The MGDO software library for data analysis in Ge neutrinoless double-beta decay experiments

The GERDA and Majorana experiments will search for neutrinoless double-beta decay of germanium-76 using isotopically enriched high-purity germanium detectors. Although the experiments differ in conceptual design, they share many aspects in common, and in particular will employ similar data analysis techniques. The collaborations are jointly developing a C++ software library, MGDO, which contains a set of data objects and interfaces to encapsulate, store and manage physical quantities of interest, such as waveforms and high-purity germanium detector geometries. These data objects define a common format for persistent data, whether it is generated by Monte Carlo simulations or an experimental apparatus, to reduce code duplication and to ease the exchange of information between detector systems. MGDO also includes general-purpose analysis tools that can be used for the processing of measured or simulated digital signals. The MGDO design is based on the Object-Oriented programming paradigm and is very flexible, allowing for easy extension and customization of the components. The tools provided by the MGDO libraries are used by both GERDA and Majorana.

💡 Research Summary

The paper presents MGDO (Majorana‑Gerda Data Objects), a jointly developed C++ software library that provides a common data model and a suite of signal‑processing tools for the GERDA and Majorana experiments, both of which search for neutrinoless double‑beta decay of ^76Ge using high‑purity germanium (HPGe) detectors. Although the two experiments differ in detector shielding (GERDA immerses detectors in liquid argon, while Majorana uses a vacuum cryostat surrounded by lead), they share many detector technologies and analysis requirements. To avoid duplicated effort and to facilitate cross‑experiment data exchange, the collaborations created MGDO as a unified framework for handling raw waveforms, detector geometry, and event‑level information.

MGDO is organized around two principal categories of classes: data objects and transforms. The core data object, MGWaveform, encapsulates a digitized waveform as an array of samples together with metadata such as sampling frequency, start time, and waveform type (voltage, current, etc.). Operator overloading enables intuitive waveform‑waveform and waveform‑scalar arithmetic. A ROOT‑specific wrapper, MGTWaveform, adds methods for converting the waveform to a TH1 histogram, fitting with TF1 functions, and other ROOT‑centric utilities. Another key object, MGEvent, aggregates a set of MGWaveform instances (one per channel) plus a timestamp and DAQ flags, thereby representing a complete physics event. All objects can be serialized into ROOT files, allowing both Monte Carlo simulations and experimental data to share the same persistent format.

Transform classes inherit from the abstract base MGWaveformTransformer, which defines a uniform interface for processing waveforms. Implemented transforms include baseline subtraction, numerical differentiation (3‑point, 5‑point, and RC‑based schemes), moving‑average and triangular smoothing, and a trapezoidal filter. Scalar‑producing transforms compute quantities such as χ² differences between two waveforms, global maxima/minima, and rise times defined between user‑specified fractions of the pulse amplitude (e.g., 10 % to 90 %). Because each transform returns either a new MGWaveform or a set of scalars, they can be chained to build complex analysis pipelines; the paper illustrates a three‑step chain that denoises a charge pulse, differentiates it, and yields a current pulse.

The library leverages external packages for consistency and performance: CLHEP provides units and physical constants, FFTW3 can be linked for fast Fourier transforms, and ROOT supplies advanced I/O, histogramming, and fitting capabilities. This modular design makes MGDO extensible and adaptable to future analysis needs.

In practice, both GERDA’s Gelatio framework and Majorana’s GAT toolkit rely on MGDO for I/O handling and basic digital filtering. Raw binary data from the detectors and test stands are converted into MGWaveform objects, stored as ROOT trees, and processed with the same MGDO transform chains regardless of detector type (HPGe or photomultiplier). This uniformity eliminates duplicated code, simplifies validation, and enables joint studies of detector performance and background rejection.

Beyond the immediate scope of ^76Ge neutrinoless double‑beta decay, the authors argue that MGDO’s generic data model and transform library are applicable to any low‑background experiment that records digitized waveforms. By providing a portable, standardized format, MGDO can facilitate data sharing, cross‑experiment benchmarking, and collaborative software development across the broader rare‑event physics community.

The paper concludes with acknowledgments to the GERDA and Majorana collaborations and lists relevant references, underscoring the collaborative spirit that made MGDO possible.