$ C in LS, the photons induced by the $β$ decay of the $^{14}$ C isotope inevitably contaminate the signal, degrading the energy resolution. In this work, we propose three models to tag $^{14}$ C photon hits in $e^+$ events with $^{14}$ C pile-up, thereby suppressing its impact on the energy resolution at the hit level: a gated spatiotemporal graph neural network and two Transformer-based models with scalar and vector charge encoding. For a simulation dataset in which each event contains one $^{14}$ C and one $e^+$ with kinetic energy below 5 MeV, the models achieve $^{14}$ C recall rates of 25%-48% while maintaining $e^+$ to $^{14}$ C misidentification below 1%, leading to a large improvement in the resolution of total charge for events where $e^+$ and $^{14}$ C photon hits strongly overlap in space and time.

Figures & tables

Panel of Figure 1 — Figure 1: Hit time distributions of pile-up events. The curves show the contributions from $\mathrm{e}^{+}$ annihilation (blue), ${}^{14}\mathrm{C}$ decay (red), and dark noise (gray), along with the total hit count (dashed black). (a) With large $\Delta t$ , the ${}^{14}\mathrm{C}$ signal appears as a weak secondary peak. (b) With small $\Delta t$ , the ${}^{14}\mathrm{C}$ hits are buried within the dominant $\mathrm{e}^{+}$ peak.

Panel of Figure 2 — Figure 2: The spatiotemporal structure of a pile-up event with $\Delta t=1.9~\mathrm{ns}$ . The truth information for the $\mathrm{e}^{+}$ event consists of a kinetic energy $E_{k}({\mathrm{e}^{+}})=1.4~\mathrm{MeV}$ and a vertex position of $(x,y,z)=(-1.9,5.7,11.1)~\mathrm{m}$ , while that for the ${}^{14}\mathrm{C}$ event consists of a deposited energy $E_{{}^{14}\mathrm{C}}=107.4~\mathrm{keV}$ and a vertex position of $(x,y,z)=(-5.4,1.9,-14.8)~\mathrm{m}$ . The plots show the spatial distribution of photon hits in $100~\mathrm{ns}$ intervals. Blue dots represent hits from the positron annihilation, red dots from the ${}^{14}\mathrm{C}$ decay, and gray dots indicate dark noise.

Figure 3: Architecture of STT-Vector. Each hit is processed through two parallel encoding branches. The spatiotemporal branch (top) maps normalized spatial coordinates and hit times to a high-dimensional representation using sinusoidal positional encodings

\psi(\cdot)

. The vector charge branch (bottom) embeds the 18-dimensional charge feature vector

\mathbf{q}_{i}

, which summarizes multi-scale local and global charge accumulation, using a dedicated multilayer perceptron. The two embeddings are concatenated, projected to the Transformer model dimension

d_{\mathrm{model}}

, and passed through

L

Transformer encoder layers to produce per-hit class logits for dark noise,

\mathrm{e}^{+}

, and

{}^{14}\mathrm{C}

Panel of Figure 4 — Figure 4: A visualization of the hit identification results of Gated-STGNN, STT-Scalar, and STT-Vector, compared with the truth for a pile-up event with $\Delta t=165.0~\mathrm{ns}$ . The truth information for the $\mathrm{e}^{+}$ event consists of a kinetic energy $E_{k}({\mathrm{e}^{+}})=0~\mathrm{MeV}$ and a vertex position of $(x,y,z)=(0.03,-0.02,-0.08)~\mathrm{m}$ , while that for the ${}^{14}\mathrm{C}$ event consists of a deposited energy $E_{{}^{14}\mathrm{C}}=82.5~\mathrm{keV}$ and a vertex position of $(x,y,z)=(7.65,5.75,11.23)~\mathrm{m}$ . The plots display the $(\theta,\phi,t)$ distribution of the hits, where $t$ is the hit time and $(\theta,\phi)$ are the polar and azimuthal angles of the PMT. Blue dots represent hits from the $\mathrm{e}^{+}$ event, red dots from the ${}^{14}\mathrm{C}$ decay, and gray dots indicate dark noise.

Panel of Figure 5 — Figure 5: Normalized confusion matrices for events with $z=0$ and $E_{k}({\mathrm{e}^{+}})=0~\mathrm{MeV}$ . The panels display the classification performance for Gated-STGNN, STT-Scalar, and STT-Vector.

Panel of Figure 6 — Figure 6: Normalized confusion matrices for events with $z=0$ and $E_{k}({\mathrm{e}^{+}})=5~\mathrm{MeV}$ . The panels display the classification performance for Gated-STGNN, STT-Scalar, and STT-Vector.

Panel of Figure 7 — Figure 7: Classification metrics as functions of positron kinetic energy $E_{k}({\mathrm{e}^{+}})$ at $z=0~\mathrm{m}$ . The panels show the dependence on $E_{k}({\mathrm{e}^{+}})$ of the fraction of $\mathrm{e}^{+}$ hits misidentified as ${}^{14}\mathrm{C}$ , the fraction of dark noise (DN) hits misidentified as ${}^{14}\mathrm{C}$ , and the ${}^{14}\mathrm{C}$ recall.

Panel of Figure 8 — Figure 8: Classification metrics as functions of the vertex position $z$ (evaluated at discrete points $z\in\{0,6,15,16.5\}~\mathrm{m}$ ) for events with a fixed positron kinetic energy $E_{k}({\mathrm{e}^{+}})=0~\mathrm{MeV}$ . The panels display the dependence on $z$ of the fraction of $\mathrm{e}^{+}$ hits misidentified as ${}^{14}\mathrm{C}$ , the fraction of dark noise (DN) hits misidentified as ${}^{14}\mathrm{C}$ , and the ${}^{14}\mathrm{C}$ recall.

Panel of Figure 9 — Figure 9: Differential ${}^{14}\mathrm{C}$ recall $R_{{}^{14}\mathrm{C}}(\Delta t,E_{{}^{14}\mathrm{C}})$ of STT-Vector, evaluated at $z=0$ for $E_{k}({\mathrm{e}^{+}})=0~\mathrm{MeV}$ and $E_{k}({\mathrm{e}^{+}})=5~\mathrm{MeV}$ , respectively.

Panel of Figure 10 — Figure 10: Distributions of the total charge of selected hits ( $Q_{\mathrm{sum}}$ ) at the detector center for events with $E_{k}({\mathrm{e}^{+}})=0~\mathrm{MeV}$ (left) and $E_{k}({\mathrm{e}^{+}})=5~\mathrm{MeV}$ (right). The gray dotted line represents $Q_{\mathrm{sum}}$ of all hits, before applying hits removal. The green dashed line shows the ideal distribution with ${}^{14}\mathrm{C}$ pile-up removed by truth label. The solid purple line represents $Q_{\mathrm{sum}}$ after hit removal based on the STT-Vector model prediction. The fitted mean value ( $\mu$ ), width ( $\sigma$ ) and corresponding resolution ( $\mathcal{R}=\sigma/\mu$ ) are also shown.

Panel of Figure 11 — Figure 11: Ratios of the resolutions of the charge sum of selected hits ( $Q_{\mathrm{sum}}$ ) under different hit-removal criteria relative to the “Total” case, in which no hit is removed. The left plot shows the ratio’s dependence on $E_{k}$ at the detector center. The right plot shows the ratio’s dependence on $z$ when $E_{k}({\mathrm{e}^{+}})=0~\mathrm{MeV}$ .

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Scintillation detectors with excellent timing resolution enable more precise localization of radiation sources in positron emission tomography, leading to substantial improvements in diagnostic capability for diseases such as cancer and dementia. At the extreme timing precision required for such applications at the picosecond scale, detector performance is governed by the microscopic dynamics of scintillation photons generated within the detector and their subsequent detection processes. However, detector signals have conventionally been treated only as collective responses of many photons due to structural constraints inherent to photodetectors. In this study, we overcome this fundamental limitation using deep learning, enabling direct access to the timing information of individual photons. The proposed method estimates photon-by-photon arrival times directly from detector waveforms without requiring any modification to the detector structure; the method operates on an event-by-event basis without ground-truth labels by integrating an unsupervised learning framework with a physically informed detector-response model. Through comprehensive validation combining Monte Carlo simulation and experimental measurements across various detector configurations, we experimentally demonstrate improved timing resolution, visualized depth-of-interaction-dependent photon transport, and classified Cherenkov and scintillation photons based on the estimated photon-level timing information using a unified deep learning-based framework. These results provide experimental access to photon dynamics, bridging the gap between theoretical modeling and experimental observation, and they open a new data-driven pathway for discovery in detector physics and optimization.

Abstract

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