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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

SU-E-T-349: Verification of a Monte Carlo Simulation Tool as a Second Check for TomoTherapy Treatment Planning

Purpose: To verify a virtual source model used in Monte Carlo (MC) TomoTherapy simulations and to provide a tool for the dose distribution second check for TomoTherapy treatment planning. Methods: Published studies adopted the full MC model to simulate helical TomoTherapy which use phase space files (PSFs) at different scoring planes to facilitate patient dose calculations. We have developed a simple virtual source model (VSM) based on the commissioning data of helical TomoTherapy unit which can be exported from the treatment planning station (TPS). To calculate the patient dose distribution, TPS-generated sinograms are extracted from archived patient XML files and fluence maps are created by incorporating the openclose leaf time with leaf filter, jaw penumbra, and leaf latency. The VSM has been validated for various geometrical set-ups including open fields, heterogeneous media and clinical DQA cases. Results: Good agreement was obtained between our VSM and a published full MC model for the test case of heterogeneous media. For the complex clinical head and neck (HN) case, the MC simulation of the DQA plan agreed with the film measurement with 98% of planar dose pixels passing the 2%/2 mm gamma value test. For the patient treatment plan itself, the MC simulation showed comparable DVHs for the planning target volumes (PTVs) and organs-at-risk (OARs). Deviations observed were consistent with literature. Conclusion: The proposed VSM can be used in the MC method to accurately simulate the patient dose distributions for helical TomoTherapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Role of the likelihood for elastic scattering uncertainty quantification

In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

TWO ACCURATE TIME-DELAY DISTANCES FROM STRONG LENSING: IMPLICATIONS FOR COSMOLOGY

Strong gravitational lenses with measured time delays between the multiple images and models of the lens mass distribution allow a one-step determination of the time-delay distance, and thus a measure of cosmological parameters. We present a blind analysis of the gravitational lens RXJ1131-1231 incorporating (1) the newly measured time delays from COSMOGRAIL, the COSmological MOnitoring of GRAvItational Lenses, (2) archival Hubble Space Telescope imaging of the lens system, (3) a new velocity-dispersion measurement of the lens galaxy of 323 {+-} 20 km s{sup -1} based on Keck spectroscopy, and (4) a characterization of the line-of-sight structures via observations of the lens' environment and ray tracing through the Millennium Simulation. Our blind analysis is designed to prevent experimenter bias. The joint analysis of the data sets allows a time-delay distance measurement to 6% precision that takes into account all known systematic uncertainties. In combination with the Wilkinson Microwave Anisotropy Probe seven-year (WMAP7) data set in flat wCDM cosmology, our unblinded cosmological constraints for RXJ1131-1231 are H{sub 0}=80.0{sup +5.8}{sub -5.7} km s{sup -1} Mpc{sup -1}, {Omega}{sub de} = 0.79 {+-} 0.03, and w=-1.25{sup +0.17}{sub -0.21}. We find the results to be statistically consistent with those from the analysis of the gravitational lens B1608+656, permitting us to combine the inferences from these two lenses. The joint constraints from the two lenses and WMAP7 are H{sub 0}=75.2{sup +4.4}{sub -4.2} km s{sup -1} Mpc{sup -1}, {Omega}{sub de}=0.76{sup +0.02}{sub -0.03}, and w = -1.14{sup +0.17}{sub -0.20} in flat wCDM, and H{sub 0}=73.1{sup +2.4}{sub -3.6} km s{sup -1} Mpc{sup -1}, {Omega}{sub {Lambda}}=0.75{sup +0.01}{sub -0.02}, and {Omega}{sub k}=0.003{sup +0.005}{sub -0.006} in open {Lambda}CDM. Time-delay lenses constrain especially tightly the Hubble constant H{sub 0} (5.7% and 4.0% respectively in wCDM and open {Lambda}CDM) and curvature of the universe. The overall information content is similar to that of Baryon Acoustic Oscillation experiments. Thus, they complement well other cosmological probes, and provide an independent check of unknown systematics. Our measurement of the Hubble constant is completely independent of those based on the local distance ladder method, providing an important consistency check of the standard cosmological model and of general relativity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

TH-C-19A-07: Output Factor Dependence On Range and Modulation for a New Proton Therapy System

Purpose: Proton treatment planning systems are not able to accurately predict output factors and do not calculate monitor units (MU) for proton fields. Output factors (cGy/MU) for patient-specific fields are usually measured in phantoms or modeled empirically. The purpose of this study is to predict the output factors (OFs) for a given proton (R90) and modulation width (Mod) for the first Mevion S250 proton therapy system. Methods: Using water phantoms and a calibrated ionization chamber-electrometer, over 100 OFs were measured for various R90 and Mod combinations for 24 different options. OFs were measured at the center of the Mod, which coincided with the isocenter. The measured OFs were fitted using an analytic model developed by Kooy (Phys.Med.Biol. 50, 2005) for each option and a derived universal empirical-based polynomial as a function of R90 and Mod for all options. Options are devised for ranges of R90 and Mod. The predicted OFs from both models were compared to measurements. Results: Using the empirical-based model, the values could be predicted to within 3% for at least 90% of measurements and within 5% for 98% of the measurements. Using the analytic model to fit each option with the same effective source position, the prediction is much more accurate. The maximal uncertainty between measured and predicted is within 2% and the averaged root-mean-square is 1.5%. Conclusion: Although the measured data was not exhaustive, both models predicted OFs within acceptable uncertainty. Both models are currently used for a sanity check of our continual patient field OF measurements. As we acquire more patient-field OFs, the model will be refined with an ultimate goal of eliminating the time-consuming patient-specific OF measurements.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Dark Energy Survey Year 1 Results: Cosmological constraints from cluster abundances and weak lensing

In this work we perform a joint analysis of the counts and weak lensing signal of redMaPPer clusters selected from the Dark Energy Survey (DES) Year 1 dataset. Our analysis uses the same shear and source photometric redshifts estimates as were used in the DES combined probes analysis. Our analysis results in surprisingly low values for $S_8 =\sigma_8(\Omega_{\rm m}/0.3)^{0.5}= 0.65\pm 0.04$, driven by a low matter density parameter, $\Omega_{\rm m}=0.179^{+0.031}_{-0.038}$, with $\sigma_8-\Omega_{\rm m}$ posteriors in $2.4\sigma$ tension with the DES Y1 3x2pt results, and in $5.6\sigma$ with the Planck CMB analysis. These results include the impact of post-unblinding changes to the analysis, which did not improve the level of consistency with other data sets compared to the results obtained at the unblinding. The fact that multiple cosmological probes (supernovae, baryon acoustic oscillations, cosmic shear, galaxy clustering and CMB anisotropies), and other galaxy cluster analyses all favor significantly higher matter densities suggests the presence of systematic errors in the data or an incomplete modeling of the relevant physics. Cross checks with X-ray and microwave data, as well as independent constraints on the observable--mass relation from SZ selected clusters, suggest that the discrepancy resides in our modeling of the weak lensing signal rather than the cluster abundance. Repeating our analysis using a higher richness threshold ($\lambda \ge 30$) significantly reduces the tension with other probes, and points to one or more richness-dependent effects not captured by our model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Author Correction: US oil and gas system emissions from nearly one million aerial site measurements

Correction to: Naturehttps://doi.org/10.1038/s41586-024-07117-5 Published online 13 March 2024 In the version of the article initially published, several errors were present and have been corrected in the HTML and PDF versions of the article and Supplementary Information. The main results, conclusions, and our interpretations of the data remain unchanged. See the new Supplementary Information Section S15 for a more detailed description of the errors corrected and the resulting effects on the analysis. Data processing and methods corrections Overflight count correction: We previously used pre-computed source coverage data for some Carbon Mapper campaigns that was computed differently than was required for our analysis. We have re-computed Carbon Mapper source coverage based on flightline polygons and source coordinates. Transition point computation, well sites: The updated version now correctly compares the cumulative emissions distribution of simulated well site emissions with that of aerially detected sources (rather than plumes) when computing the transition point. Transition point computation, midstream: Additionally, the transition point calculation has been corrected to exclude aerially detected midstream emissions below the transition point, which was previously leading to double counting of these emissions. This error was not present for upstream (well site) emissions. Calculation errors Unit error: We corrected a specific unit conversion error affecting well site emissions in the Kairos Fort Worth dataset. Across all datasets, we also correct the conversion factor for converting from standard volume to mass for midstream emissions. Sorting error: We correct code that was applying incorrect sorting when computing correction factors to account for partial detection at well sites. Small typographical corrections were made in Fig. 1b and SI Section S4.1. Data processing and methods corrections Overflight count correction: We previously used pre-computed source coverage data for some Carbon Mapper campaigns that was computed differently than was required for our analysis. We have re-computed Carbon Mapper source coverage based on flightline polygons and source coordinates. Transition point computation, well sites: The updated version now correctly compares the cumulative emissions distribution of simulated well site emissions with that of aerially detected sources (rather than plumes) when computing the transition point. Transition point computation, midstream: Additionally, the transition point calculation has been corrected to exclude aerially detected midstream emissions below the transition point, which was previously leading to double counting of these emissions. This error was not present for upstream (well site) emissions. Calculation errors Unit error: We corrected a specific unit conversion error affecting well site emissions in the Kairos Fort Worth dataset. Across all datasets, we also correct the conversion factor for converting from standard volume to mass for midstream emissions. Sorting error: We correct code that was applying incorrect sorting when computing correction factors to account for partial detection at well sites. Small typographical corrections were made in Fig. 1b and SI Section S4.1. The following practices may help researchers conducting similar analyses avoid making similar errors: 1, Clear, accessible documentation explaining the interpretation of all columns in data input tables and all internal variables within the model, 2, Simple cross-check calculations computed before and after unit conversions.

Sherwin, Evan D↗
DOE OSTI2013

THE STAR FORMATION HISTORY OF THE VERY METAL-POOR BLUE COMPACT DWARF I Zw 18 FROM HST/ACS DATA

We have derived the star formation history (SFH) of the blue compact dwarf galaxy I Zw 18 through comparison of deep HST/ACS data with synthetic color-magnitude diagrams (CMDs). A statistical analysis was implemented for the identification of the best-fit SFH and relative uncertainties. We confirm that I Zw 18 is not a truly young galaxy, having started forming stars earlier than ∼1 Gyr ago, and possibly at epochs as old as a Hubble time. In I Zw 18's main body we infer a lower limit of ≈2 × 10{sup 6} M {sub ☉} for the mass locked up in old stars. I Zw 18's main body has been forming stars very actively during the last ∼10 Myr, with an average star formation rate (SFR) as high as ≈1 M {sub ☉} yr{sup –1} (or ≈2 × 10{sup –5} M {sub ☉} yr{sup –1} pc{sup –2}). On the other hand, the secondary body was much less active at these epochs, in agreement with the absence of significant nebular emission. The high current SFR can explain the very blue colors and the high ionized gas content in I Zw 18, resembling primeval galaxies in the early universe. Detailed chemical evolution models are required to quantitatively check whether the SFH from the synthetic CMDs can explain the low measured element abundances, or if galactic winds with loss of metals are needed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

VALID Past, Present, and Future [Slides]

This presentation discusses the Verified, Archived Library of Inputs and Data (VALID) procedure which is managed per computational procedure under the overall SCALE quality assurance plan. The principle behind VALID is that two independent, qualified people prepare and review the model, while a dual, independent check acts as a primary barrier to prevent errors in the library. A final check by VALID QAC of procedural compliance is then performed. The future for VALID includes plans to add more experiments, a review for all ICSBEP cases containing Deuterium, ZEUS intermediate and fast spectrum evaluations, intermediate enrichment experiments, other cases of interest to sponsors, and mixed/intermediate spectrum experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Towards a Semantically-Enabled Control Strategy for Building Simulations: Integration of Semantic Technologies and Model Predictive Control

State-of-the-art building simulation control methods incorporate physical constraints into their mathematical models, but omit implicit constraints associated with policies of operation and dependency relationships among rules representing those constraints. To overcome these shortcomings, there is a recent trend in enabling the control strategies with inference-based rule checking capabilities. One solution is to exploit semantic web technologies in building simulation control. Such approaches provide the tools for semantic modeling of domains, and the ability to deduce new information based on the models through use of Description Logic (DL). In a step toward enabling this capability, this paper presents a cross-disciplinary data-driven control strategy for building energy management simulation that integrates semantic modeling and formal rule checking mechanisms into a Model Predictive Control (MPC) formulation. The results show that MPC provides superior levels of performance when initial conditions and inputs are derived from inference-based rules.

Delgoshaei, Parastoo↗
DOE OSTI2015

The bispectrum of cosmic string temperature fluctuations including recombination effects

We calculate the cosmic microwave background temperature bispectrum from cosmic strings, including the contributions from the last scattering surface, using a well-established Gaussian model for the string energy-momentum correlation functions, and a simplified model for the cosmic fluid. We check our approximation for the integrated Sachs-Wolfe (ISW) contribution against the bispectrum obtained from the full sky map of the cosmic string ISW signal used by the Planck team, obtaining good agreement. We validate our model for the last scattering surface contribution by comparing the predicted temperature power spectrum with that obtained from a full Boltzmann code treatment applied to the Unconnected Segment Model of a string network. We find that including the last scattering contribution has only a small impact on the upper limit on the string tension resulting from the bispectrum at Planck resolutions, and argue that the bispectrum is unlikely to be competitive with the power spectrum at any resolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Process Parameter Optimization in Refill Friction Spot Welding of 6061 Aluminum Alloys Using Response Surface Methodology

6061-T6 aluminum alloy joint was fabricated by refill friction stir spot welding (RFSSW) on which three process parameters of tool rotation speed, sleeve moving rate, and plunge depth make an important effect. The response surface methodology (RSM) was applied to establish a mathematical model to study the effect of process parameters on lap shear fracture load (LSFL) of the RFSSWed joints which were performed in Box–Behnken designs with three factors, three levels and 15 runs. Analysis of variance used to check the adequacy of the developed model indicates that the mathematical model is significant. LSFL increases with the increase in tool rotation speed, sleeve plunge depth, and sleeve moving rate to maximum and then decreases. Sleeve plunge depth makes the most effect on LSFL in all process parameters. The RFSSW process parameters were also optimized using RSM to predict maximize LSFL. The joint produced using a tool rotational speed of 1506 rpm, sleeve moving rate of 1.01 mm/s and sleeve plunge depth of 2.46 mm displays higher LSFL.

36 MATERIALS SCIENCE↗
DOE OSTI2026

elm-diagnostics

elm-diagnostics is a Python package for computing diagnostic analyses and visualizations for the E3SM Land Model (ELM) component and is meant to support new feature development in ELM. The tool reads model history files and performs quantitative analyses including budget-closure checking, variable transformations, temporal aggregations, and statistical summaries to support model evaluation, validation, and scientific interpretation. The framework is designed for extensibility, with modular architecture enabling straightforward addition of new diagnostic methods, derived variables, analysis types, visualization approaches, and model-specific adaptations

Hoffman, Matt [Los Alamos National Laboratory]↗
DOE OSTI2021

SPECs Early-Stage Decision Model: User Manual

The SPECs Early-Stage Decision (ESD) model is central to the SPECs procurement solutions toolkit. The ESD model is an Excel-based spreadsheet model, which provides information about the economic and strategic value of a proposed battery-storage project or solar-plus-storage (solar-plus) project. The model can be used to explore combinations of storage-related project value streams in order to define a potential project, while educating co-op decision-makers about project benefits and costs. A sensitivity analysis function speeds the development of "what-if" scenarios. A gap analysis function solves for top-priority metrics and supports the inclusion of hard-to-monetize strategic values, such as the value of storage to defer costly system upgrades in light of increasing distributed solar and other distributed energy resources (DERs). Model outputs include the utility data, assumptions, and use-case scenarios that are recommended content for the requests for proposals (RFPs). The model may also provide an initial "sanity check" for RFP responses, supporting further discussions among utility staff, vendors and stakeholders. The ESD is not a "finance-grade" modeling tool, and users are cautioned to be mindful of its limitations, but the model has been reviewed by users, who recommend it as a way to drive faster and better project design and planning, as well as to facilitate better communications with vendors, grid partners, and stakeholders.

14 SOLAR ENERGY↗
DOE OSTI2025

A Bayesian approach to time-domain photonic Doppler velocimetry analysis

Photonic Doppler velocimetry (PDV) is an established technique for measuring the velocities of fast-moving surfaces in high-energy-density experiments. In the standard approach to PDV analysis, the short-time Fourier transform (STFT) is used to generate a spectrogram from which the velocity history of the target is inferred. The user chooses the form, duration, and separation of the window function. Here, in this study, we present a Bayesian approach to infer the velocity directly from the PDV oscilloscope trace, without using the spectrogram for analysis. This is clearly a difficult inference problem due to the highly periodic nature of the data, but we find that with carefully chosen prior distributions for the model parameters, we can accurately recover the injected velocity from synthetic data. We validate this method using PDV data collected at the STAR two-stage light gas gun at Sandia National Laboratories, recovering shock-front velocities in quartz that are consistent with those inferred using the STFT-based approach and are interpolated across regions of low signal-to-noise data. Although this method does not rely on the same user choices as the STFT, we caution that it can be prone to misspecification if the chosen model is not sufficient to capture the velocity behavior. Analysis using posterior predictive checks can be used to establish whether a better model is required, although more complex models come with additional computational cost, often taking more than several hours to converge when sampling the Bayesian posterior. We, therefore, recommend it be viewed as a complementary method to that of the STFT-based approach.

Allison, James R. [First Light Fusion Ltd., Yarnto↗
DOE OSTI2016

In Situ Data Infrastructure for Scientific Unit Testing Platform

Testing is a significant software development process for the management of software systems and scientific code. However, as the complexity of scientific codes increases, extra checks are needed to monitor impacts to dependent models and to verify system constraints. The software complexity also impedes the efforts of module developers and software engineers to rapidly develop and extend their code. Recently, we have developed an automatic methodology and prototype platform to facilitate scientific verification of individual functions within complex scientific codes. With this system, the scientific module builders are able to track variables conveniently in one module or track variables’ changes among different modules. In this paper, we present a procedure for automatic unit testing generation. For the interest of a general audience of this conference, we are emphasizing the technical details of integrating the In Situ data infrastructure into our platform. At the end of this paper, we have included an implementation of unit testing for the ACME Land Model (ALM) to demonstrate the usefulness and correctness of the platform. We have also used single- and multipoint checks to demonstrate the efficient variable tracking capability of this platform.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Activity Characterization for Modeling Behavioral-driven Human Mobility in Platial Networks

The population is increasingly becoming tractable as more and more people carry handheld devices as part of their everyday activities. Recent studies have shown that handheld devices' generated traffic share is now more than 50% of total global online traffic. This has created an unprecedented opportunity for modeling human mobility behavior. For example, aggregate check-ins and dwell time can reveal building level occupancies. However, there are clear limits to accurate modeling (e.g. reproducible, repeatable, and realistic), unless we decipher the underlying reason causing typical mobility patterns. We know that human behavior is a reflection of a set of activities, such as going to the gym or work, and which can be seen as a catalyst for humans to move from one location to another. This work envisions the use of activity characterization for modeling human mobility by introducing a context that maps activities to certain mobility patterns. In the end, we highlight the efficacy of the proposed approach by analyzing the impact of public policies surrounding stay at home order on human mobility.

Thakur, Gautam Malviya↗
DOE OSTI2016

MO-FG-CAMPUS-TeP1-03: Pre-Treatment Surface Imaging Based Collision Detection

Purpose: Modern radiotherapy increasingly employs large immobilization devices, gantry attachments, and couch rotations for treatments. All of which raise the risk of collisions between the patient and the gantry / couch. Collision detection is often achieved by manually checking each couch position in the treatment room and sometimes results in extraneous imaging if collisions are detected after image based setup has begun. In the interest of improving efficiency and avoiding extra imaging, we explore the use of a surface imaging based collision detection model. Methods: Surfaces acquired from AlignRT (VisionRT, London, UK) were transferred in wavefront format to a custom Matlab (Mathworks, Natick, MA) software package (CCHECK). Computed tomography (CT) scans acquired at the same time were sent to CCHECK in DICOM format. In CCHECK, binary maps of the surfaces were created and overlaid on the CT images based on the fixed relationship of the AlignRT and CT coordinate systems. Isocenters were added through a graphical user interface (GUI). CCHECK then compares the inputted surfaces to a model of the linear accelerator (linac) to check for collisions at defined gantry and couch positions. Note, CCHECK may be used with or without a CT. Results: The nominal surface image field of view is 650 mm × 900 mm, with variance based on patient position and size. The accuracy of collision detections is primarily based on the linac model and the surface mapping process. The current linac model and mapping process yield detection accuracies on the order of 5 mm, assuming no change in patient posture between surface acquisition and treatment. Conclusions: CCHECK provides a non-ionizing method to check for collisions without the patient in the treatment room. Collision detection accuracy may be improved with more robust linac modeling. Additional gantry attachments (e.g. conical collimators) can be easily added to the model.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs

We develop the technology for Polyakov-Mellin (PM) bootstrap in one- dimensional conformal field theories (CFT 1 ). By adding appropriate contact terms, we bootstrap various effective field theories in AdS 2 and analytically compute the CFT data to one loop. The computation can be extended to higher orders in perturbation theory, if we ignore mixing, for any external dimension. We develop PM bootstrap for O(N) theories and derive the necessary contact terms for such theories (which also involves a new higher gradient contact term absent for N = 1). We perform cross-checks which include considering the diagonal limit of the 2d Ising model in terms of the 1d PM blocks. As an independent check of the validity of the results obtained with PM bootstrap, we propose a suitable basis of transcendental functions, which allows to fix the four-point correlators of identical scalar primaries completely, up to a finite number of ambiguities related to the number of contact terms in the PM basis. We perform this analysis both at tree level (with and without exchanges) and at one loop. We also derive expressions for the corresponding CFT data in terms of harmonic sums. Finally, we consider the Regge limit of one-dimensional correlators and derive a precise connection between the latter and the large-twist limit of CFT data. Exploiting this result, we study the crossing equation in the three OPE limits and derive some universal constraints for the large-twist limit of CFT data in Regge-bounded theories with a finite number of exchanges.

1/N expansion↗