Bayesian network 3D event reconstruction in the Cygno optical TPC for dark matter direct detection

Abstract

The CYGNO experiment is developing a high-resolution gaseous Time Projection Chamber with optical readout for directional dark matter searches. The detector uses a helium-tetrafluoromethane (He:CF $_4^{}$ 60:40) gas mixture at atmospheric pressure and a triple Gas Electron Multiplier amplification stage, coupled with a scientific camera for high-resolution 2D imaging and fast photomultipliers for time-resolved scintillation light detection. This setup enables 3D event reconstruction: photomultiplier signals provide depth information, while the camera delivers high-precision transverse resolution. In this work, we present a Bayesian Network-based algorithm designed to reconstruct the events using only the photomultiplier signals, inferring a 3D description of the particle trajectories. The algorithm models the light collection process probabilistically and estimates spatial and intensity parameters on the Gas Electron Multiplier plane, where light emission occurs. It is implemented within the Bayesian Analysis Toolkit and uses Markov Chain Monte Carlo sampling for posterior inference. Validation using data from the CYGNO LIME prototype shows accurate reconstruction of localized and extended straight tracks. Results demonstrate that the Bayesian approach enables robust 3D description and, when combined with camera data, opens the way to future improvements in spatial and energy resolution. This methodology represents a significant step forward in directional dark matter detection, enhancing the identification of nuclear recoil tracks with high spatial resolution.

Fig. 1

Schematic view of the LIME detector. The He:CF$_4^{}$ (60:40) gas mixture is contained in a PMMA vessel housing a copper field cage. Ionization electrons drift from the cathode (right) toward the amplification region (left), where a triple-GEM structure produces charge multiplication and scintillation light. This light is collected by a centrally aligned APS-sCMOS camera and four PMTs located above the GEM plane, on the optical readout side

Fig. 2

Relative disposition of the sensors with respect to the GEM plane, where light is emitted. Top: side view showing the field cage and the vertical distances between the PMTs and the GEMs. Bottom: front view, showing the camera position (centered) and the four PMTs (at the corners)

Fig. 3

Example of an event recorded with the LIME’s optical readout, illustrating a the image acquired by the APS-sCMOS camera during a 300 ms exposure with four distinct tracks: two localized clusters; one extended straight ionization trail; and a curly scattered track (electron recoil). Figure b shows the PMT signals (inverted for clarity) recorded within the same acquisition window, each associated to one of the ionization in the picture

Fig. 4

Schematic representation of the illumination of the i-th PMT by the radiating source with coordinates $(X_j,Y_j)$ on the GEMs. The distance between the centers of the two surfaces is denoted by $R_{\mathit{ij}}$, and the angle with respect to the z-axis is ${\theta }_{\mathit{ij}}$

Fig. 5

Relative standard deviation, for each PMT, of the measured charge as a function of the expected value ${\mu }_{\mathit{ij}}$ from Eq. (4). The expected value spans over the dynamic range because of a $_{}^{55}$Fe mono-energetic source occurring at different positions on the GEM plane. The colored points are the measured data, the black curve is the fit of the model described in Eq. (5) for all the PMTs and the blue band represents the $3\sigma$ uncertainty range of the inference process. The insets display the relative charge dispersion for the three points indicated by the arrows with the relative Gaussian model superimposed

Fig. 6

Bayesian network adopted in the PMT reconstruction. Each event $j\in N$ produces a light yield $L_j$ at position $(X_j,Y_j)$, while each PMT $i\in N_{\mathit{PMTs}}$ is characterized by a calibration coefficient $C_i$ and position $(X_i,Y_i)$. The expected mean signal ${\mu }_{\mathit{ij}}$ depends on these quantities, on global parameters $(\alpha ,h)$, while ${\sigma }_{\mathit{ij}}$ depends also on nuisance terms (A, B). The observed charge $Q_{\mathit{ij}}$ is modeled as a Gaussian distribution $\mathcal{N}$ with mean ${\mu }_{\mathit{ij}}$ and width ${\sigma }_{\mathit{ij}}$. Plates indicate repetition over events (j) and over PMTs (i); solid arrows indicate probabilistic links, dashed arrows deterministic ones. Primordial nodes are either fixed (grey) or assigned a prior (white)

Fig. 7

Corner plot of the posterior distributions obtained from the calibration algorithm, normalized to $C_1$. The diagonal panels show the 1D histograms of each PMT calibration parameter $C_i$, while the off-diagonal panels display the scatter plots of the corresponding parameter pairs, along with their correlation. The labels in the diagonal histograms report the 16th, 50th, and 84th percentiles of each distribution

Fig. 8

Corner plot of the posterior distributions obtained from the reconstruction algorithm applied to localized tracks. The diagonal panels show the 1D histograms of the X, Y, and L parameters, while the off-diagonal panels display the corresponding scatter plots and their correlations. Each histogram is labeled with the 16th, 50th, and 84th percentiles of the respective distribution

Fig. 9

Reconstructed (X, Y) positions obtained through the Bayesian fitting procedure (shown as red crosses) overlaid on the camera image. The size of each cross represents the uncertainty of the fit in both dimensions. The yellow dots visible in the image correspond to the highly localized electron recoils induced by the $_{}^{55}$Fe radioactive source

Fig. 10

Planar distribution of the tracks in the camera field of view reconstructed using a the APS-sCMOS analysis, and b the PMT-based Bayesian algorithm, using a dataset acquired in with a $_{}^{55}$Fe radioactive source positioned above the detector. c Reconstructed energy spectrum with both analysis

Fig. 11

Distribution of the residuals $\mathrm{\Delta }X$ and $\mathrm{\Delta }Y$ between the PMT-based and camera-based track reconstructions for localized events. The dataset includes only events featuring a single localized track in the image and a single PMT waveform, allowing for a direct match between the two sensors’ information

Fig. 12

3D reconstruction of an extended alpha particle track. a PMT signals with highlighted time windows used for the BAT fit; b overlay of the BAT-reconstructed positions (red stars) on the corresponding camera image; c final 3D representation of the alpha track combining PMT and camera information

Fig. 13

Distribution of the residuals $\mathrm{\Delta }X$ and $\mathrm{\Delta }Y$ between the PMT-based and camera-based track reconstructions for extended events. The tracks reconstructed from the camera images are resampled to match the number of points in the corresponding PMT waveform, and a point-by-point distance is computed