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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

SPT-3G D1: Compton-$y$ maps using data from the SPT-3G and Planck surveys

We present thermal Sunyaev-Zel'dovich (tSZ) Compton-$y$ parameter maps constructed from two years (2019-2020) of observations with the South Pole Telescope (SPT) third-generation camera, SPT-3G, combined with data from the Planck satellite. Using a linear combination (LC) pipeline, we obtain a suite of reconstructions that explore different trade-offs between statistical sensitivity and suppression of astrophysical contaminants, including minimum-variance, CMB-deprojected, and CIB-deprojected $y$-maps. We validate these maps through different statistical techniques such as auto- and cross-power spectra with large-scale structure tracers as well as stacking on cluster locations. These tests are used to understand the balance between noise and astrophysical foreground residuals (such as the CIB) in combination with the recovery of the tSZ signal for different maps. For example, results from stacking at the location of clusters confirm the robustness of the recovered tSZ signal over the $\sim 1500\: {\rm deg}^2$ SPT-3G survey field used in this analysis. The high-resolution and low-noise maps produced here provide an important cosmological tool for future studies, including measurements of the Compton-$y$ map power spectrum, cross-correlations with other tracers of the large-scale structure, detailed modeling of cluster pressure profiles, and study of the thermodynamic state of the baryons in the Universe.

Maniyar, A. S. [Harvard-Smithsonian Ctr. Astrophys↗
DOE OSTI2020

Software-Defined Network for End-to-end Networked Science at the Exascale

Domain science applications and workflow processes are currently forced to view the network as an opaque infrastructure into which they inject data and hope that it emerges at the destination with an acceptable Quality of Experience. There is little ability for applications to interact with the network to exchange information, negotiate performance parameters, discover expected performance metrics, or receive status/troubleshooting information in real time. The work we presen here is motivated by a vision for a new smart network and smart application ecosystem that will provide a more deterministic and interactive environment for domain science workflows. The Software-Defined Network for End-to-end Networked Science at Exascale (SENSE) system includes a model-based architecture, implementation, and deployment which enables automated end-to-end network service instantiation across administrative domains. An intent based interface allows applications to express their high-level service requirements, an intelligent orchestrator and resource control systems allow for custom tailoring of scalability and real-time responsiveness based on individual application and infrastructure operator requirements. This allows the science applications to manage the network as a first-class schedulable resource as is the current practice for instruments, compute, and storage systems. Deployment and experiments on production networks and testbeds have validated SENSE functions and performance. Emulation based testing verified the scalability needed to support research and education infrastructures. Key contributions of this work include an architecture definition, reference implementation, and deployment. This provides the basis for further innovation of smart network services to accelerate scientific discovery in the era of big data, cloud computing, machine learning and artificial intelligence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Contribution of IAEA coordinated research projects to light water reactors advanced technology fuel testing and simulation

The Fukushima-Daiichi accident in 2011 highlighted the pressing need for enhanced design and safety analysis of nuclear fuels, especially under accident conditions in nuclear power plants (NPPs). To address this need, the international nuclear fuel community has developed several concepts of Accident Tolerant and Advanced Technology Fuels (ATFs) for light water reactors. The International Atomic Energy Agency (IAEA), at the request of its Member States, has initiated a series of three Coordinated Research Projects (CRPs) to aid in the development and testing of these ATFs. Further, these projects, known as FUMAC, ACTOF, and ATF-TS, focus on the experimentation and simulation of ATFs under various accident conditions, including design basis accidents and design extension conditions. This paper provides a comprehensive overview of the main activities, as well as the achieved or anticipated results of these three CRPs. The insights and advancements gained from these projects will enable IAEA Member States to further refine nuclear fission technology, thereby contributing to efforts aimed at mitigating climate change.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

An obscured quasar census with the 4MOST IR AGN survey: design, predicted properties, and scientific goals

ABSTRACT We present the 4MOST (4-metre Multi-Object Spectroscopic Telescope) infrared (IR) AGN survey, the first large-scale optical spectroscopic survey characterizing mid-infrared (MIR) selected obscured active galactic nuclei (AGNs). The survey targets $\approx 212\,000$ obscured IR AGN candidates over $\approx 10\,000 \rm \: deg^2$ down to a magnitude limit of $r_{\rm AB}=22.8 \, \rm mag$ and will be $\approx 100 \times$ larger than any existing obscured IR AGN spectroscopic sample. We select the targets using an MIR colour criterion applied to the unWISE catalogue from the WISE (Wide-field Infrared Survey Explorer) all-sky survey, and then apply a $r-W2\ge 5.9 \rm \: mag$ cut; we demonstrate that this selection will mostly identify sources obscured by $N_{\rm H}>10^{22} \rm \: cm^{-2}$. The survey complements the 4MOST X-ray survey, which will follow up $\sim 1\,\rm M$ eROSITA (extended ROentgen Survey with an Imaging Telescope Array)-selected (typically unobscured) AGN. We perform simulations to predict the quality of the spectra that we will obtain and validate our MIR–optical colour-selection method using X-ray spectral constraints and UV-to-far-IR spectral energy distribution (SED) modelling in four well-observed deep-sky fields. We find that: (1) $\approx 80-87{{\ \rm per\ cent}}$ of the WISE-selected targets are AGN down to $r_{\rm AB}=22.1-22.8 \: \rm mag$ of which $\approx 70{{\ \rm per\ cent}}$ are obscured by $N_{\rm H}>10^{22} \: \rm cm^{-2}$, and (2) $\approx 80{{\ \rm per\ cent}}$ of the 4MOST IR AGN sample will remain undetected by the deepest eROSITA observations due to extreme absorption. Our SED-fitting results show that the 4MOST IR AGN survey will primarily identify obscured AGN and quasars ($\approx 55{{\ \rm per\ cent}}$ of the sample is expected to have $L_{\rm AGN,IR}>10^{45} \rm \: erg \: s^{-1}$) residing in massive galaxies ($M_{\star }\approx 10^{10}-10^{12} \rm \: M_{\odot }$) at $z\approx 0.5-3.5$ with $\approx 33{{\ \rm per\ cent}}$ expected to be hosted by starburst galaxies.

Andonie, Carolina (ORCID:0000000255804298)↗
DOE OSTI2021

Superconductivity in the doped quantum spin liquid on the triangular lattice

Abstract Broad interest in quantum spin liquid (QSL) phases was triggered by the notion that they can be viewed as insulating phases with preexisting electron pairs, such that upon light doping they might automatically yield high temperature superconductivity. Yet despite intense experimental and numerical efforts, definitive evidence showing that doping QSLs leads to superconductivity has been lacking. We address the problem of a lightly doped QSL through a large-scale density-matrix renormalization group study of the t - J model on finite-circumference triangular cylinders with a small but nonzero concentration of doped holes. We provide direct evidences that doping QSL can naturally give rise to d -wave superconductivity. Specifically, we find power-law superconducting correlations with a Luttinger exponent, K s c ≈ 1, which is consistent with a strongly diverging superconducting susceptibility, $${\chi }_{sc} \,\sim\, {T}^{-(2\,-\,{K}_{sc})}$$ χ s c ~ T − ( 2 − K s c ) as the temperature T → 0. The spin–spin correlations—as in the undoped QSL state—fall exponentially which suggests that the superconducting pair-pair correlations evolve smoothly from the insulating parent state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Experimental and theoretical examination of shock-compressed copper through the fcc to bcc to melt phase transitions

Recent studies show a face-centered cubic (fcc) to body-centered cubic (bcc) transformation along the shock Hugoniot for several metals (i.e., Cu, Au, and Ag). Here, we combine laser-shock compression of Cu foils on nanosecond timescales with in situ x-ray diffraction (XRD) to examine the microstructural changes with stress. We study the fcc phase and the phase transition from fcc to bcc (pressures greater than 180 GPa). Textural analysis of the azimuthal intensities from the XRD images is consistent with transformation into the bcc phase through the Pitsch-distortion mechanism. We use embedded atom model molecular dynamics simulations to determine the stability of the bcc phase in pressure–temperature space. Finally, our results indicate that the bcc phase is stabilized only at high temperatures and remains stable at pressures greater than 500 GPa.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Coherent elastic neutrino-nucleus scattering: Terrestrial and astrophysical applications

Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) is a process in which neutrinos scatter on a nucleus which acts as a single particle. Though the total cross section is large by neutrino standards, CE$\nu$NS has long proven difficult to detect, since the deposited energy into the nucleus is $\sim$ keV. In 2017, the COHERENT collaboration announced the detection of CE$\nu$NS using a stopped-pion source with CsI detectors, followed up the detection of CE$\nu$NS using an Ar target. The detection of CE$\nu$NS has spawned a flurry of activities in high-energy physics, inspiring new constraints on beyond the Standard Model (BSM) physics, and new experimental methods. The CE$\nu$NS process has important implications for not only high-energy physics, but also astrophysics, nuclear physics, and beyond. This whitepaper discusses the scientific importance of CE$\nu$NS, highlighting how present experiments such as COHERENT are informing theory, and also how future experiments will provide a wealth of information across the aforementioned fields of physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Discovery and characterization of two Neptune-mass planets orbiting HD 212729 with TESS

ABSTRACT We report the discovery of two exoplanets orbiting around HD 212729 (TOI 1052, TIC 317060587), a Teff = 6146 K star with V = 9.51 observed by TESS in Sectors 1 and 13. One exoplanet, TOI-1052b, is Neptune-mass and transits the star, and an additional planet TOI-1052c is observed in radial velocities but not seen to transit. We confirm the planetary nature of TOI-1052b using precise radial velocity observations from HARPS and determined its parameters in a joint RV and photometry analysis. TOI-1052b has a radius of $2.87^{+0.29}_{-0.24}$ R⊕, a mass of 16.9 ± 1.7 M⊕, and an orbital period of 9.14 d. TOI-1052c does not show any transits in the TESS data, and has a minimum mass of $34.3^{+4.1}_{-3.7}$ M⊕ and an orbital period of 35.8 d, placing it just interior to the 4:1 mean-motion resonance. Both planets are best fit by relatively high but only marginally significant eccentricities of $0.18^{+0.09}_{-0.07}$ for planet b and $0.24^{+0.09}_{-0.08}$ for planet c. We perform a dynamical analysis and internal structure model of the planets as well as deriving stellar parameters and chemical abundances. The mean density of TOI-1052b is $3.9^{+1.7}_{-1.3}$ g cm−3 consistent with an internal structure similar to Neptune. A nearby star is observed in Gaia DR3 with the same distance and proper motion as TOI-1052, at a sky projected separation of $\scriptstyle \sim$1500 au, making this a potential wide binary star system.

Armstrong, David J. (ORCID:0000000250804117)↗
DOE OSTI2021

Constraining the baryon abundance with the kinematic Sunyaev-Zel’dovich effect: Projected-field detection using Planck , WMAP , and unWISE

The kinematic Sunyaev-Zel'dovich (kSZ) effect -- the Doppler boosting of cosmic microwave background (CMB) photons scattering off free electrons with non-zero line-of-sight velocity -- is an excellent probe of the distribution of baryons in the Universe. In this paper, we measure the kSZ effect due to ionized gas traced by infrared-selected galaxies from the \emph{unWISE} catalog. We employ the "projected-field" kSZ estimator, which does not require spectroscopic galaxy redshifts. To suppress non-kSZ foreground signals associated with the galaxies (e.g., dust emission and thermal SZ), this estimator requires cleaned CMB maps, which we obtain from \emph{Planck} and \emph{WMAP} data. Using a new "asymmetric" estimator that combines different foreground-cleaned CMB maps to maximize the signal-to-noise, we measure the kSZ$^2$-galaxy cross-power spectrum for three subsamples of the \emph{unWISE} galaxy catalog, which peak at mean redshifts $z \approx$ 0.6, 1.1, and 1.5, have average halo mass $\sim 1$-$5\times 10^{13}$ $h^{-1} M_{\odot}$, and in total contain over 500 million galaxies. After marginalizing over CMB lensing contributions, we measure the amplitude of the kSZ signal $A_{\rm kSZ^2} = 0.42 \pm 0.31$, $5.02 \pm 1.01$, and $8.23 \pm 3.23$, for the three subsamples, where $A_{\rm kSZ^2} = 1$ corresponds to our fiducial model. The combined kSZ detection S/N $>$ 5. We discuss possible explanations for the excess kSZ signal associated with the $z \approx 1.1$ sample, and show that foreground contamination in the CMB maps is very unlikely to be the cause. Our measurements illustrate clearly that no baryons are missing on large scales at low redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

(Anti-)deuteron production in pp collisions at $\sqrt{s}=13 \ \text {TeV}$

The study of (anti-)deuteron production in pp collisions has proven to be a powerful tool to investigate the formation mechanism of loosely bound states in high-energy hadronic collisions. In this paper the production of $\text {(anti-)deuterons}$ is studied as a function of the charged particle multiplicity in inelastic pp collisions at $\sqrt{s}=13$ TeV using the ALICE experiment. Thanks to the large number of accumulated minimum bias events, it has been possible to measure (anti-)deuteron production in pp collisions up to the same charged particle multiplicity ( ${\mathrm {d} N_{ch}/\mathrm {d} \eta } \sim 26$ ) as measured in p–Pb collisions at similar centre-of-mass energies. Within the uncertainties, the deuteron yield in pp collisions resembles the one in p–Pb interactions, suggesting a common formation mechanism behind the production of light nuclei in hadronic interactions. In this context the measurements are compared with the expectations of coalescence and statistical hadronisation models (SHM).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Dark Energy Survey Year 6 Results: Galaxy-galaxy lensing

We present galaxy--galaxy lensing (GGL) measurements from the full six years of data from the Dark Energy Survey (DES Y6), covering $4031\,\mathrm{deg}^2$ and used in the DES Y6 $3\times2$pt cosmological analysis. We use the MagLim++ lens sample, containing $\sim 9$ million galaxies divided into six redshift bins, and the Metadetection source catalog, including $\sim 140$ million galaxies divided into four redshift bins. The mean tangential shear signal achieves a total signal-to-noise ratio (S/N) of $173$, corresponding to a $17\%$ improvement over DES Y3. After applying the scale cuts used in the cosmological analysis, with $R_{\min}=6\,\mathrm{Mpc}/h$ ($4\,\mathrm{Mpc}/h$) for the linear (nonlinear) galaxy-bias model, the S/N is reduced to $75$ (90). A comprehensive suite of validation tests demonstrates that the measurement is robust against observational and astrophysical systematics at the statistical precision required for the DES Y6 analysis. Although not used in the main cosmological analysis, we extract high--signal-to-noise geometric shear-ratio measurements from the galaxy--galaxy lensing signal on small angular scales. These measurements provide an internal consistency check on the photometric redshift distributions and shear calibration used in the $3\times2$pt analysis.

Giannini, G. [Barcelona, IEEC; Chicago U., KICP; B↗
DOE OSTI2022

Mass spectral imaging showing the plant growth-promoting rhizobacteria's effect on the Brachypodium awn

The plant growth-promoting rhizobacteria (PGPR) on the host plant surface play a key role in biological control and pathogenic response in plant functions and growth. However, it is difficult to elucidate the PGPR effect on plants. Such information is important in biomass production and conversion. Brachypodium distachyon (Brachypodium), a genomics model for bioenergy and native grasses, was selected as a C3 plant model; and the Gram-negative Pseudomonas fluorescens SBW25 ( P.) and Gram-positive Arthrobacter chlorophenolicus A6 ( A.) were chosen as representative PGPR strains. The PGPRs were introduced to the Brachypodium seed's awn prior to germination, and their possible effects on the seeding and growth were studied using different modes of time-of-flight secondary ion mass spectrometry (ToF-SIMS) measurements, including a high mass-resolution spectral collection and delayed image extraction. We observed key plant metabolic products and biomarkers, such as flavonoids, phenolic compounds, fatty acids, and auxin indole-3-acetic acid in the Brachypodium awns. Furthermore, principal component analysis and two-dimensional imaging analysis reveal that the Brachypodium awns are sensitive to the PGPR, leading to chemical composition and morphology changes on the awn surface. Our results show that ToF-SIMS can be an effective tool to probe cell-to-cell interactions at the biointerface. This work provides a new approach to studying the PGPR effects on awn and shows its potential for the research of plant growth in the future.

metabolite↗
DOE OSTI2022

Search for Higgs Portal Scalars and Heavy Neutral Leptons Decaying in the MicroBooNE Detector

This thesis presents a search for Higgs Portal Scalars (HPS) and Heavy Neutral Leptons (HNL) decaying in the MicroBooNE liquid argon time projection chamber (LArTPC). The measurement was performed using data collected in-time with the Neutrino at the Main Injector (NuMI) beam with a total exposure corresponding to $7.01 \times 10^{20}$ protons on target. Mono-energetic HPS and HNL would be produced from kaons decaying at rest in the NuMI hadron absorber, before travelling ${\sim}100$~m to the MicroBooNE detector where they decay. A single selection and search strategy is used to target decays of HPS to $\mu\mu$ pairs and HNL to $\mu\pi$ pairs. The results are expressed as limits, at the $90\%$ confidence level, on the mixing angles that control the rates of production and decay for each new particle. For the HNL model, upper limits are set on the mixing parameter $\mumix$ in the range [$12.9 \times 10^{-8}$, $0.54 \times 10^{-8}$] for HNL with masses in the region $246$--$385$~MeV. % This represents an order of magnitude increase in sensitivity to the previous MicroBooNE HNL result. For the HPS model, limits on the scalar-Higgs mixing angle $\theta^2$ are set, excluding a region with a lower boundary between [$31.3 \times10^{-9}$, $1.09 \times 10^{-9}$] and an upper boundary between [$2.50 \times 10^{-5}$, $5.05 \times 10^{-9}$] for scalars with a mass of $212$--$275$ MeV. These results set the first constraints in this region of parameter space from a dedicated experimental search for HPS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Reliable photometric membership (RPM) of galaxies in clusters – I. A machine learning method and its performance in the local universe

ABSTRACT We introduce a new method to determine galaxy cluster membership based solely on photometric properties. We adopt a machine learning approach to recover a cluster membership probability from galaxy photometric parameters and finally derive a membership classification. After testing several machine learning techniques (such as stochastic gradient boosting, model averaged neural network and k-nearest neighbours), we found the support vector machine algorithm to perform better when applied to our data. Our training and validation data are from the Sloan Digital Sky Survey main sample. Hence, to be complete to $M_r^* + 3$, we limit our work to 30 clusters with $z$phot-cl ≤ 0.045. Masses (M200) are larger than $\sim 0.6\times 10^{14} \, \mathrm{M}_{\odot }$ (most above $3\times 10^{14} \, \mathrm{M}_{\odot }$). Our results are derived taking in account all galaxies in the line of sight of each cluster, with no photometric redshift cuts or background corrections. Our method is non-parametric, making no assumptions on the number density or luminosity profiles of galaxies in clusters. Our approach delivers extremely accurate results (completeness, C $\sim 92{\rm{ per\ cent}}$ and purity, P $\sim 87{\rm{ per\ cent}}$) within R200, so that we named our code reliable photometric membership. We discuss possible dependencies on magnitude, colour, and cluster mass. Finally, we present some applications of our method, stressing its impact to galaxy evolution and cosmological studies based on future large-scale surveys, such as eROSITA, EUCLID, and LSST.

Lopes, Paulo A. A.↗
DOE OSTI2024

Primeval very low-mass stars and brown dwarfs – VIII. The first age benchmark L subdwarf, a wide companion to a halo white dwarf

ABSTRACT We report the discovery of five white dwarf + ultracool dwarf systems identified as common proper motion wide binaries in the Gaia Catalogue of Nearby Stars. The discoveries include a white dwarf + L subdwarf binary, VVV 1256−62AB, a gravitationally bound system located 75.6$^{+1.9}_{-1.8}$ pc away with a projected separation of 1375$^{+35}_{-33}$ au. The primary is a cool DC white dwarf with a hydrogen dominated atmosphere, and has a total age of $10.5^{+3.3}_{-2.1}$ Gyr, based on white dwarf model fitting. The secondary is an L subdwarf with a metallicity of [M/H] = $-0.72^{+0.08}_{-0.10}$ (i.e. [Fe/H] = $-0.81\pm 0.10$) and $T_{\rm eff}$ = 2298$^{+45}_{-43}$ K based on atmospheric model fitting of its optical to near infrared spectrum, and likely has a mass just above the stellar/substellar boundary. The subsolar metallicity of the L subdwarf and the system’s total space velocity of 406 km s−1 indicates membership in the Galactic halo, and it has a flat eccentric Galactic orbit passing within 1 kpc of the centre of the Milky Way every $\sim$0.4 Gyr and extending to 15–31 kpc at apogal. VVV 1256−62B is the first L subdwarf to have a well-constrained age, making it an ideal benchmark of metal-poor ultracool dwarf atmospheres and evolution.

Zhang, Z. H. (ORCID:000000033047607X)↗
DOE OSTI2022

Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency $\omega_\ast \sim J q_{EA}$, and for $\omega < \omega_\ast$, the spectral density is linear in $\omega$, thus quenching the extensive zero temperature entropy of the spin liquid. Furthermore, the linear $\omega$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T \rightarrow 0$ to an extensive complexity of the spin glass state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Impact of the continuum on the γ decay of the lowest 2 + states in 14 C

The half-life, T 1/2 =14.6(33) fs, of the 7012-keV 2$^{+}_{1}$ state in 14 C was measured in an experiment employing the 9 Be( 6 Li,pγ) fusion-evaporation reaction and the GODDESS setup. The γ decay from the 2$^{+}_{2}$ near-threshold resonance, located 142 keV above the 8176-keV neutron-emission threshold, was also investigated. An upper limit of 4.0 × 10 –5 was established for the γ-decay branching ratio with respect to the neutron-decay channel. The B(E2) transition probabilities for these 2$^{+}_{1}$ and 2$^{+}_{2}$ states were compared to predictions from the Shell Model Embedded in the Continuum (SMEC). Significant modifications of these B(E2) probabilities, with respect to the standard shell model, are expected due to the coupling to the continuum. For calculations using the YSOX interaction, agreement was found for large negative values of V 0 , the coupling constant to the continuum. The central value V 0 = −645 MeV fm 3 results in a retardation by a factor ∼ 3.5 for the 2$^{+}_{1}$ → 0$^{+}_{1}$ transition, and an enhanced probability by a factor ∼ 2.5 for the γ-decay out of the 2$^{+}_{2}$ state. The latter factor reflects the effect of collectivization of the 2$^{+}_{2}$ excitation when the coupling to the continuum is taken into account.

14C↗
DOE OSTI2022

Gravitational Contact Interactions -- Does the Jordan Frame Exist?

Scalar--tensor theories, with Einstein Hilbert and non-minimal interactions, $\sim M^2R/2 -\alpha\phi^2R/12 $, have graviton exchange induced contact interactions. These always pull the theory back into a formal Einstein frame in which $\alpha$ does not exist. In the Einstein frame, contact terms are induced, that are then absorbed back into other couplings to define the effective potential (or equivalently, the renormalization group). We show how these effects manifest themselves in a simple model by computing the effective potential in both frames displaying the discrepancy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗