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

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 (11)

• 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.
• 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 $^{14}\mathrm{C}$.
• 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.
• 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.