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DOE OSTI2024

Superhorizon isocurvature fluctuations relax tensions

Here, we present a new class of models that have potential to alleviate tensions present in the cosmological data today. We postulate about variation in the sound horizon scale on superhorizon scales, i.e., on scales that are larger than that of the present observable low-redshift Universe (≳ 1Gpc) while at the same time smaller than the largest scales probed by the cosmic microwave background (CMB) (≲ 10Gpc). In this scenario, CMB peaks are naturally smoothed as preferred by the Planck data, while at the same time the low-redshift baryon acoustic oscillation calibration is partially decoupled from the CMB. Taking superhorizon variations in baryon fraction as an example and using approximate modeling, we find improvement in the best fit Planck power spectrum model Δχ 2 ~ 6 for 1 extra degree of freedom with the relevant extension parameter 10 3 σ b = 2.10 ± 0.60, implying about 10% variations in baryon fraction across the Universe. At the same time, S 8 drops by about 1 sigma, easing tension with weak lensing surveys. We find that the combination of Planck 2018 data, eBOSS BAO data, and Riess et al. distance ladder Hubble parameter determination produce a satisfactory fit in our model if we allow for a phantom dark energy equation of state.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Explainability and extrapolation of machine learning models for predicting the glass transition temperature of polymers

Abstract Machine learning (ML) offers promising tools to develop surrogate models for polymers' structure–property relations. Surrogate models can be built upon existing polymer data and are useful for rapidly predicting the properties of unknown polymers. The accuracy of such ML models appears to depend on the feature space representation of polymers, the range of training data, and learning algorithms. Here, we establish connections between these factors for predicting the glass transition temperature (T g ) of polymers. Our analysis suggests linear models with fewer fitting parameters are as accurate as nonlinear models with many hidden and unexplainable parameters. Also, the performance of a monomer topology‐based ML model is found to be qualitatively identical to that of a physicochemical descriptor‐based ML model. We find that the ML models's performance in the extrapolative region is enhanced as the property range of the training data increases. Moreover, we establish newT g – polymer chemistry correlations via ML. Our work illustrates how ML can advance the fundamental understanding of polymer structure–property correlations and its efficacy for extrapolation problems.

Polymer Science↗
DOE OSTI2024

Generating synthetic signaling networks for in silico modeling studies

Predictive models of signaling pathways have proven to be difficult to develop. Reasons include the uncertainty in the number of species, the complexity in species’ interactions, and the sparseness and uncertainty in experimental data. Traditional approaches to developing mechanistic models rely on collecting experimental data and fitting a single model to that data. This approach works for simple systems but has proven unreliable for complex systems such as biological signaling networks. For example, uncertainty and sparseness of the data often result in overfitted models that have little predictive value beyond recapitulating the experimental data itself. Thus, there is a need to develop new approaches to create predictive mechanistic models of complex systems. However, to determine the effectiveness of any new algorithm, a baseline model is needed to test its performance. To meet this need, we developed a method for generating artificial synthetic networks that are reasonably realistic and thus can be treated as ground truth models. These synthetic models can then be used to generate synthetic data for developing and testing algorithms designed to recover the underlying network topology and associated parameters. Here, we describe a simple approach for generating synthetic signaling networks that can be used for this purpose.

42 ENGINEERING↗
DOE OSTI2023

Extended Donnan-Manning theory for selective ion partition and transport in ion exchange membrane

The use of ion exchange membranes (IEMs) for electrochemical ion-ion separation leverages the selectivity of the IEMs toward like-charged species via valence difference and/or other ion membrane interactions. A mechanistic model that relates selectivity with membrane structural and chemical properties is lacking in the literature. Here, in this study, we extend the Manning’s counter-ion condensation model for describing ion partition and ion mobility inside IEMs to mixed salts scenarios. We evaluate the extended Donnan-Manning model against experimental data from literature and compare the performance the Donnan-Manning model to that of the ideal Donnan model and the Donnan-Affinity model. Our analysis shows that, despite its structural complexity, the Donnan-Manning model has less fitting parameters than the Donnan-Affinity model and generally outperforms the two other models in predicting counter-ion and co-ion partition. With the assumption of a higher mobility of condensed ions than that of uncondensed ions, the generalized Manning’s model can also predict counter-ion mobility selectivity for cation exchange membranes, but its performance for predicting mobility selectivity for anion exchange membranes is still unsatisfactory.

42 ENGINEERING↗
DOE OSTI2022

Atacama Cosmology Telescope: Constraints on prerecombination early dark energy

The early dark energy (EDE) scenario aims to increase the value of the Hubble constant (H0) inferred from cosmic microwave background (CMB) data over that found in the standard cosmological model (Λ CDM ), via the introduction of a new form of energy density in the early Universe. The EDE component briefly accelerates cosmic expansion just prior to recombination, which reduces the physical size of the sound horizon imprinted in the CMB. Previous work has found that nonzero EDE is not preferred by Planck CMB power spectrum data alone, which yield a 95% confidence level (C.L.) upper limit f EDE < 0.087 on the maximal fractional contribution of the EDE field to the cosmic energy budget. In this paper, we fit the EDE model to CMB data from the Atacama Cosmology Telescope (ACT) data release 4. We find that a combination of ACT, large-scale Planck TT (similar to WMAP), Planck CMB lensing, and BAO data prefers the existence of EDE at >99.7 % C .L . : f EDE = 0.091$^{+0.020}_{-0.036}$, with H 0 = 70.9$^{+1.0}_{-2.0}$ km/s/Mpc (both 68% C.L.). From a model-selection standpoint, we find that EDE is favored over Λ CDM by these data at roughly 3 σ significance. In contrast, a joint analysis of the full Planck and ACT data yields no evidence for EDE, as previously found for Planck alone. We show that the preference for EDE in ACT alone is driven by its TE and EE power spectrum data. The tight constraint on EDE from Planck alone is driven by its high-ℓ TT power spectrum data. Understanding whether these differing constraints are physical in nature, due to systematics, or simply a rare statistical fluctuation is of high priority. Here, the best-fit EDE models to ACT and Planck exhibit coherent differences across a wide range of multipoles in TE and EE, indicating that a powerful test of this scenario is anticipated with near-future data from ACT and other ground-based experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Neutron-proton pairing correction in the extended isovector and isoscalar pairing model

An extended O ST (8) model with multi j-orbits is constructed based on the angular momentum decomposition with “pseudo”-spin S for valence nucleons in a j-orbit. It is shown that the isovector S = 0 and T=1 pairs are exactly the J=0 and T=1 pairs in a given j-orbit, while the isoscalar S = 1 pairs are linear combinations of J=odd pairs, with which the pairing Hamiltonian can be used to estimate isovector and isoscalar pairing interactions. As an example of the model application, some low-lying J = 0 + level energies of even-even and odd-odd A=18 – 28 nuclei up to the half-filling in the ds-shell above the 16 O core are fit by the model and compared with the fitting results of the same Hamiltonian in the O LST (8) form. It has been verified from the fitting of both the models that the isoscalar pairing interaction can be neglected in the lower energy part of the spectra of these ds-shell nuclei as far as binding energies and a few J=0 + excited levels of these nuclei are concerned. With the mean-field plus isovector pairing interaction only, neutron-neutron, proton-proton, and neutron-proton pairing contributions at the ground or the lowest J=0 + state of these nuclei are estimated. It is shown that the isovector np-pairing contribution to the binding in the odd-odd N=Z nuclei is systematically larger than that in the even-even nuclei. Furthermore, the isoscalar np-pair content at the lowest J=0+ state of these nuclei is also estimated. In both the O ST (8) and O LST (8) models, it is clearly shown that the isoscalar-pair content in the lowest J=0 + state of the N=Z and N=Z±2 nuclei increases with increasing of the valence nucleons, especially in those even-even nuclei, which indicates the isoscalar pairing correlation to be of importance at low-lying states of N=Z and N=Z±2 nuclei, especially in those even-even nuclei with more valence nucleons up to the half-filling, even though the isoscalar pairing interaction is negligible.

20 ≤ A ≤ 38↗
DOE OSTI2023

Adjoint Waveform Tomography for Crustal and Upper Mantle Structure the Middle East and Southwest Asia for Improved Waveform Simulations Using Openly Available Broadband Data

We present a new model of radially anisotropic seismic wavespeeds for the crust and upper mantle of a broad region of the Middle East and Southwest Asia (MESWA) derived from adjoint waveform tomography. We inverted waveforms from 192 Global Centroid Moment Tensor earthquakes (MW 5.5-7.0) recorded by over 1000 openly available broadband seismic stations from permanent and temporary networks in the region. Spatial coverage of the available data is highly uneven due to earthquakes clustered along plate boundaries and sparse coverage of open seismic networks in the region. We considered three possible starting models: the SPiRaL global model (Simmons et al., 2021); MEC-1 (Kaviani et al., 2020); and CSEM2.0 (Noe et al., 2023). Because the SPiRaL model provides good fits to the observed waveforms measured by the time-bandwidth product of selected windows in several period bands, provides all the necessary parameters and covers the entire domain we used it for the starting model with the period band 50-100 seconds. Inversion iterations proceeded using time-frequency phase misfits in six stages and 54 total iterations reducing the minimum period to 30 seconds. Our final model, MESWA, provides improved waveform fits compared to the starting model for both the data used in the inversion and an independent validation data set of 66 events. Two metrics of waveform fit (the time-frequency phase misfit used in the optimization and normalized L2 misfit) were both reduced by nearly 60% for both data sets and MESWA provides significantly larger misfit reductions relative to the SPiRaL model than the MEC-1 or CSEM models. We also find that MESWA provides a larger time-bandwidth product of selected windows indicating that more information content of the observed waveforms is explained by MESWA than the other models. Our new model reveals tectonic features imaged by other studies and methods but in a new holistic model of shear and compressional wavespeeds (v S and v P , respectively) with anisotropy covering the crust and uppermost mantle of a larger domain. MESWA has smaller scale-length features and tends to sharpen some features relative to the SPiRaL starting model. Examples include: low crustal v S in the TurkishIranian Plateau, Zagros Mountains, Afghan Central Blocks and Sulaiman Fold Belt; low mantle vSfollowing divergent (Gulf of Aden, Red Sea) and transform (Dead Sea Fault) margins of the Arabian Plate; low and high v S in the mantle beneath the Arabian Shield and Platform, respectively. Low vS is imaged below Cenozoic volcanic centers of the Arabian Peninsula, the so-called Mecca-Madina-Nafud (MMN) Line. Positive anisotropy (v SH > v SV ) is inferred for asthenospheric depths across the region except where up/downwelling may influence fabric alignment (e.g. Afar, Red Sea, Arabian Shield). Elevated vS tracks Makran subduction under southeast Iran. MESWA resembles the SPiRaL model in its long-wavelength structure, but enhances shorter wavelengths features on the order of 200 km and smaller. The resulting model could be used for as a starting model for further improvements, say using waveforms from in-country seismic networks that are not openly available or smaller-scale studies targeting shorter period waveforms. The model also could be used for source characterization and moment tensor inversion to improve earthquake hazard studies and nuclear explosion monitoring.

58 GEOSCIENCES↗
DOE OSTI2025

Oxygen Defect Configurations in Single-Phase UO 2.15

Hyperstoichiometric UO 2.15 was characterized by neutron total scattering at high temperature in the single-phase UO 2+x region of the U/O phase diagram. The diffraction data confirmed a single-phase fluorite structure at high temperature. Analysis of the short-range data showed that the same structural model does not fit the pair distribution functions well. Instead, structural models containing specific configurations of oxygen defect clusters best represent the local atomic arrangement. In conclusion, prevalent defect clusters previously proposed were fit to the experimental data, and moderately distorted oxygen cuboctahedra hypothesized by recent molecular dynamics simulations fit the data most accurately.

neutron pair-distribution function analysis↗
DOE OSTI2025

Toward shell model interactions with credible uncertainties

Background: The nuclear shell model is a powerful framework for predicting nuclear structure observables, but relies on interaction matrix elements fit to experimental data as its inputs. Extending the shell model's applicability, particularly toward dripline nuclei, requires efficient fitting methods and credible uncertainty quantification. Traditional approaches face computational challenges and may underestimate uncertainties. Purpose: We develop and test a framework combining eigenvector continuation and Markov chain Monte Carlo to efficiently fit shell model interaction matrix elements and quantify their uncertainties. Methods: Eigenvector continuation is used to emulate shell model calculations, reducing computational costs. The emulator enables Markov chain Monte Carlo sampling to optimize interaction matrix elements and rigorously assess parametric uncertainties. Here, the framework is benchmarked using the USDB interaction in the 𝑠⁢𝑑 shell. Results: The emulator reproduces the USDB interaction with negligible error, validating its use in shell model fitting applications. However, we find that to obtain credible predictive intervals, the model defect of the shell model itself, rather than experimental or emulator error, must be taken into account in order to obtain credible uncertainties. Conclusions: The proposed framework provides an efficient and rigorous approach for fitting shell model interactions and quantifying uncertainties. Further, the normality assumption used in the past appears sufficient to describe the distribution of interaction matrix elements. However, it is crucial to account for model correlations to avoid underestimating uncertainties.

Nuclear forces↗
DOE OSTI2023

Synthesis of a novel multifunctional organic–inorganic nanocomposite for metal ions and organic dye removals

In this study, we used solvent assisted mechano-synthesis strategies to form multifunctional organic–inorganic nanocomposites capable of removing both organic and inorganic contaminants. A zeolite X (Ze) and activated carbon (AC) composite was synthesized via state-of-the-art mechanical mixing in the presence of few drops of water to form Ze/AC. The second composite (Ze/L/AC) was synthesized in a similar fashion, however this composite had the addition of disodium terephthalate as a linker. Both materials, Ze/AC and Ze/L/AC, were characterized using scanning electron microscope (SEM), energy-dispersive X-ray spectroscopy (EDS), Powdered X-ray diffraction (P-XRD), Fourier-transform infrared spectrometry (FTIR), Accelerated Surface Area and Porosimetry System (ASAP), and thermal gravimetric analysis (TGA). The SEM–EDS displayed the surface structure and composition of each material. The sodium, oxygen and carbon contents increased after linker connected Ze and AC. The P-XRD confirmed the crystallinity of each material as well as the composites, while FTIR indicated the function groups (C=C, O–H) in Ze/L/AC. The contaminant adsorption experiments investigated the effects of pH, temperature, and ionic strength on the adsorption of methylene blue (MB) and Co(II) for each material. In MB adsorption, the first-order reaction rate of Ze/L/AC (0.02 h -1 ) was double that of Ze/AC (0.01 h -1 ). The reaction rate of Ze/L/AC (4.8 h -1 ) was also extraordinarily higher than that of Ze/AC (0.6 h -1 ) in the adsorption of Co(II). Ze/L/AC composite achieved a maximum adsorption capacity of 44.8 mg/g for MB and 66.6 mg/g for Co(II) ions. The MB adsorption of Ze/AC and Ze/L/AC was best fit in Freundlich model with R 2 of 0.96 and 0.97, respectively, which indicated the multilayer adsorption. In the Co(II) adsorption, the data was highly fit in Langmuir model with R 2 of 0.94 and 0.92 which indicated the monolayer adsorption. These results indicated both materials exhibited chemisorption. The activation energy of Ze/L/AC in MB adsorption (34.9 kJ mol -1 ) was higher than that of Ze/L/AC in Co (II) adsorption (26 kJ mol -1 ).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Networked HIL Simulation System for Modeling Large-scale Power Systems

This paper presents a networked hardware-in-the-loop (HIL) simulation system for modeling large-scale power systems. Researchers have developed many HIL test systems for power systems in recent years. Those test systems can model both microsecond-level dynamic responses of power electronic systems and millisecond-level transients of transmission and distribution grids. By integrating individual HIL test systems into a network of HIL test systems, we can create large-scale power grid digital twins with flexible structures at required modeling resolution that fits for a wide range of system operating conditions. This will not only significantly reduce the need for field tests when developing new technologies but also greatly shorten the model development cycle. In this paper, we present a networked OPAL-RT based HIL test system for developing transmission-distribution coordinative Volt-VAr regulation technologies as an example to illustrate system setups, communication requirements among different HIL simulation systems, and system connection mechanisms. Impacts of communication delays, information exchange cycles, and computing delays are illustrated. Simulation results show that the performance of a networked HIL test system is satisfactory.

Xie, Fuhong↗
DOE OSTI2025

Expansion-history preferences of DESI DR2 and external data

We explore the origin of the preference of Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) baryon acoustic oscillation measurements and external data from cosmic microwave background (CMB) and type Ia supernovae (SNIa) that dark energy behavior departs from that expected in the standard cosmological model with vacuum energy (Λ ⁢CDM). In our analysis, we allow a flexible scaling of the expansion rate with redshift that nevertheless allows reasonably tight constraints on the quantities of interest, and adopt and validate a simple yet accurate compression of the CMB data that allows us to constrain our phenomenological model of the expansion history. We find that data consistently show a preference for a 3%–4% increase in the expansion rate at 𝑧 ≃ 0.7 relative to that predicted by the standard Λ⁢ CDM model, in excellent agreement with results from the less flexible (𝑤 0 ,𝑤 𝑎 ) parametrization which was used in previous analyses. Even though our model allows a departure from the best-fit Λ⁢ CDM model at zero redshift, we find no evidence for such a signal. We also find no evidence (at greater than 1⁢𝜎 significance) for a departure of the expansion rate from the Λ ⁢CDM predictions at higher redshifts for any of the data combinations that we consider. Altogether, our results strengthen the robustness of the findings using the combination of DESI, CMB, and SNIa data to dark-energy modeling assumptions.

Cosmological parameters↗
DOE OSTI2022

Comparison of AGR-3/4 Fission Product Transport Model to Measurements and Extraction of Diffusivities via Analytical Fits

A one-dimensional finite-element model based on the MOOSE framework has been constructed, and overall transport estimates are predicted based on available diffusivities and sorption isotherms in the extant literature. The predicted transport profiles are compared to experimental results, where such results are available, including total inventory analysis of gamma emitters, liquid scintillation results for Sr-90 concentrations, radial deconsolidation leach-burn-leach within compacts, tomographic reconstructions based on detailed gamma scanning and destructive physical sampling of several rings. The magnitude of expected transport to the sink ring is generally predicted by the model for silver and cesium, however, modeled detailed concentration profiles are not consistent with experimental results. Strontium and europium transport is not well characterized by model results.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2024

Deep energy-pressure regression for a thermodynamically consistent EOS model

Abstract In this paper, we aim to explore novel machine learning (ML) techniques to facilitate and accelerate the construction of universal equation-Of-State (EOS) models with a high accuracy while ensuring important thermodynamic consistency. When applying ML to fit a universal EOS model, there are two key requirements: (1) a high prediction accuracy to ensure precise estimation of relevant physics properties and (2) physical interpretability to support important physics-related downstream applications. We first identify a set of fundamental challenges from the accuracy perspective, including an extremely wide range of input/output space and highly sparse training data. We demonstrate that while a neural network (NN) model may fit the EOS data well, the black-box nature makes it difficult to provide physically interpretable results, leading to weak accountability of prediction results outside the training range and lack of guarantee to meet important thermodynamic consistency constraints. To this end, we propose a principled deep regression model that can be trained following a meta-learning style to predict the desired quantities with a high accuracy using scarce training data. We further introduce a uniquely designed kernel-based regularizer for accurate uncertainty quantification. An ensemble technique is leveraged to battle model overfitting with improved prediction stability. Auto-differentiation is conducted to verify that necessary thermodynamic consistency conditions are maintained. Our evaluation results show an excellent fit of the EOS table and the predicted values are ready to use for important physics-related tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The Dark Energy Survey Year 3 and eBOSS: constraining galaxy intrinsic alignments across luminosity and colour space

ABSTRACT We present direct constraints on galaxy intrinsic alignments (IAs) using the Dark Energy Survey Year 3 (DES Y3), the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), and its precursor, the Baryon Oscillation Spectroscopic Survey (BOSS). Our measurements incorporate photometric red sequence (redMaGiC) galaxies from DES with median redshift z ∼ 0.2–1.0, luminous red galaxies from eBOSS at z ∼ 0.8, and also an SDSS-III BOSS CMASS sample at z ∼ 0.5. We measure two-point IA correlations, which we fit using a model that includes lensing, magnification, and photometric redshift error. Fitting on scales 6 Mpc h−1 < rp < 70 Mpc h−1, we make a detection of IAs in each sample, at 5σ–22σ (assuming a simple one-parameter model for IAs). Using these red samples, we measure the IA–luminosity relation. Our results are statistically consistent with previous results, but offer a significant improvement in constraining power, particularly at low luminosity. With this improved precision, we see detectable dependence on colour between broadly defined red samples. It is likely that a more sophisticated approach than a binary red/blue split, which jointly considers colour and luminosity dependence in the IA signal, will be needed in future. We also compare the various signal components at the best-fitting point in parameter space for each sample, and find that magnification and lensing contribute $\sim 2\!-\!18~{{\ \rm per\ cent}}$ of the total signal. As precision continues to improve, it will certainly be necessary to account for these effects in future direct IA measurements. Finally, we make equivalent measurements on a sample of emission-line galaxies from eBOSS at z ∼ 0.8. We constrain the non-linear alignment amplitude to be $A_1=0.07^{+0.32}_{-0.42}$ (|A1| < 0.78 at 95 per cent CL).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

LASSO for CALPHAD Model Selection Enables Data-Efficient Thermodynamic Modeling: An Application in Thermochemical Hydrogen Production Materials

Phenomenological CALPHAD (CALculation of PHAse Diagrams) models, widely used for multicomponent materials, often contain a considerable number of parameters and require fitting using data from a relatively small number of experimental measurements or theoretical calculations. Sometimes these parameters are introduced for the purpose of improving model fits but without clear physical justification, which leads to overparametrized models with poor generalization performance. Automated approaches for optimal model selection based on the available data therefore become critical. Here, in this work, a least absolute shrinkage and selection operator (LASSO)-based approach is developed for model selection by leveraging the linearity of the CALPHAD model with respect to its parameters to convert the model selection and fitting to a LASSO minimization problem. We demonstrate its utility for thermodynamic modeling of thermochemical hydrogen (TCH) production materials using lanthanum strontium manganite (LSM) as an example. Various TCH-relevant properties, including oxygen stoichiometry as a function of oxygen partial pressure, enthalpy of reduction, and entropy of reduction, are successfully predicted with reasonable accuracy using a minimal set of model parameters. Importantly, the model selection and fitting involve minimal human decision; it can therefore be applied to high-throughput DFT defect calculations and yield efficient workflows for TCH material modeling and optimization.

CALPHAD↗
DOE OSTI2023

Polarimetric Geometric Modeling for mm-VLBI Observations of Black Holes

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric “m-ring” model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Dark photon and dark Z mediated B meson decays

We study flavor changing neutral current decays of B and K mesons in the dark U(1) D model, with the dark photon/dark Z mass between 10 MeV and 2 GeV. Although the model provides an improved fit (compared to the standard model) to the differential decay distributions of B → K ($\ast$) ℓ + ℓ – , with ℓ = μ, e, and B s → $\phi$μ + μ – , the allowed parameter space is ruled out by measurements of atomic parity violation, K + → μ + + invisible decay, and ${B}_s-{\overline{B}}_s$ mixing, among others. To evade constraints from low energy data, we extend the model to allow for (1) additional invisible Z D decay, (2) a direct vector coupling of Z D to muons, and (3) a direct coupling of Z D to both muons and electrons, with the electron coupling fine-tuned to cancel the Z D coupling to electrons via mixing. We find that only the latter case survives all constraints.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗