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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9

Electron reconstruction and identification efficiency measurements with the ATLAS detector using the 2011 LHC proton–proton collision data

Many of the interesting physics processes to be measured at the LHC have a signature involving one or more isolated electrons. The electron reconstruction and identification efficiencies of the ATLAS detector at the LHC have been evaluated using proton–proton collision data collected in 2011 at √s = 7 TeV and corresponding to an integrated luminosity of 4.7 fb -1 . Tag-and-probe methods using events with leptonic decays of W and Z bosons and J/ψ mesons are employed to benchmark these performance parameters. The combination of all measurements results in identification efficiencies determined with an accuracy at the few per mil level for electron transverse energy greater than 30 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Bayesian method for using simulator data to enhance human error probabilities assigned by existing HRA methods

In the past several years, several international organizations have begun to collect data on human performance in nuclear power plant simulators. The data collected provide a valuable opportunity to improve human reliability analysis (HRA), but these improvements will not be realized without implementation of Bayesian methods. Bayesian methods are widely used to incorporate sparse data into models in many parts of probabilistic risk assessment (PRA), but Bayesian methods have not been adopted by the HRA community. In this paper, we provide a Bayesian methodology to formally use simulator data to refine the human error probabilities (HEPs) assigned by existing HRA methods. We demonstrate the methodology with a case study, wherein we use simulator data from the Halden Reactor Project to update the probability assignments from the SPAR-H method. The case study demonstrates the ability to use performance data, even sparse data, to improve existing HRA methods. Furthermore, this paper also serves as a demonstration of the value of Bayesian methods to improve the technical basis of HRA.

99 GENERAL AND MISCELLANEOUS↗

Suppressing simulation bias in multi-modal data using transfer learning

Abstract Many problems in science and engineering require making predictions based on few observations. To build a robust predictive model, these sparse data may need to be augmented with simulated data, especially when the design space is multi-dimensional. Simulations, however, often suffer from an inherent bias. Estimation of this bias may be poorly constrained not only because of data sparsity, but also because traditional predictive models fit only one type of observed outputs, such as scalars or images, instead of all available output data modalities, which might have been acquired and simulated at great cost. To break this limitation and open up the path for multi-modal calibration, we propose to combine a novel, transfer learning technique for suppressing the bias with recent developments in deep learning, which allow building predictive models with multi-modal outputs. First, we train an initial neural network model on simulated data to learn important correlations between different output modalities and between simulation inputs and outputs. Then, the model is partially retrained, or transfer learned, to fit the experiments; a method that has never been implemented in this type of architecture. Using fewer than 10 inertial confinement fusion experiments for training, transfer learning systematically improves the simulation predictions while a simple output calibration, which we design as a baseline, makes the predictions worse. We also offer extensive cross-validation with real and carefully designed synthetic data. The method described in this paper can be applied to a wide range of problems that require transferring knowledge from simulations to the domain of experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

COVID-19 Data Curation Effort: An Initial Analysis of the Data

During the COVID-19 pandemic of 2020, major case reporting outlets quickly coalesced around two or three primary vendors. Johns Hopkins University and The New York Times were among the more prominent, and all were of great value to the nation, particularly during the uncertain early stages of the pandemic. They primarily focused on three major attributes: number of new cases, deaths, and recovery. Recognizing that many states were reporting very detailed data sets (e.g., hospital beds) at a county level or finer, the ORNL Pandemic Modeling team embarked on a major data curation effort from March to June 2020 for the purpose of capturing this wealth of detailed data. The challenge of curating this data was daunting. The number of attributes reported by the states grew on almost on a weekly basis. States were routinely shifting their web tool strategies away from easily parsable HTML-based formatting to new Tableau and ArcGIS content. This growth in the sheer number of attributes, combined with the unpredictable shifts in data format, meant an aggressive and agile combination of automated scripting and manual scraping was required to capture new daily streams. Further, the team had to scale up staff and widen its approach for capture and storage. As a result, the team collected more than 11 million data points. Following the close of this data collection effort on June 30 th , 2020, the team embarked on a major effort to appraise what had been collected, including an inventory list, spatial completeness, temporal completeness, scale and geographic characteristics, and a determination. A report on this matter was submitted on September 15 th , 2020, titled “DOE COVID-19 Data Curation Effort: Overview of Data Collection Coverage”. Over 2000 unique attributes had been netted over a wide range of spatial scales, including state, county, zip codes, health regions, and census blocks. Over 11 million individual data points were collected across these attributes, and spatial coverage (in total) included all 50 states and multiple territories. What became apparent in the process is that in the absence of any data standards, many states reported a wide variety of unique attributes that were not always compatible with attributes reported in other states. As time continued, states began adding new attributes and offering finer grain detail in some older attributes. This meant that not all data streams existed for the entire time period; in fact, the number tended to increase dramatically towards the end. Often, states would begin an attribute series and then stop altogether. These highly variable and uncertain conditions illuminated the need for harmonization approaches that would reconcile and conflate changing attribute names and detail over time. For example, grouping racial data reported as either Black or African American, depending on the state, into a single harmonized attribute. These choices would make a within-state analysis possible during the time period and lead to potential between-state analytics later on. This was almost entirely a manual decision process, requiring some subjective decision-making at times, to prevent a fragmented, short-lived collection of time series fragments that would offer few insights into trends, patterns, and correlates. This report imports harmonized data for state and county into the World Spatio-Temporal Analytics and Mapping Project (WSTAMP). WSTAMP is a major space-time analysis and visualization tool developed at ORNL for the National Geospatial-Intelligence Agency specifically for this kind of exploratory analysis. WSTAMP offers a rich analytical and graphical environment consisting of a wide range of analytics. These include time series plots, statistical summaries, data mining techniques, trend and pattern detection, and hypothesis generation.

59 BASIC BIOLOGICAL SCIENCES↗

Estimating List-Mode Data Sensitivities to Nuclear Data with MCNP6

Nuclear data are a vital component of predictive simulations used in applications like experiment design, stockpile stewardship, nuclear nonproliferation/safeguards, health physics, and criticality safety. A singular simulation requires the coalescence of different areas of nuclear data such as cross sections, angular distributions, and energy distributions of emitted neutrons for different materials and energy ranges. Improving nuclear data and thus reducing the uncertainty in simulated parameters could enable smaller, better-informed safety factors and ultimately reduce operational and procedural costs. There is a constant effort to garner a better understanding of the physical quantities represented by nuclear data through experiments. Integral experiment benchmarks use simulated and measured results to validate current nuclear data values. In the past, benchmarks primarily focused on the effective multiplication factor (k eff ); however, this limited scope has caused compensating errors and areas of nuclear data that lack validation. Compensating errors are inaccuracies in nuclear data that are obfuscated by cancellation when observing integrated values such as k eff . Diverse integral benchmark experiments that look for quantities of interest other than k eff and include multiple responses minimize the possibility of compensating errors and provides validation to areas of nuclear data previously lacking experimental validation. Benchmark experiments can be optimized during the design process to be highly dependent on specific areas of nuclear data. The dependence of a response in an experiment to a specific area/type of nuclear data is defined as sensitivity. A larger sensitivity means that nuclear data uncertainties will play a larger role in the response(s) resulting in larger bias. Currently, the sensitivity capabilities of the Monte Carlo N-Particle (MCNP ®1 ) transport code are limited to responses of k eff and tallied values (e.g., flux, surface current). As a part of the EUCLID project, this work explores estimating list-mode nuclear data sensitivities that can be used to design experiments aimed to constrain and reduce compensating errors in nuclear data by focusing on responses other than k eff . Tallied values are ideal quantities that are estimated with detectors during experiments. List-mode data (a list of neutron collection times) are the direct output of detector systems in subcritical neutron noise experiments. Expanding MCNP sensitivity capabilities to include the sensitivity of responses estimated from list-mode data, such as the prompt neutron decay constant (α) and multiplicity estimates (S and D), enables more direct comparison of simulated and measured experimental quantities. Additionally, deterministic tools such as SENSMG are capable of obtaining sensitivities to a wide variety of responses; however, these tools cannot handle complex geometries due to the assumptions made in discretizing the phase-space variables of the Boltzman transport equation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Closing the Gap between FAIR Data Repositories and Hierarchical Data Formats

Many in the scientific community, particularly in publicly funded research, are pushing to adhere to more accessible data standards to maximize the findability, accessibility, interoperability, and reusability (FAIR) of scientific data, especially with the growing prevalence of machine learning augmented research. Online FAIR data repositories, such as the Open Science Framework (OSF), help facilitate the adoption of these standards by providing frameworks for storage, access, search, APIs, and other features that create organized hubs of scientific data. However, the wider acceptance of such repositories is hindered by the lack of support of hierarchical data formats, such as Technical Data Management Streaming (TDMS) and Hierarchical Data Format 5 (HDF5), that many researchers rely on to organize their datasets. Various tools and strategies should be used to allow hierarchical data formats, FAIR data repositories, and scientific organizations to work more seamlessly together. A pilot project at Los Alamos National Laboratory (LANL) addresses the disconnect between them by integrating the OSF FAIR data repository with hierarchical data renderers, extending support for additional file types in their framework. The multifaceted interactive renderer displays a tree of metadata alongside a table and plot of the data channels in the file. This allows users to quickly and efficiently load large and complex data files directly in the OSF webapp. Users who are browsing files can quickly and intuitively see the files in the way they or their colleagues structured the hierarchical form and immediately grasp their contents. This solution helps bridge the gap between hierarchical data storage techniques and FAIR data repositories, making both of them more viable options for scientific institutions like LANL which have been put off by the lack of integration between them.

97 MATHEMATICS AND COMPUTING↗

ENDFtk: A robust tool for reading and writing ENDF-formatted nuclear data

ENDFtk is a recently developed C++ and Python interface to interact with ENDF-6 formatted nuclear data files. It provides a robust and complete interface, allowing the reading and writing of all formats currently part of the ENDF-6 formats manual, as well as some non-ENDF formats used by the NJOY processing code. It provides an interface that mimics the names in the ENDF-6 formats manual as well as an equivalent interface using human-readable attribute names. It is robust and powerful enogh for nuclear data experts to develop complex applications, while also simple enough to be used non-experts to retrieve and manipulate evaluated nuclear data. ENDFtk offers the ability to easily interrogate and manipulate data either in large-scale code projects or in simple Python scripts. Here, in this paper, a brief overview of the interface is given, as well as more substantial examples demonstrating plotting simple data, interacting with more complex data, and writing new data to files. ENDFtk is open source and available for download via GitHub (https://github.com/njoy/ENDFtk).

97 MATHEMATICS AND COMPUTING↗

Nuclear Data Uncertainty Quantification: Past, Present and Future

An historical overview is provided of the mathematical foundations of uncertainty quantification and the roles played in the more recent past by nuclear data uncertainties in nuclear data evaluations and nuclear applications. Significant advances that have established the mathematical framework for contemporary nuclear data evaluation methods, as well as the use of uncertainty information in nuclear data evaluation and nuclear applications, are described. This is followed by a brief examination of the current status concerning nuclear data evaluation methodology, covariance data generation, and the application of evaluated nuclear data uncertainties in contemporary nuclear technology. A few possible areas for future investigation of this subject are also suggested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Efficiency and Reliability Analyses of AC and 380V DC Distribution in Data Centers

Modern data centers consume large amounts of electricity, resulting in high operational costs. The efficiency of a data center power distribution system can be increased, and the operational cost reduced, if the number of power conversion stages can be minimized and more efficient converters, such as wide bandgap (WBG) converters, are used. This can be achieved by using DC distribution voltage at the rack level by eliminating extra conversion stages. In this paper, benchmarks for both AC and 380V DC data centers were developed and efficiency analyses were performed for an entire year. The impact of integrating photovoltaic (PV) systems into the data centers has also been analyzed in both cases in terms of efficiency. The results show that 380V DC data centers are more efficient than AC data centers with and without PV integration. Furthermore, the reliability of an AC system was compared to a 380V DC architecture with Tier-IV standard. Monte-Carlo simulations were used to perform reliability analyses for different levels of redundancy in the Uninterruptible Power Supply (UPS) system for both cases. In conclusion, the simulation results showed that the 380V DC distribution system had a higher level of reliability than the AC distribution system in data centers.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Delineating Facies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics with Level-Set Transformation

The facies-based approach has been widely adopted to delineate an aquifer into distinct geological units with unique distributions of hydraulic, physical, and/or chemical properties. The recent development in ensemble-based data assimilation methods allows both the direct and indirect data to be used to improve facies delineation. A major difficulty in those applications is to honor the spatial continuity and avoid overfitting after data assimilation. We introduce a new facies delineation framework to integrate ensemble data assimilation with traditional transition probability-based geostatistics. A level-set concept is used to parametrize discrete facies indicators and for updating facies shape. During the iterative data assimilation process, we impose spatial continuity by conditioning facies field generation on points selected adaptively based on their sensitivity to observation data. This reconditioning step is a key step to maintain spatial continuity and overcome over-fitting problems in inversion. We selected two examples to evaluate the performance of the new framework in estimating facies-based permeability field. The first example is a two-dimensional synthetic system with transient head data induced by pumping tests used for delineating two facies. The second example is a three-dimensional case with three facies, conceptualized from a field tracer experiment within the Columbia River corridor in Washington State, USA. Both examples demonstrate that the new method can adequately capture the spatial pattern of hydrofacies with reconditioning, which leads to the improved prediction of system behaviors.

Song, Xuehang↗

RDMA vs. RPC for Implementing Distributed Data Structures

Distributed data structures are key to implementing scalable applications for scientific simulations and data analysis. In this paper we look at two implementation styles for distributed data structures: remote direct memory access (RDMA) and remote procedure call (RPC). We focus on operations that require individual accesses to remote portions of a distributed data structure, e.g., accessing a hash table bucket or distributed queue, rather than global operations in which all processors collectively exchange information. We look at the trade-offs between the two styles through microbenchmarks and a performance model that approximates the cost of each. The RDMA operations have direct hardware support in the network and therefore lower latency and overhead, while the RPC operations are more expressive but higher cost and can suffer from lack of attentiveness from the remote side. We also run experiments to compare the real-world performance of RDMA- and RPC-based data structure operations with the predicted performance to evaluate the accuracy of our model, and show that while the model does not always precisely predict running time, it allows us to choose the best implementation in the examples shown. We believe this analysis will assist developers in designing data structures that will perform well on current network architectures, as well as network architects in providing better support for this class of distributed data structures.

distributed data structures↗

Data and scripts from: “Denoising autoencoder for reconstructing sensor observation data and predicting evapotranspiration: noisy and missing values repair and uncertainty quantification”

This data package includes data and scripts from the manuscript “Denoising autoencoder for reconstructing sensor observation data and predicting evapotranspiration: noisy and missing values repair and uncertainty quantification”.The study addressed common challenges faced in environmental sensing and modeling, including uncertain input data, missing sensor observations, and high-dimensional datasets with interrelated but redundant variables. Point-scaled meteorological and soil sensor observations were perturbed with noises and missing values, and denoising autoencoder (DAE) neural networks were developed to reconstruct the perturbed data and further predict evapotranspiration. This study concluded that (1) the reconstruction quality of each variable depends on its cross-correlation and alignment to the underlying data structure, (2) uncertainties from the models were overall stronger than those from the data corruption, and (3) there was a tradeoff between reducing bias and reducing variance when evaluating the uncertainty of the machine learning models.This package includes:(1) Four ipython scripts (.ipynb): “DAE_train.ipynb” trains and evaluates DAE neural networks, “DAE_predict.ipynb” makes predictions from the trained DAE models, “ET_train.ipynb” trains and evaluates ET prediction neural networks, and “ET_predict.ipynb” makes predictions from trained ET models.(2) One python file (.py): “methods.py” includes all user-defined functions and python codes used in the ipython scripts.(3) A “sub_models” folder that includes five trained DAE neural networks (in pytorch format, .pt), which could be used to ingest input data before being fed to the downstream ET models in ‘ET_train.ipynb” or ‘ET_predict.ipynb’.(4) Two data files (.csv). Daily meteorological, vegetation, and soil data is in “df_data.csv”, where “df_meta.csv” contains the location and time information of “df_data.csv”. Each row (index) in “df_meta.csv” corresponds to each row in “df_data.csv”. These data files are formatted to follow the data structure requirements and be directly used in the ipython scripts, and they have been shuffled chronologically to train machine learning models. The meteorological and soil data was collected using point sensors between 2019-2023 at(4.a) Three shrub-dominated field sites in East River, Colorado (named “ph1”, “ph2” and “sg5” in “df_meta.csv”, where “ph1” and “ph2” were located at PumpHouse Hillslopes, and “sg5” was at Snodgrass Mountain meadow) and(4.b) One outdoor, mesoscale, and herbaceous-dominated experiment in Berkeley, California (named “tb” in “df_meta.csv”, short for Smartsoils Testbed at Lawrence Berkeley National Lab).- See "df_data_dd.csv" and "df_meta_dd.csv" for variable descriptions and the Methods section for additional data processing steps. See "flmd.csv" and "README.txt" for brief file descriptions.- All ipython scripts and python files are written in and require PYTHON language software.

54 ENVIRONMENTAL SCIENCES↗

CORAL: A framework for rigorous self-validated data modeling and integrative, reproducible data analysis

Abstract Background Many organizations face challenges in managing and analyzing data, especially when relevant datasets arise from multiple sources and methods. Analyzing heterogeneous datasets and additional derived data requires rigorous tracking of their interrelationships and provenance. This task has long been a Grand Challenge of data science and has more recently been formalized in the FAIR principles: that all data objects be Findable, Accessible, Interoperable, and Reusable, both for machines and for people. Adherence to these principles is necessary for proper stewardship of information, for testing regulatory compliance, for measuring the efficiency of processes, and for facilitating reuse of data-analytical frameworks. Findings We present the Contextual Ontology-based Repository Analysis Library (CORAL), a platform that greatly facilitates adherence to all 4 of the FAIR principles, including the especially difficult challenge of making heterogeneous datasets Interoperable and Reusable across all parts of a large, long-lasting organization. To achieve this, CORAL's data model requires that data generators extensively document the context for all data, and our tools maintain that context throughout the entire analysis pipeline. CORAL also features a web interface for data generators to upload and explore data, as well as a Jupyter notebook interface for data analysts, both backed by a common API. Conclusions CORAL enables organizations to build FAIR data types on the fly as they are needed, avoiding the expense of bespoke data modeling. CORAL provides a uniquely powerful platform to enable integrative cross-dataset analyses, generating deeper insights than are possible using traditional analysis tools.

97 MATHEMATICS AND COMPUTING↗

RC-SFA Data Management Templates and Guidance for Standardized, Reusable AI-Ready Data Packages

This data package provides templates and supporting documentation developed by the River Corridor Science Focus Area (RC-SFA; https://www.pnnl.gov/projects/river-corridor) to communicate its approach to managing and publishing AI-ready data. The package is intended to help data users and data producers understand the structures, metadata practices, and quality-control approaches that support consistent, reusable, and machine-actionable data products across RC-SFA studies. Rather than focusing on a single experimental dataset, this package documents the data management framework used to make RC-SFA data easier to find, ingest, navigate, and interpret. The materials in this package reflect RC-SFA practices for standardized data package organization, including the use of a human- and machine-readable README, file-level metadata, data dictionaries, descriptive file naming, method identifiers, and automated and review-based quality assurance procedures. Together, these components illustrate how RC-SFA extends FAIR data principles toward AI-readiness by prioritizing deep metadata, consistency across data packages, and support for informed downstream reuse by both humans and computational tools. This dataset is comprised of (1) readme; (2) presentation slides with an overview of RC-SFA approach and guidance; (3) document of RC-SFA best practices; (4) data dictionary (dd); (5) file level metadata (flmd); and a subfolder containing templates for dd and flmd. All files are .csv and .pdf. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About.

AI-readiness↗

Recommended Nuclear Data for the Production of Selected Therapeutic Radionuclides

Increasing interest in the treatment of human disease by means of targeted radionuclide-based therapies requires an accurate understanding of achievable yields and quantification of realisable degrees of purity. Important studies within a more extensive Coordinated Research Project of the International Atomic Energy Agency (IAEA CRP) have included in-depth assessments and evaluations of all available measured cross-section data for ten nuclear reactions leading to the formation of 131 Cs, 131 Ba, 225 Ac, 225 Ra, 227 Th, 227 Ac, 230 U and 230 Pa for various on-going and proposed therapeutic applications in nuclear medicine. Equivalent studies were also undertaken of possible reactions to produce the 178W /low-spin 178m Ta generator system that has been clinically applied in diagnosis by means of SPECT - these particular cross-section studies and recommendations are included in this paper for completeness. All available measured data have been critically reviewed and assessed to produce statistically consistent datasets. Selected datasets have been fitted by a least-squares method with Padé approximations of variable order to evaluate the production cross sections and corresponding uncertainties. New measurements have been made in some instances, and reported data have been adjusted to accommodate new nuclear decay or monitor reaction data which altered the original reported quantities adversely. Insufficient measured data are available in many cases to permit a reliable evaluation of cross sections, and these instances are discussed. Finally, recommended therapeutic radionuclide production reaction data and their uncertainties are available on the Web page of the IAEA Nuclear Data Section at www-nds.iaea.org/radionuclides/ and also at the IAEA medical portal www-nds.iaea.org/medportal/.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Scidac-Data: Enabling Data Driven Modeling of Exascale Computing

Here, the SciDAC-Data project is a DOE-funded initiative to analyze and exploit two decades of information and analytics that have been collected by the Fermilab data center on the organization, movement, and consumption of high energy physics (HEP) data. The project analyzes the analysis patterns and data organization that have been used by NOvA, MicroBooNE, MINERvA, CDF, D0, and other experiments to develop realistic models of HEP analysis workflows and data processing. The SciDAC-Data project aims to provide both realistic input vectors and corresponding output data that can be used to optimize and validate simulations of HEP analysis. These simulations are designed to address questions of data handling, cache optimization, and workflow structures that are the prerequisites for modern HEP analysis chains to be mapped and optimized to run on the next generation of leadership-class exascale computing facilities. We present the use of a subset of the SciDAC-Data distributions, acquired from analysis of approximately 71,000 HEP workflows run on the Fermilab data center and corresponding to over 9 million individual analysis jobs, as the input to detailed queuing simulations that model the expected data consumption and caching behaviors of the work running in high performance computing (HPC) and high throughput computing (HTC) environments. In particular we describe how the Sequential Access via Metadata (SAM) data-handling system in combination with the dCache/Enstore-based data archive facilities has been used to develop radically different models for analyzing the HEP data. We also show how the simulations may be used to assess the impact of design choices in archive facilities.

97 MATHEMATICS AND COMPUTING↗

BRAINformat: A Data Standardization Framework for Neuroscience Data

Neuroscience is entering the era of `extreme data` with little experience and few plans for the associated volume, velocity, variety, and veracity challenges. This is a serious impediment for both the sharing of data across labs, as well as the utilization of modern and high-performance computing capabilities to enable data driven discovery. Here, we introduce BRAINformat, a novel file format and model for management and storage of neuroscience data. The BRAINformat library defines application-independent design concepts and modules that together create a general framework for standardization of scientific data. We describe the formal specification of scientific data standards, which facilitates sharing and verification of data and formats. We introduce the concept of Managed Objects, enabling semantic components of data formats to be specified as self-contained units, supporting modular and reusable design of data format components and file storage. The BRAINformat is built off of HDF5, enabling portable, scalable, and self-describing data storage. We introduce the novel concept of Relationship Attributes for modeling and use of semantic relationships between data objects, and discuss the annotation of data using dedicated data annotation modules provided by the BRAINformat library. Based on these concepts we implement dedicated, application-oriented modules and design a data standard for neuroscience data.The BRAINformat software library is open source, easy-to-use, and provides detailed user and developer documentation and is freely available at: https://bitbucket.org/oruebel/brainformat.

59 BASIC BIOLOGICAL SCIENCES↗

Proton radius from electron scattering data

Background: The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. The discrepancy has become known as the proton radius puzzle. Purpose: In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. Methods: We make use of stepwise regression techniques using the F-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. Results: Starting with the precision, low four-momentum transfer (Q 2 ) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the F-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on GE from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-Q 2 data on G E to select functions which extrapolate to high Q 2 , we find that a Pad´e (N = M = 1) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, G E (Q 2 ) = (1 + Q 2 /0.66 GeV 2 ) -2 . Conclusions: Rigorous applications of stepwise regression techniques and multivariate error estimates result in the extraction of a proton charge radius that is consistent with the muonic hydrogen result of 0.84 fm; either from linear extrapolation of the extreme low-Q 2 data or by use of the Pad´e approximant for extrapolation using a larger range of data. Thus, based on a purely statistical analysis of electron scattering data, we conclude that the electron scattering result and the muonic hydrogen result are consistent. Lastly, it is the atomic hydrogen results that are the outliers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗