Pmt waveform simulation and reconstruction with conditional diffusion network

Abstract

Photomultiplier tubes (PMTs) are widely employed in particle and nuclear physics experiments. The accuracy of PMT waveform reconstruction directly impacts the vertex and energy resolution of detectors. A key challenge arises when multiple photons arrive within a few nanoseconds, making it difficult to resolve individual photoelectrons (PEs). Although supervised machine learning methods have surpassed traditional methods in performance, their practical applicability is limited by the lack of ground-truth PE labels in real data. To address this issue, we propose an innovative weakly supervised waveform simulation and reconstruction approach based on a bidirectional conditional diffusion network framework. The method is fully data-driven and requires only raw waveforms and coarse estimates of PE information as input. It first employs a PE-conditioned diffusion model to simulate realistic waveforms from PE sequences, thereby learning the features of overlapping waveforms. Subsequently, these simulated waveforms are used to train a waveform-conditioned diffusion model to reconstruct the PE sequences from waveforms, reinforcing the learning of features of overlapping waveforms. Through iterative refinement between the two conditional diffusion processes, the model progressively improves reconstruction accuracy. Experimental results demonstrate that the proposed method achieves an average normalized PE-number resolution over 1–5 p.e. that is about 1% worse than that of fully supervised learning, and a timing resolution that is about 25% worse.