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Results for “Derived quantities preservation”

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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18 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Online and Scalable Data Compression Pipeline with Guarantees on Quantities of Interest

Data compression is becoming critical for data-intensive scientific applications. Scientists require compression techniques that accurately preserve derived quantities of interest (QoIs). Prior work has shown that a pipeline can be built to guarantee error on the primary data (PD) within user-defined bounds and achieve near-floating point QoI errors. In this paper, we present novel computational approaches for accelerating the pipeline and demonstrate results that enable concurrent execution of compression in parallel with the simulation nodes. This allows compression, including the writing of the required compression data, for the previous time step to be completed while the simulation proceeds with the current time step. Overall, the approach presented in this paper results in a 6–8 times improvement in computational overhead compared to previous work. These results were obtained using data generated by a large-scale fusion code called XGC, which produces hundreds of terabytes of data in a single day.

Banerjee, Tania↗
DOE OSTI2025

Scalable Hybrid Learning Techniques for Scientific Data Compression

Data compression is becoming critical for storing scientific data because many scientific applications need to store large amounts of data and post process this data for scientific discovery. Unlike image and video compression algorithms that limit errors to primary data (PD), scientists require compression techniques that accurately preserve derived quantities of interest (QoIs). Here, this article presents a physics-informed compression technique implemented as an end-to-end, scalable, GPU-based pipeline for data compression that addresses this requirement. Our hybrid compression technique combines machine learning techniques and standard compression methods. Specifically, we combine an autoencoder, an error-bounded lossy compressor to provide guarantees on raw data error, and a constraint satisfaction post-processing step to preserve the QoIs within a minimal error (generally less than floating point error). The effectiveness of the data compression pipeline is demonstrated by compressing nuclear fusion simulation data generated by a large-scale fusion code, XGC, which produces hundreds of terabytes of data in a single day. Our approach works within the ADIOS framework and results in compression by a factor of more than 150 while requiring only a few percent of the computational resources necessary for generating the data, making the overall approach highly effective for practical scenarios.

ITER↗
NASA NTRS1991

A Variational Assimilation Method for Satellite and Conventional Data: a Revised Basic Model 2B

A variational objective analysis technique that modifies observations of temperature, height, and wind on the cyclone scale to satisfy the five 'primitive' model forecast equations is presented. This analysis method overcomes all of the problems that hindered previous versions, such as over-determination, time consistency, solution method, and constraint decoupling. A preliminary evaluation of the method shows that it converges rapidly, the divergent part of the wind is strongly coupled in the solution, fields of height and temperature are well-preserved, and derivative quantities such as vorticity and divergence are improved. Problem areas are systematic increases in the horizontal velocity components, and large magnitudes of the local tendencies of the horizontal velocity components. The preliminary evaluation makes note of these problems but detailed evaluations required to determine the origin of these problems await future research.

Achtemeier, Gary L.↗
DOE OSTI2023

Fast Algorithms for Scientific Data Compression

Many scientific simulations and experiments generate terabytes to petabytes of data daily, necessitating data compression techniques. Unlike video and image compression, scientists require methods that accurately preserve primary data (PD) and derived quantities of interest (QoIs). In our previous work, we demonstrated the effectiveness of hybrid compression techniques that combine machine learning with traditional approaches. This paper presents innovative computational techniques aimed at expediting the compression pipeline. Our experiments, conducted on two distinct platforms with a large-scale XGC-based fusion simulation, demonstrate that the overhead incurred by these new approaches is less than one percent of the computational resources needed for the simulation.

Banerjee, Tania↗
NASA NTRS1985

The evolution of impact basins - Cooling, subsidence, and thermal stress

The present study is concerned with an assessment of the contribution of thermal contraction and thermal stress to the topography and tectonics of large lunar impact basins. Exploratory models are developed, giving attention to the temperature structure following basin formation, the subsequent cooling of the basin region, and the resulting thermal displacements and stresses as functions of time. The subsidence and stress at the surface are compared with topography and tectonic features in the comparatively well-preserved Orientale basin. The results of the comparison are used as a basis to derive approximate constraints on the quantity and distribution of heat implanted during the basin-formation process.

Bratt, S. R.↗
NASA NTRS1975

Development of the mare regolith - Some model considerations

This investigation uses results obtained in an earlier Monte Carlo study by Oberbeck et al. (1973) to shed light on the consequences of mare-regolith origin by impact comminution of primarily local basaltic rocks by evaluating regolith growth and mixing as a function of time. The study demonstrates that regolith growth is self-regulated and has the same trend and nearly the same terminal growth rates whatever the history of bombardment: rapid initial accumulation followed by diminishing rates of growth. Mixing and all other processes investigated are growth regulated. Mixing increases as growth slows, but never to the extent that the regolith is homogenized. Because the average regolith is never homogenized, products of growth-regulated processes are preserved in the stratigraphy. This model indicates that deeper levels contain thinner depositional units, lesser quantities of meteoritic and exotic components, and more debris derived from shallow levels in the mare basalts than material in near-surface layers.

Quaide, W.↗
DOE OSTI2025

Hybrid learning techniques for scientific data reduction with performance guarantees

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Final report- UFL - RAPIDS2: A SciDAC Institute for Computer Science, Data, and Artificial Intelligence

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Including the vacuum energy in stellarator coil design

Being three-dimensional, stellarators have the advantage that plasma currents are not essential for creating rotational-transform; however, the external current-carrying coils in stellarators can have strong geometrical shaping, which can complicate the construction. Reducing the inter-coil electromagnetic forces acting on strongly shaped 3D coils and the stress on the support structure while preserving the favorable properties of the magnetic field is a design challenge. In this work, we recognize that the inter-coil forces are the gradient of the vacuum magnetic energy. We introduce an objective functional built on the usual quadratic flux on a prescribed target surface together with a weighed penalty on the vacuum energy. The Euler–Lagrange equation for stationary states is derived, and numerical illustrations are computed using a modern stellarator optimization framework. A study of the effect of the energy functional on the inter-coil forces is conducted and the energy is shown to be a promising quantity in producing coils with low forces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

Nitrogen geochemistry of a Cretaceous-Tertiary boundary site in New Zealand

Nitrogen in the basal layer of the K-T boundary clay at Woodside Creek, New Zealand, has an abundance of 1100 ppm, a 20-fold enrichment over Cretaceous and Tertiary values. The enrichment parallels that for Ir and elemental carbon (soot); all decrease over the next 6 mm of the boundary clay. The C/N ratio, assuming the nitrogen to be associated with organic rather than elemental carbon, is approximately 5 for the basal layer compared to 20 to 30 for the remainder of the boundary clay. The correlation between N and Ir abundances appears to persist above the boundary, implying that the N is intimately associated with the primary fallout and remained with it during the secondary redeposition processes that kept the Ir abundance relatively high into the lowermost Tertiary. Apparently the basal layer of the boundary clay represents the accumulation of a substantial quantity of N with an isotopic composition approximately 10 percent heavier than background delta value of N-15 values. If the boundary clay represents an altered impact glass from a meteorite impact than it probably denotes a time period of less than 1 year. Therefore, the changes in nitrogen geochemistry apparently occurred over a very short period of time. The high abundance of N and the correspondingly low C/N ratio may reflect enhanced preservation of organic material as a result of the rapid sweepout and burial of plankton by impact ejecta, with little or no bacterial degradation. It is conceivable that the shift in delta value of N-15 may represent an influx of nitrogen from a different source deposited contemporaneously with the impact ejecta. An interesting possibility is that it may be derived from nitrate, produced from the combustion of atmospheric nitrogen.

Gilmour, Iain↗
NASA NTRS2011

Post-Fragmentation Whole Genome Amplification-Based Method

This innovation is derived from a proprietary amplification scheme that is based upon random fragmentation of the genome into a series of short, overlapping templates. The resulting shorter DNA strands (<400 bp) constitute a library of DNA fragments with defined 3 and 5 termini. Specific primers to these termini are then used to isothermally amplify this library into potentially unlimited quantities that can be used immediately for multiple downstream applications including gel eletrophoresis, quantitative polymerase chain reaction (QPCR), comparative genomic hybridization microarray, SNP analysis, and sequencing. The standard reaction can be performed with minimal hands-on time, and can produce amplified DNA in as little as three hours. Post-fragmentation whole genome amplification-based technology provides a robust and accurate method of amplifying femtogram levels of starting material into microgram yields with no detectable allele bias. The amplified DNA also facilitates the preservation of samples (spacecraft samples) by amplifying scarce amounts of template DNA into microgram concentrations in just a few hours. Based on further optimization of this technology, this could be a feasible technology to use in sample preservation for potential future sample return missions. The research and technology development described here can be pivotal in dealing with backward/forward biological contamination from planetary missions. Such efforts rely heavily on an increasing understanding of the burden and diversity of microorganisms present on spacecraft surfaces throughout assembly and testing. The development and implementation of these technologies could significantly improve the comprehensiveness and resolving power of spacecraft-associated microbial population censuses, and are important to the continued evolution and advancement of planetary protection capabilities. Current molecular procedures for assaying spacecraft-associated microbial burden and diversity have inherent sample loss issues at practically every step, particularly nucleic acid extraction. In engineering a molecular means of amplifying nucleic acids directly from single cells in their native state within the sample matrix, this innovation has circumvented entirely the need for DNA extraction regimes in the sample processing scheme.

Benardini, James↗
DOE OSTI2026

A Unified Workflow for Sensitivity-Based Kinetic Analysis in Microkinetic Models

Degrees of rate control (DRC), apparent activation energies, and apparent reaction orders are established local sensitivity diagnostics for interpreting microkinetic models, but applying them routinely to large mechanisms often requires substantial reaction-specific bookkeeping, perturbation design, and postprocessing. Here, in this study, we present a unified derivative-based workflow that evaluates these quantities from a single compiled reaction-network model and target-rate definition. For any user-provided microkinetic model, the workflow compiles the mechanism into stoichiometrically consistent mass-action rate equations, solves the surface dynamics, and uses automatic differentiation to compute sensitivities with respect to rate constants, temperature, and gas partial pressures. By combining their calculations in the same framework, the workflow clearly demonstrates the relationships between different DRCs and the apparent activation energy. Using existing examples of propylene partial oxidation and methane oxidation on Pd(100), we verify expected transient redistribution of rate control, distinguish net Campbell DRCs from one-sided directional sensitivities, and show how apparent activation energy can be reconstructed either from one-sided DRCs or from state-based DRCs while critical mechanistic insights are obtained consistently. In the methane oxidation case, a pathway-subset test further illustrates how a simplified mechanism preserves key kinetic signatures of a full model, showing the potential of our user-friendly tool for model construction beyond kinetic analysis.

36 MATERIALS SCIENCE↗
NASA NTRS2007

Large Solar-Rejection Filter

NASA utilized Image Intensified Video Cameras for ATV data acquisition from a jet flying at 12.8 km. Afterwards the video was digitized and then analyzed with a modified commercial software package, Image Systems Trackeye. Astrometric results were limited by saturation, plate scale, and imposed linear plate solution based on field reference stars. Time-dependent fragment angular trajectories, velocities, accelerations, and luminosities were derived in each video segment. It was evident that individual fragments behave differently. Photometric accuracy was insufficient to confidently assess correlations between luminosity and fragment spatial behavior (velocity, deceleration). Use of high resolution digital video cameras in future should remedy this shortcoming. A scenically accurate description of matter interpreted as a substance made up of corpuscular constituents was established during the course of the 19th century. In this description, atoms--the building blocks of the matter--form molecules. The properties of the molecules were described by chemistry or thermodynamics depending on what characteristics of the matter were investigated. In both theories, the molecules can dissociate to atoms when the kinetic energies of the atoms exceed the strength of the chemical bonds. The number of atoms is always preserved in a closed system. This is not true, however, when the matter takes up much higher energies at relativistic scales. New particles can be produced at the expense of the kinetic energy. The number of particles is no longer preserved. There are other conserved quantities, however, these quantities, the charge, baryon number, lepton number, are associated with particles that are considered elementary today. The properties and behavior of these elementary particles is the subject of Particle Physics or High Energy Physics. Practice Page: A crewmember touching a positively charged surface was thought to be galvanically isolated from the vehicle ground analogous to a bird on a high voltage power wire. Recent analysis confirms that positive floating potentials, ionospheric currents to the EVA suit, can be hazardous. The analysis is wrong in that the ionospheric plasma itself can close the circuit. Parametric analysis of very low voltage exposures (2 to 15 volts) could cause pain and/or involuntary muscle tetani or spinal cord shock. NASA worked with the Naval Health Research Center Detachment Directed Energy Bioeffects Laboratory to examine the affects electrical hazards could have on extravehicular activity using two models. The results of the two computational models were combined to predict areas of the body in which neurons of different diameters would be excited. They predicted that physiologically active current could be conducted across the crew member causing catastrophic hazards. Future work to analyze additional current paths was proposed. The FUSE spectrum of BB Dor, observed in a high state, is modeled with an accretion disk with a very low inclination (possibly lower than 10 degrees). Assuming an average WD mass of 0.8 solar mass leads to a distance of the order of approximately 650pc, consistent with the extremely low galactic reddening in its direction, and a mass accretion rate of 10 (exp -9) solar mass a year. The spectrum presents some broad and deep silicon and sulfur absorption lines, indicating that these elements are over-abundant: silicon is 3 times solar, and sulfur is 20 times solar. The FUSE spectrum of BB Dor, observed in a high state, is modeled with an accretion disk with a very low inclination (possibly lower than 10 degrees). Assuming an average WD mass of 0.8 solar mass leads to a distance of the order of approximately 650pc, consistent with the extremely low galactic reddening in its direction, and a mass accretion rate of 10 (exp -9) solar mass a year. The spectrum presents some broad and deep silicon and sulfur absorption lines, indicating that these elements are over-abundant: silicon is times solar, and sulfur is 20 times solar. From its previously observed optical emission lines, P831-57 (WD 0334 6400 or Ret 1 in A Catalog and Atlas of Cataclysmic Variables: Living Edition) has been suspected to contain an accretion disk associated with a companion star in orbit around a subdwarf star with a temperature T is greater than 21,000K. P831-57 has therefore been classified as a nova-like. However, our present observations show it to be a DA + dMe binary. The analysis of its Far Ultraviolet Spectroscopic Explorer (FUSE) spectrum (continuum and lines) reveal an average mass white dwarf (Log(g) approximately equals 7.8 plus or minus 0.1)with a temperature T approximately equals 37,000 plus or minus 500K, an extremely low projected rotational velocity, and a distance of about 115 plus or minus 5pc. The photosphere contains C, N, Si, and S (at about 1% of solar abundances). The dMe star is seen as a flux excess in near-infrared photometry and appears to show occasional flaring of about one magnitude as seen in the Harvard plates. There is no evidence of periodic variability in the spectroscopic or photometric data. We find no evidence of a an accretion disk, instead we find evidence of wind accretion as the stellar carbon abundance (N(C)/N(H) = 2.5 x 10 (exp -6) is about ten times larger than predicted by radiative levitation for such a gravity and temperature. The power needs and solutions for the space exploration and lunar mobility program are discussed. Long term missions in space and on the lunar surface require high energy batteries. Rechargeable batteries for mobility systems and portable utility pallet are needed for successful exploration missions. Nanomaterial usage increases the energy density of the cells apart from increasing the power density. The symptoms and threats from acute mountain sickness (AMS) are discussed. The underlying assumptions concerning spacecraft atmosphere mean there is a potential risk to astronauts. The baseline worst case scenario is about 25% based on direct ascent to 8.0 psia with 32% O2. The practical mitigation approach is a staged depressurization scheme. Due to the uncertainty about potential AMS risk the flight surgeon should prepare, focused research should proceed, and current analytical efforts should continue. This slide presentation reviews the threat astronauts face from acute mountain sickness (AMS). The incidence of AMS is highly variable and the risk to astronauts is unclear. However, the potential risk is higher than current EAAs suggest and precautions should be implemented. Due to the uncertain nature of the risk flight surgeons should prepare, and focused research should proceed. Quasiparticle tunneling can be understood at low temperatures using a non-equilibrium kinetic theory. Low-temperature tunneling can be suppressed using existing techniques: island-lead gap engineering, lead cooling with SIN junctions, and quasiparticle traps. The slide presentation reviews the science goals and mission planning for the proposed Jupiter System Observer (JSO). The spacecraft would accommodate 9 instruments making the instrument payload more capable than any previously flown to Jupiter. The would-be mission includes study programs for Jupiter's satellites, interior, magnetosphere and atmosphere. The power needs and solutions for the space exploration and lunar mobility program are discussed. Long term missions in space and on the lunar surface require high energy batteries. Rechargeable batteries for mobility systems and portable utility pallet are needed for successful exploration missions. Nanomaterial usage increases the energy density of the cells apart from increasing the power density. This slide presentation reviews the power requirements for the space exploration and the lunar surface mobility programs. It includes information about the specifications for high energy batteries and the power requirements for lunar rovers,

Roberts, William↗
NASA NTRS1990

A computational procedure for the dynamics of flexible beams within multibody systems

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Downer, Janice Diane↗
NASA NTRS2013

Improving Photometry and Stellar Signal Preservation with Pixel-Level Systematic Error Correction

The Kepler Mission has demonstrated that excellent stellar photometric performance can be achieved using apertures constructed from optimally selected CCD pixels. The clever methods used to correct for systematic errors, while very successful, still have some limitations in their ability to extract long-term trends in stellar flux. They also leave poorly correlated bias sources, such as drifting moiré pattern, uncorrected. We will illustrate several approaches where applying systematic error correction algorithms to the pixel time series, rather than the co-added raw flux time series, provide significant advantages. Examples include, spatially localized determination of time varying moiré pattern biases, greater sensitivity to radiation-induced pixel sensitivity drops (SPSDs), improved precision of co-trending basis vectors (CBV), and a means of distinguishing the stellar variability from co-trending terms even when they are correlated. For the last item, the approach enables physical interpretation of appropriately scaled coefficients derived in the fit of pixel time series to the CBV as linear combinations of various spatial derivatives of the pixel response function (PRF). We demonstrate that the residuals of a fit of soderived pixel coefficients to various PRF-related components can be deterministically interpreted in terms of physically meaningful quantities, such as the component of the stellar flux time series which is correlated with the CBV, as well as, relative pixel gain, proper motion and parallax. The approach also enables us to parameterize and assess the limiting factors in the uncertainties in these quantities.

Kolodzijczak, Jeffrey J.↗
DOE OSTI2025

A Class of Sparse Johnson–Lindenstrauss Transforms and Analysis of their Extreme Singular Values

The Johnson–Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be projected into lower dimensions while approximately preserving pairwise Euclidean distances. Random matrices satisfying this lemma are called JL transforms (JLTs). Inspired by existing $s$-hashing JLTs with exactly $s$ nonzero elements on each column, the present work introduces an ensemble of sparse matrices encompassing so-called $s$-hashing-like matrices whose expected number of nonzero elements on each column is $s$. The independence of the sub-Gaussian entries of these matrices and the knowledge of their exact distribution play an important role in their analyses. Using properties of independent sub-Gaussian random variables, these matrices are demonstrated to be JLTs, and their smallest nontrivial singular values and largest singular values are estimated nonasymptotically using a technique from geometric functional analysis. As the dimensions of the matrix grow to infinity, these singular values are proved to converge almost surely to fixed quantities (by using the universal Bai–Yin law) and in distribution to the Gaussian orthogonal ensemble Tracy–Widom law after proper rescalings. Understanding the behaviors of extreme singular values is important in general because they are often used to define a measure of stability of matrix algorithms. For example, JLTs were recently used in derivative-free optimization algorithmic frameworks to select random subspaces in which are constructed random models or poll directions to achieve scalability, and hence estimating their smallest singular value in particular helps determine the dimension of these subspaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

High precision tests of QCD without scale or scheme ambiguities: The 40th anniversary of the Brodsky–Lepage–Mackenzie method

A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale μ r and thus determining the correct values of the QCD running coupling α s (μ r ) at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process Q and vary it in the range μ r $\in$ [Q/2, 2Q] in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist’s choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann–Low scheme in the N c → 0 Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. In particular, we present a recently developed method the PMC ∞ and its applications, comparing the results with CSS. The method preserves the property of renormalizable SU(N)/U(1) gauge theories defined as Intrinsic Conformality (iCF). This property underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in pQCD. This new method reflects the underlying conformal properties displayed by pQCD at NNLO, eliminates the scheme dependence of pQCD predictions and is consistent with the general properties of the PMC. A new method to identify conformal and β-terms, which can be applied either to numerical or to theoretical calculations is also shown. We present results for the thrust and C-parameter distributions in e + e - annihilation showing errors and comparison with the CSS. We also show results for a recent innovative comparison between the CSS and the PMC ∞ applied to the thrust distribution investigating both the QCD conformal window and the QED N c → 0 limit. In order to determine the thrust distribution along the entire renormalization group flow from the highest energies to zero energy, we consider the number of flavors near the upper boundary of the conformal window. In this flavor-number regime the theory develops a perturbative infrared interacting fixed point. These results show that PMC ∞ leads to higher precision and introduces new interesting features in the PMC. In fact, this method preserves with continuity the position of the peak, showing perfect agreement with the experimental data already at NNLO. We also show a detailed comparison of the PMC ∞ with the other PMC approaches: the multi-scale-setting approach (PMCm) and the single-scale-setting approach (PMCs) by comparing their predictions for three important fully integrated quantities R e+e- , R$_Τ$ and Γ (H→$b\bar{b}$) up to the four-loop accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗