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Register a new userComputational Techniques for the Analysis of Small Signals in High-Statistics Neutrino Oscillation Experiments
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The current and upcoming generation of Very Large Volume Neutrino Telescopes---collecting unprecedented quantities of neutrino events---can be used to explore subtle effects in oscillation physics, such as (but not restricted to) the neutrino mass ordering. The sensitivity of an experiment to these effects can be estimated from Monte Carlo simulations. With the high number of events that will be collected, there is a trade-off between the computational expense of running such simulations and the inherent statistical uncertainty in the determined values. In such a scenario, it becomes impractical to produce and use adequately-sized sets of simulated events with traditional methods, such as Monte Carlo weighting. In this work we present a staged approach to the generation of binned event distributions in order to overcome these challenges. By combining multiple integration and smoothing techniques which address limited statistics from simulation it arrives at reliable analysis results using modest computational resources.
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We propose a novel method for computing $p$-values based on nested sampling (NS) applied to the sampling space rather than the parameter space of the problem, in contrast to its usage in Bayesian computation. The computational cost of NS scales as $log^2{1/p}$, which compares favorably to the $1/p$ scaling for Monte Carlo (MC) simulations. For significances greater than about $4sigma$ in both a toy problem and a simplified resonance search, we show that NS requires orders of magnitude fewer simulations than ordinary MC estimates. This is particularly relevant for high-energy physics, which adopts a $5sigma$ gold standard for discovery. We conclude with remarks on new connections between Bayesian and frequentist computation and possibilities for tuning NS implementations for still better performance in this setting.
GELATIO is a new software framework for advanced data analysis and digital signal processing developed for the GERDA neutrinoless double beta decay experiment. The framework is tailored to handle the full analysis flow of signals recorded by high purity Ge detectors and photo-multipliers from the veto counters. It is designed to support a multi-channel modular and flexible analysis, widely customizable by the user either via human-readable initialization files or via a graphical interface. The framework organizes the data into a multi-level structure, from the raw data up to the condensed analysis parameters, and includes tools and utilities to handle the data stream between the different levels. GELATIO is implemented in C++. It relies upon ROOT and its extension TAM, which provides compatibility with PROOF, enabling the software to run in parallel on clusters of computers or many-core machines. It was tested on different platforms and benchmarked in several GERDA-related applications. A stable version is presently available for the GERDA Collaboration and it is used to provide the reference analysis of the experiment data.
Bayesian modeling techniques enable sensitivity analyses that incorporate detailed expectations regarding future experiments. A model-based approach also allows one to evaluate inferences and predicted outcomes, by calibrating (or measuring) the consequences incurred when certain results are reported. We present procedures for calibrating predictions of an experiments sensitivity to both continuous and discrete parameters. Using these procedures and a new Bayesian model of the $beta$-decay spectrum, we assess a high-precision $beta$-decay experiments sensitivity to the neutrino mass scale and ordering, for one assumed design scenario. We find that such an experiment could measure the electron-weighted neutrino mass within $sim40,$meV after 1 year (90$%$ credibility). Neutrino masses $>500,$meV could be measured within $approx5,$meV. Using only $beta$-decay and external reactor neutrino data, we find that next-generation $beta$-decay experiments could potentially constrain the mass ordering using a two-neutrino spectral model analysis. By calibrating mass ordering results, we identify reporting criteria that can be tuned to suppress false ordering claims. In some cases, a two-neutrino analysis can reveal that the mass ordering is inverted, an unobtainable result for the traditional one-neutrino analysis approach.
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.
We introduce a filter-construction method for pulse processing that differs in two respects from that in standard optimal filtering, in which the average pulse shape and noise-power spectral density are combined to create a convolution filter for estimating pulse heights. First, the proposed filters are computed in the time domain, to avoid periodicity artifacts of the discrete Fourier transform, and second, orthogonality constraints are imposed on the filters, to reduce the filtering procedures sensitivity to unknown baseline height and pulse tails. We analyze the proposed filters, predicting energy resolution under several scenarios, and apply the filters to high-rate pulse data from gamma-rays measured by a transition-edge-sensor microcalorimeter.
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