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Improving Subsurface Stress Characterization for Carbon Dioxide Storage Projects

Researchers at New Mexico Tech, Los Alamos National Laboratory (LANL), Sandia National Laboratory (SNL), and other collaborators are developing a methodology to improve characterization of stress in the subsurface by means of a model-based inversion of reservoir engineering data, time lapse seismic measurements, and microseismicity. Historically, various geophysical techniques have been used in efforts to understand the state of stress in the subsurface through direct and indirect imaging of stress sensitive features (faults and fractures) and observations of transient stress related observations (time variant elastic moduli and microseismicity). Standard direct and indirect techniques for seismic fault and fracture imaging suffer from detectability limits due to reliance on high data quality and multiplicity. Variations in effective elastic properties from inversion of high quality seismic (Vertical Seismic Profile (VSP)) data may be used to infer stress near the wellbore through integration with independent experimental characterization of the stress-velocity relationship. Given a sufficiently robust observation network, microseismic emissions may be inverted to characterize focal mechanisms which, together with supporting assumptions and constraints, inform estimates of in-situ stress. While each of these techniques contributes in part to the characterization of stress within limited spatial and temporal domains, no one method provides an unambiguous stress measurement or a predictive capability over a site scale spatial extent. Challenges associated with solution non-uniqueness, measurement ambiguity, and irregular sampling may be greatly minimized through combination of one or more of independent measurements within a common framework in which realistic geological, hydrodynamic, geomechanical, and seismological constituent process models may act as constraints.

02 PETROLEUM↗

SPANet: Generalized permutationless set assignment for particle physics using symmetry preserving attention

The creation of unstable heavy particles at the Large Hadron Collider is the most direct way to address some of the deepest open questions in physics. Collisions typically produce variable-size sets of observed particles which have inherent ambiguities complicating the assignment of observed particles to the decay products of the heavy particles. Current strategies for tackling these challenges in the physics community ignore the physical symmetries of the decay products and consider all possible assignment permutations and do not scale to complex configurations. Attention based deep learning methods for sequence modelling have achieved state-of-the-art performance in natural language processing, but they lack built-in mechanisms to deal with the unique symmetries found in physical set-assignment problems. We introduce a novel method for constructing symmetry-preserving attention networks which reflect the problem's natural invariances to efficiently find assignments without evaluating all permutations. This general approach is applicable to arbitrarily complex configurations and significantly outperforms current methods, improving reconstruction efficiency between 19% - 35% on typical benchmark problems while decreasing inference time by two to five orders of magnitude on the most complex events, making many important and previously intractable cases tractable. A full code repository containing a general library, the specific configuration used, and a complete dataset release, are available at https://github.com/Alexanders101/SPANet

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Holographic Weyl anomaly in string theory

We compute the worldsheet sphere partition function of string theory on global AdS 3 with pure NS-NS flux. Because of an unfixed Möbius symmetry on the worldsheet, there is a cancellation of infinities and only a part of the answer is unambiguous. We show that it precisely reproduces the holographic Weyl anomaly and the ambiguous terms correspond to the possible counterterms of the boundary CFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Lattice regularization of reduced Kähler-Dirac fermions and connections to chiral fermions

We show how a path integral for reduced Kähler-Dirac fermions suffers from a phase ambiguity associated with the fermion measure that is an analog of the measure problem seen for chiral fermions. However, unlike the case of chiral symmetry, a doubler free lattice action exists which is invariant under the corresponding onsite symmetry. This allows for a clear diagnosis and solution to the problem using mirror fermions resulting in a unique gauge invariant measure. By introducing an appropriate set of Yukawa interactions which are consistent with ’t Hooft anomaly cancellation we conjecture the mirrors can be decoupled from low energy physics. Moreover, the minimal such Kähler-Dirac mirror model yields a light sector which corresponds, in the flat space continuum limit, to the Pati-Salam GUT model.

Physics↗

Higher-order $β$-functions in the Standard Model and beyond

In this contribution we consider the recent computation of the gauge coupling \beta β -function at four loops and the Yukawa matrix \beta β -function at three loops in the most general, renormalizable and four-dimensional quantum field theory. Furthermore, we discuss ambiguities and divergences arising in Yukawa matrix \beta β -functions.

Herren, Florian↗

Update of ASHRAE Standard 140 Section 5.2 and Related Sections (BESTEST Building Thermal Fabric Test Cases)

This report documents new work intended to update the current building thermal fabric software-to-software comparative test specifications and example results of ANSI/ASHRAE Standard 140-2017, Sections 5.2.1, 5.2.2, 5.2.3, and related supporting sections. The Building Energy Simulation Test and Diagnostic Method (BESTEST) test specification and example results that provide the basis for these Standard 140 sections were originally published in 1995. The state of the art in building energy simulation modeling has advanced since then. Additionally, comments on the test specification over the years highlighted ambiguities, further necessitating the update to the original work. This new work was conducted for the U.S. Department of Energy (DOE) by Argonne National Laboratory (Argonne) and National Renewable Energy Laboratory (NREL), in collaboration with a working group of international experts associated with the American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) Standing Standard Project Committee (SSPC) 140. SSPC 140 is responsible for ANSI/ASHRAE Standard 140. The new work, presented in this report, defined the test cases and specifications such that building energy simulation programs with time steps of one hour or less can perform the tests. Revisions to the test specification and update of example results follow the vetting process of iterative field trials established for previous BESTEST work that has been adapted for ASHRAE Standard 140.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Technical Procedures Writer's Guide

Technical procedures systematically describe a series of steps for the operation, maintenance, or testing of systems or components. They are widely used as a method for ensuring consistency, reducing human error, and improving the quality of the end-product. This guide provides specific guidance to procedure writers to help them generate high-quality technical procedures. The guidance is aimed at reducing confusion or ambiguity on the part of the operator, thereby increasing efficiency and reducing errors and rework. The appendices to this document define key terms associated with the creation of technical procedures, list common error traps, and define a set of action verbs that should be used in technical procedures.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Retaining Systems Engineering Model Meaning Through Transformation: Demo 2

Digital engineering strategies typically assume that digital engineering models interoperate seamlessly across the multiple different engineering modeling software applications involved, such as model- based systems engineering (MBSE), mechanical computer-aided design (MCAD), electrical computer-aided design (ECAD), and other engineering modeling applications. The presumption is that the data schema in these modeling software applications are structured in the familiar flat- tabular schema like any other software application. Engineering domain-specific applications (e.g., systems, mechanical, electrical, simulation) are typically designed to solve domain-specific problems, necessarily excluding explicit representations of non-domain information to help the engineer focus on the domain problems (system definition, design, simulation). Such exclusions become problematic in inter-domain information exchange. The obvious assumptions of one domain might not be so obvious to experts in another domain. Ambiguity in domain-specific language can erode the ability to enable different domain modeling applications to interoperate, unless the underlying language is understood and used as the basis for translation from one application to another. The engineering modeling software application industry has struggled for decades to enable these applications to interoperate. Industry standards have been developed, but they have not unified the industry. Why is this? The authors assert that the industry has relied on traditional database integration methods. The basic issue prohibiting successful application integration then is that traditional database-driven integration does not consider the distinct languages of each domain. An engineering models meaning is expressed through the underlying language of that engineering domain. In essence, traditional integration methods do not retain the semantic context (meaning) of the model. The basis of this research stems from the widely held assumption that systems engineering models are (or can be) structured according to the underlying semantic ontology of the model. This assumption can be imagined from two thoughts. 1) Digital systems engineering models are often represented using graph theory (the graph of a complex systems model can contain millions of nodes and edges). When examining the nodes one at a time and following the outbound edges of each node one by one, one can end up with rudimentary statements about the model (i.e., node A relates to node B), as in a semantic graph. 2) Likewise, from the study of natural languages, a sentence can be structured into unambiguous triples of subject-predicate-object within formal and highly expressive semantic ontologies. The rudimentary statements about a systems model discerned with graph theory closely mimic the triples used in the ontologies that try to structure natural languages. In other words, a systems models semantic graph can be (or is) structured into an ontology. Additionally, it is well established in industry that through natural language processing (NLP), which provides the means to create language structures, that computers can interpret ontological graphs. Therefore, the authors hypothesized that if the integrity of the underlying semantic structure of a systems model is retained, the contextual meaning of the model is retained. By structuring system models into the triples of the underlying ontology during the transformation from one MBSE application to another, the authors have provided a proof of the concept that the meaning of a system model can be retained during transformation. The authors assert that this is the missing ingredient in effective systems model-to-model interoperability. ACKNOWLEDGEMENTS The authors would like to thank the FY19 Model Interoperability team members who provided a solid foundation for the FY20 team to leverage: John McCloud, for the work he did to guide us toward the right use of technology that will appropriately discover and manipulate ontologies. Carlos Tafoya, for the work he did to develop an application programming interface (API)/Adapter that would export ontology-based data from GENESYS. Peter Chandler, for the work he did to architect our overall integration solution, with an eye toward the future that would influence a large-scale federated production-level systems engineering digital model ecosystem.

42 ENGINEERING↗

Knowledge Spillovers and Cost Reductions in Solar Soft Costs

Despite the commonly acknowledged importance of knowledge spillovers in reducing solar soft costs, we are only beginning to answer a fundamental question: who learns what (knowledge acquisition), from whom (knowledge production), and how (spillover mechanisms)? Until recently, this important topic has been largely unexplored in the case of solar soft costs. Thus, this project set out to identify how knowledge spillovers affect soft costs in the U.S. photovoltaic (PV) installation industry, specifically how important spillovers are, what types of knowledge are most likely to spillover, and how networks of actors affect spillovers. Our findings offer insights for designing solutions that address problems associated with knowledge spillovers and that leverage spillovers to reduce solar soft costs. Recognizing the ambiguity in the definition of soft costs, i.e., “non-hardware costs,” and variability in soft cost categories, we developed the Solar Soft Cost Ontology (SSCO) to systematically identify key concepts related to soft costs, network actors, learning processes, and the relationships between them. This ontology served as a foundational organizational structure for the methodology of the remaining tasks: case studies, surveys, pricing analysis, patent analysis, network analysis, and project integration across tasks. While there is substantial learning among installers that is reducing the soft costs for PV installations, most of that learning is retained by firms rather than spread across the industry. The positive relationship between experience accumulation and cost reductions is typically explained as learning by doing (LBD), but we find that LBD effects are mediated by other learning mechanisms, including learning by searching and learning by interacting. Knowledge spillovers have significant potential to reduce solar PV soft costs, but successful knowledge spillover pathways are complex and non-trivial. There are a wide variety of ways to construct an installation business, thus categories of firms that can effectively cross-learn directly are small and what knowledge is relevant to whom is challenging and costly for firms to assess. This fragmentation limits the critical mass needed for spillover related soft cost reductions. Knowledge does not flow directly between installers. Indirect knowledge transfer pathways are critical: distributors, software providers, collaboratives, and hiring. Furthermore, diverse, more integrated knowledge networks tend to promote successful learning by organizations and across the system as a whole. Accordingly, we find the need to supporting the whole ecosystem using an integrated policy and programmatic approach to support installers, distributors, complementary sector, and facilitators. Overall, a deliberate policy-mix design is needed to reduce the solar PV deployment barrier in terms of installation cost reductions, because deployment policies could potentially interact with policies that facilitate network-building and technological innovation. A combination of deployment policies, innovation-support policies, and network-facilitating policies could potentially lead to a more desired market outcome through achieving higher joint learning rates from firms’ cumulative experiences developed in a more integrated production and deployment ecosystem.

14 SOLAR ENERGY↗

Federal Oversight of Hydrogen Systems

The application of hydrogen as an energy carrier has been expanding into industrial and transportation sectors enabling sustainable energy resources and providing a zero-emission energy infrastructure. The hydrogen supply infrastructure includes processes from production and storage, to transportation and distribution, to end use. Each portion of the hydrogen supply infrastructure is regulated by international, federal, state, and local entities. Regulations are enforced by entities which provide guidance and updates as necessary. While energy sources such as natural gas are currently regulated via the Code of Federal Regulations and United States Code, there might be some ambiguity as to which regulations are applicable to hydrogen and where regulatory gaps may exist. This report contains an overview of the regulations that apply to hydrogen, and those that may indirectly cover hydrogen as an energy carrier participating in a sustainable zero emission global energy system. As part of this effort, the infrastructure of hydrogen systems and regulation enforcement entities are defined, and a visual map and reference table are developed. This regulatory map and table can be used to identify the boundaries of federal oversight for each component of the hydrogen supply value chain which includes production, storage, distribution, and use.

08 HYDROGEN↗

Miscalculation, Misperception and Risk Reduction

In the current security environment, the most likely wars for which the US and its allies must be prepared are wars against nuclear-armed states. Such wars bring unique risks of both vertical and horizontal escalation. Some are “accepted risks;” for example, the US may choose to escalate a conflict to clarify its commitment to an issue and defend its interest. Other are “unacceptable risks;” especially, the risk of miscalculation by the U.S. or an adversary. The focus here is on this latter category. Miscalculation is an error of judgment—the failure to accurately assess a situation. Miscalculation can result from hidden, incomplete, or ambiguous information, or from inaccurate processing of available information because of bias, overconfidence, denial, delusion, etc. Miscalculation is related to misperception. For some, they are synonymous. This paper characterizes the risks of miscalculation and introduces a discussion of a risk mitigation strategy.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

A Machine Learns to Predict the Stability of Highly Diverse Multi-planetary Systems

Machine learning has proven to be an invaluable tool for characterizing the stability of planets in simplified planetary systems. In this work, we investigate the performance of a machine learning classifier on tightlypacked systems containing a rich diversity of planets, from Earths to Jupiters. Using information derived from short numerical simulations about a planet’s early orbital evolution and its relationship with the most massive planets in the system, we train a random forest classifier to predict instability with a > 88 percent accuracy. Our classifier relies on relative planet masses and the standard deviation of eccentricity for much of its predictive power. Most misclassified planets lie along a multi-dimensional boundary between stable and unstable planets, indicating that their early orbital evolution is ambiguous. The major reason for misclassification in this work is timescale: because our classifier uses information from only the first 137 years of simulation data, it is blind to late time interactions that cause or prevent instability. Machine learning methods like those utilized in this work provide powerful tools to complement numerical simulations across a wide range of planetary architectures.

79 ASTRONOMY AND ASTROPHYSICS↗

Photo-cleaned Backgroundless Ion Chambers (Final Report for PDRD SR18010)

Ion chambers are often employed to measure the concentration of tritium within flowing gases. In real world environments the active surfaces of ion chambers become covered with tritiated surface contaminants. This tritiated surface contamination will create a large background response that can mask the signature of interest, which is the tritium concentration in the gas phase. Previous efforts to reduce the effects of surface contamination in ion chambers utilize inert coatings (e.g., gold) and low surface area electrodes (e.g., wire mesh), but this route only reduces the effect and does not necessarily alter the ratio of surface contamination to current collection area. Additionally, gold coating may add a substantial cost to the instrument. In the Tritium Facility, ion chambers are periodically cleaned using an alcohol-based process. This process is time consuming and often leads to ion chamber wear and breakage. In addition, periodic cleaning does not address tritium level ambiguities in gloveboxes. An ideal solution to this issue would be to either develop an ion chamber that does not accrue surface contamination, or one that is self-cleaning while it is in operation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

On the Determination of the Radiation Doses at Hiroshima [Slides]

Essentially all knowledge regarding the chronic effects of radiation exposure is derived from statistical analyses of the survivors of Hiroshima and Nagasaki. However, we were then, and are now, uncertain about the exposures. That is: We know the effects through observations and statistical analyses, but we can only estimate the doses. Other complications include the fact that Little Boy was truly unique. It was never tested, measurements of yield were ambiguous, calculations of yield were not consistent, and calibration measurements were not made, could not be made.

61 RADIATION PROTECTION AND DOSIMETRY↗

Geothermal Fault Zone and Fluid Imaging through Joint Airborne ZTEM and Ground MT Data Inversion Analysis

This project has aimed to achieve detailed electrical resistivity resolution at geothermal reservoir scales by combining airborne natural electromagnetic (EM) field surveying (ZTEM) with ground magnetotelluric (MT) measurements to approximate an airborne MT geophysical method. MT alone is relatively expensive and may have permitting challenges in sensitive areas. Airborne ZTEM field data contains only the magnetic field, requires a background assumption, and has been limited to relatively high frequencies, thus suffering uniqueness problems. Based on proto-type 2D simulations, ZTEM ambiguities may be reduced through formal incorporation with possibly sparse ground MT soundings, which we pursued in full 3D for this project. The methodology was tested at the high-temperature Roosevelt Hot Springs geothermal system, Utah, which was considered advantageous given the near total exposure of crystalline reservoir rocks across the project area. ZTEM and ground MT survey data were acquired in 2017, subcontracted to outside parties with which we have worked in the past. These included 80 remote-referenced tensor MT soundings over the Mineral Mountains and adjacent Roosevelt Hot Spring producing geothermal system. These MT stations abut later coverage of a similar number of MT stations taken for the Utah FORGE project providing excellent total data aperture to re-solve structure beneath both project areas better than either set alone. The airborne ZTEM survey covered 704 line kilometers in E-W flight lines with a 250 m line spacing. Although this survey was timed during a maintenance-related shutdown of power production at the Roosevelt Hot Springs, other noise sources difficult to identify but including two high-voltage state-scale transmission lines compromised the ZTEM survey badly leading to unusable responses. Thus, with DOE management concurrence, the project proceeded to emphasize inversion and interpretation of the joint SubTER-FORGE MT data sets with regard to the Roosevelt Hot Springs reservoir recharge and to deep heat sources for both it and the Utah FORGE EGS project area. We also investigated the joint ZTEM-MT sampling concept with data sets from the Eleven Mile Canyon prospect area donated by the U.S. Navy (A. Sabin, PoC). Inversion of the SubTER-FORGE MT data using the HexMT 3D finite element algorithm reveals a large, low-resistivity anomaly extending sub-vertically through the depth range of the crust beneath the western Mineral Mountains. The steep conductive zone connects in the lower crust to a more tabular conductor characteristic of much of the Great Basin that generally is ascribed to current mafic magmatic underplating, hybridization and fluid release. The location of the resolved anomaly relative to the recent (0.5-0.8 Ma) eruptive centers of the Mineral Mountains implicates it as remnants of the magma body which fed these centers. This structure appears to be currently feeding heat and fluids upward into the Roosevelt Hot Springs hydrothermal system, as well as heat laterally to the FORGE project area. Separate and joint inversion models were carried out for the donated Eleven Mile Canyon MT-ZTEM data set to demonstrate concept. ZTEM only inversion showed two main alteration zones in the western portion of the project area known from geological mapping. Joint inversion including an E-W profile of MT soundings sharpened these features considerably. It also resolved in much greater detail the graben related normal faulting structure of the central project area which lies at depths exceeding the sensitivity of ZTEM alone. The sparse number of MT da-ta relative to the ZTEM required upweighting the former by a factor of several, but an exact procedure awaits future research. Our final impression is that sparse MT data can improve resolution of the subsurface over that of ZTEM alone. However, well sampled MT data are to be preferred and offer the simplicity of interpreting just one data type, and possess the superior resolution capability coming with the electric field everywhere, and from their high bandwidth.

15 GEOTHERMAL ENERGY↗

Big Data Synchrophasor Monitoring and Analytics for Resiliency Tracking (BDSMART)

This report contains key findings from a project titled Big Data Synchrophasor Monitoring and Analytics for Resiliency Tracking (BDSMART), which was carried out through a collaborative effort of a team of researchers from Texas A&M Engineering Experiment Station, Temple University, and Quanta Technology, LLC. The in-kind support came from OSIsoft (acquired by AVEVA), which provided their PI Historian software to demonstrate the use case of streaming PMU data. The first section of the report describes the project goals and objectives related to the development of Machine Learning (ML) models capable of detecting and classifying events by processing phasor measurements captured in the field by Phasor Measurement Units (PMUs). The data for this study was contributed by the utilities/ISOs from the Western and Eastern interconnects and ERCOT, further referred to as Interconnect B (IC B), Interconnect A (IC A), and Interconnect C (IC C), respectively. The approach that the BDSMART Research Team proposed and the key research tasks defined by the team are outlined in this section. The next section describes the technical approach. We first discuss the data constraints related to the PMU measurements and data interpretation constraints imposed by the data contributors. They provided neither the topological information of the grid nor PMU placement locations and captured recorded data at very few locations in the system with the reporting rate of either 30 or 60 fps. The recordings are mostly positive sequence voltage, frequency, and ROCOF, and in some limited cases, three-phase voltages and currents. We then reflect on the bad data issues that stem from poor recording practices and vague definitions of the PMU status bits to supposedly be used for bad data identification. Finally, the data discovery points to imprecise time stamps with incomplete event start/end time, as well as inconsistent and incomplete event labeling, which combined make the implementation of the data models using supervising learning quite challenging. Following the data discovery study, we hypothesize that because the IC B data has the most complete labels, we should focus our model development on that data and then test it on data from other interconnects. We also define the common metrics used to evaluate the results from the ML algorithm tests. We concluded this section by summarizing the common ML models we used and explaining how we implemented and tested them. The issues from this section are expanded in the Training Dataset Report from this project. The final section of this report deals with the accomplishments and conclusions. As the accomplishments, we formulate the problem we are solving and what is achieved by solving the problem. We then reflect on each of the analytics tools we developed and point out the performance of each tool when applied to solving the mentioned problems. We reference this work for further details to the papers we published on each tool. In the conclusions, we give recommendations on how to improve future PMU recording practices to facilitate the ML algorithm implementation and guidance for the future standardization work aimed at clarifying the ambiguities associated with the PMU status bits. We finally list future tasks that can bring about further improvements in the proposed algorithms. The issues from this section are expanded in the Training, and Test Dataset Report filed at the project completion date.

97 MATHEMATICS AND COMPUTING↗

(U) Average Scattering Angle Cosine Sensitivities

The Evaluated Nuclear Data File (ENDF) provides covariances of the average scattering angle cosine $\overline{μ}$ for 117 nuclides, and the NJOY nuclear data processing code can process these covariances. To propagate them to the uncertainty of a response due to uncertainties in $\overline{μ}$ requires sensitivities of the response with respect to $\overline{μ}$. This report uses NJOY’s definition of $\overline{μ}$ and derives a relationship between the sensitivity of a response to $\overline{μ}$ and the sensitivity of the response to the anisotropic P 1 elastic scattering cross section. This relationship has been implemented in the multigroup neutron sensitivity code SENSMG, which relies on the discrete ordinates code PARTISN for the neutron transport calculations. Kodeli has also calculated sensitivities with respect to $\overline{μ}$ and associated uncertainties. However, the formal derivation of this paper shows that the definition of the sensitivity with respect to $\overline{μ}$ is ambiguous because there are multiple ways to change $\overline{μ}$ by changing scattering cross sections. Here we derive two such ways. Both are implemented in SENSMG. This report is organized as follows. Section II discusses $\overline{μ}$ and its significance. Section III presents the equations used for the sensitivity of a response with respect to $\overline{μ}$, and Section IV discusses how to compute these sensitivities with SENSMG and MCNP6.3. Section V is a fast-spectrum test problem, and Sec. VI is a thermal-spectrum problem. Section VII is a summary. The example problem inputs are listed in the appendix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Systematic Extraction of Pion Parton Distributions Using Threshold Resummation and Applications to Pion TMDs

Following our recent Monte Carlo determination of the pion?s PDFs from Drell-Yan (DY) and leading neutron electroproduction data from the Jefferson Lab Angular Momentum (JAM) collaboration, we extend the analysis by including effects from threshold resummation. At higher orders in the strong coupling, ?S, soft gluon emissions cause large logarithmic corrections, which become important in the qq¯ channel of the DY partonic cross section near threshold. These corrections can be summed over all orders of ?S. However, different prescriptions exist for how the threshold resummation is implemented, for instance, using varying levels of approximation in the Minimal Prescription with cosine, expansion, and double Mellin methods. We present the Monte Carlo results of the first simultaneous fit of the valence, sea, and gluon distributions in the pion taking into account the ambiguities in the resummation calculations. The wide ranges of valence distributions at large x and the effective behavior of the valence distribution as x approaches 1 is discussed. While the PDFs are extracted through collinear factorization, we additionally present a dedicated study to the low and large lepton pair transverse momentum distributions (TMDs) in the same DY experimental data. By adjusting the nonperturbative TMD components, we analyze the degree of compatibility between data and theory across all regions of transverse momentum dependence. We attempt to match the description of the low transverse momentum region using Collins-Soper-Sterman (CSS) formalism and the large transverse momentum region, which is best described using collinear factorization.

Sato, Nobuo↗