Data-Driven Calibration of Large Liquid Detectors with Unsupervised Learning

TL;DR

The study addresses PMT timing calibration in massive liquid scintillator detectors by learning per-PMT timing constants directly from physics data through an unsupervised, regression-style approach. It combines a physics-informed time-walk model with a transformer-based vertex reconstructor and a skew-$t$ loss on time residuals to jointly optimize $>22{,}000$ calibration parameters. Validation on MC with injected truth models shows timing precision of $\approx$0.14 FWHM, and data-driven checks demonstrate improved BiPo-based position resolution and the ability to monitor detector performance. The method reduces reliance on hardware calibration campaigns and is adaptable to other large-scale detectors, offering a practical path to frequent, end-to-end calibration using standard data streams.

Abstract

This paper demonstrates a novel method to extract photomultiplier tube (PMT) calibration timing constants in large liquid scintillation detectors from physics data using the machinery of unsupervised deep learning. The approach uses a simplified physical model of optical photon transport in the loss function, with PMT calibration constants treated as free parameters, and the simple assumption that individual events represent point-like emission. The problem is, thus, effectively reduced to that of regression on a very large scale, made tractable by deep learning architectures and automatic differentiation frameworks. Using data from the 9,300 PMTs in the SNO+ detector, the method has been shown to reliably extract 3 calibration constants for each of the over 7,500 online PMTs using radioactive background events. We believe that this basic approach can be straightforwardly generalised for a wide range of applications.

Figures (10)

• Figure 1: Time walk effect
• Figure 2: Time residual distribution for ^210Po decays from MC. The Jones and Faddy skew-$t$ distribution is fit to the distribution and used as a loss function during training.
• Figure 3: Distributions of PMT timing model residuals over all PMTs. The standard deviation of the residuals is estimated by taking the interquartile range and dividing by 1.35 for a robust estimate.
• Figure 4: Examples of PMT timing models from MC truth and as fitted by the calibration method. The inset histogram shows the distribution of charges for this PMT. Time walks are only shown for charge bins which have non-zero counts.
• Figure 5: Each blue dot represents the delay residual for a PMT. For the PMT $z$ position plot, a linear fit is shown in orange to illustrate the small dependence on $z$ position. The "bottom to top" shows the difference in delay residual from the bottom to the top of the detector based on the linear fit.