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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

The Qweak Experiment: First Determination of the Weak Charge of the Proton

The $Q_{weak}$ Collaboration has completed a challenging measurement of the parity-violating asymmetry in elastic electron-proton ($\vec{e}$p) scattering at the Thomas Jefferson National Accelerator Facility (Jefferson Lab). The initial result reported here is extracted from the commissioning part of the experiment, constituting about 4% of the full data set. The parity-violating asymmetry at a low momentum transfer $Q^2$=0.025 GeV$^2$ is $A_{ep}$ = -279 $\pm$ 35 (stat) $\pm$ 31 (syst) ppb, which is the smallest and most precise asymmetry ever measured in $\vec{e}$p scattering. This result allowed the first determination of the weak charge of the proton $Q_W^p$ from a global fit of parity-violating elastic scattering (PVES) results from nuclear targets, where earlier data at higher $Q^2$ constrain uncertainties of hadronic structure. The value extracted from the global fit is $Q_W^p$ (PVES) = 0.064 $\pm$ 0.012, in agreement with the standard model prediction $Q_W^p$ (SM) = 0.0710 $\pm$ 0.0007. The neutral weak charges of up and down quarks are extracted from a combined fit of the PVES results with a previous atomic parity violation (APV) measurement on $^{133}$Cs. The analysis of the full $Q_{weak}$ data is ongoing and expected to yield a value for the asymmetry within 10 ppb of precision. Because of the suppression of $Q_W^p$, such a high precision measurement will place significant constraints to models of physics beyond the standard model.

Kargiantoulakis, Emmanouil↗
DOE OSTI2022

CREx Transverse Asymmetry Measurements

A number of recent experiments have been able to successfully measure the parity violating asymmetry of electron-nucleus scattering and use its value to constrain the nuclear structure. The most recent of these, the Calcium Radius Experiment (CREX), finished taking data in Hall A of Jefferson Lab in 2021, and successfully extracted a neutron radius for 48Ca. While the main measurements of these experiments are parity violating, there is an increasing amount of interest in the parity conserving Beam Normal Single Spin Asymmetry (BNSSA) systematic. If not properly suppressed, the BNSSA can compete with or exceed the parity violating measurement. Recent attempts to model the contributions from standard model suppressed higher order diagrams have struggled to predict behavior of BNSSA for all nuclei. This document reports new measurements of the BNSSA at a beam energy of 2.18 GeV for 12C, 40Ca, 48Ca, and 208Pb from the CREX running period.

Radloff, Robert↗
DOE OSTI2023

Spectroscopy of 13 Be through isobaric analog states in 13 B

Spectroscopy of the exotic, neutron-unbound beryllium isotope, 13 Be, is still a puzzle despite significant experimental efforts. To observe T = 5/2 states in 13 B, establish spin parities and spectroscopic factors, and use isospin symmetry to inform spectroscopy of 13 Be, excitation functions for resonance elastic scattering of 12 Be on protons were measured in the c.m. energy range from 1 MeV to 5 MeV. Two T = 5/2 states in 13 B at excitation energies 18.25 MeV and 19.95 MeV were observed. Unambiguous 1/2 + and 5/2 + spin-parity assignments were made, and spectroscopic factors were established using R-matrix analysis of the measured 12 Be + p excitation functions. Here, we provide the first direct and unambiguous spin-parity assignments and spectroscopic factor measurements for the resonances in the A = 13, T = 5/2 isobaric multiplet. This puts us on a solid footing to identify the 2.3 MeV state in 13 Be as 5/2 + and infer the existence of an s-wave (1/2 + ) resonance at around 0.6 MeV with a relatively small spectroscopic factor.

6 ≤ A ≤ 19↗
DOE OSTI2016

What is a particle-conserving Topological Superfluid? The fate of Majorana modes beyond mean-field theory

We investigate Majorana modes of number-conserving fermionic superfluids from both basic physics principles, and concrete models perspectives. After reviewing a criterion for establishing topological superfluidity in interacting systems, based on many-body fermionic parity switches, we reveal the emergence of zero-energy modes anticommuting with fermionic parity. Those many-body Majorana modes are constructed as coherent superpositions of states with different number of fermions. While realization of Majorana modes beyond mean field is plausible, we show that the challenge to quantum-control them is compounded by particle-conservation, and more realistic protocols will have to balance engineering needs with astringent constraints coming from superselection rules. Majorana modes in number-conserving systems are the result of a peculiar interplay between quantum statistics, fermionic parity, and an unusual form of spontaneous symmetry breaking. We test these ideas on the Richardson–Gaudin–Kitaev chain, a number-conserving model solvable by way of the algebraic Bethe ansatz, and equivalent in mean field to a long-range Kitaev chain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Axino dark matter in light of an anomalous X-ray line

Axino as the superpartner of axion that solves the strong CP problem can be a good candidate of dark matter. Inspired by the 3.5 keV X-ray line signal found to be originated from galaxy clusters and Andromeda galaxy, we study axino models with R-parity violations, and point out that axino dark matter with trilinear R-parity violations is an attractive scenario that reproduces the X-ray line. The Peccei-Quinn scale is required to be f{sub a} ∼ O(10{sup 9}–10{sup 11}) GeV for trilinear R-parity violating couplings λ ∼ O(10{sup −3}–10{sup −1}) in order to explain the line signal. Moreover, the right-handed stau is predicted to be light, i.e. ∼ O(100) GeV, and thus can be looked for at the LHC. Cosmological aspects of the model are also discussed in this study.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Fermionic systems for quantum information people

The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity superselection in the fermionic case on the other. We discuss these two fundamental differences extensively, and illustrate these through the Jordan–Wigner representation in a coherent, self-contained, pedagogical way, from the point of view of quantum information theory. Our perspective leads us to develop useful new tools for the treatment of fermionic systems, such as the fermionic (quasi-)tensor product, fermionic canonical embedding, fermionic partial trace, fermionic products of maps and fermionic embeddings of maps. We formulate these by direct, easily applicable formulas, without mode permutations, for arbitrary partitionings of the modes. It is also shown that fermionic reduced states can be calculated by the fermionic partial trace, containing the proper phase factors. We also consider variants of the notions of fermionic mode correlation and entanglement, which can be endowed with the usual, local operation based motivation, if the parity superselection rule is imposed. We also elucidate some other fundamental points, related to joint map extensions, which make the parity superselection inevitable in the description of fermionic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

In-beam γ-ray spectroscopy of 32 Mg via direct reactions

Background: The nucleus 32 Mg (N=20 and Z=12) plays a central role in the so-called “island of inversion,” where in the ground states sd-shell neutrons are promoted to the fp-shell orbitals across the shell gap, resulting in the disappearance of the canonical neutron magic number N=20. Purpose: The primary goals of this work are to extend the level scheme of 32Mg, provide spin-parity assignments to excited states, and discuss the microscopic structure of each state through comparisons with theoretical calculations. Method: In-beam γ-ray spectroscopy of 32 Mg was performed using two direct-reaction probes: one-neutron (two-proton) knockout reactions on 33 Mg ( 34 Si). Final-state exclusive cross sections and parallel momentum distributions were extracted from the experimental data and compared with eikonal-based reaction model calculations combined with shell-model overlap functions. Results: Owing to the remarkable selectivity of the one-neutron and two-proton knockout reactions, a significantly updated level scheme for 32 Mg, which exhibits negative-parity intruder and positive-parity normal states, was constructed. The experimental results were confronted with four different nuclear structure models. Conclusions: In some of these models, different aspects of 32 Mg and the transition into the island of inversion are well described. However, unexplained discrepancies remain, and, even with the help of these state-of-the-art theoretical approaches, the structure of this key nucleus is not yet fully captured.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Engineering of mixed pairing and non-Abelian Majorana states in chiral p-wave superconductor Sr 2 RuO 4 and other materials

This project deals with odd-parity superconductor Sr 2 RuO 4 and related material systems, aiming at understanding the unconventional nature of superconductivity in this material. An odd-parity superconductor is expected to feature a novel topological object, the half-flux-quantum vortex that hosts a Majorana anyons. Majorana anyons carry non-Abelian statistics that can be used as the building block for constructing a fault-tolerated topological quantum computer. Half-flux-quantum vortices form in an odd-parity superconductor because of the availability of charge neutral spin supercurrent in addition to the normal supercurrent. Half-height magnetization steps were found in a cantilever magnetometry measurement of doubly connected mesoscopic samples of Sr 2 RuO 4 in the presence of an in-plane magnetic field (J. Jang, D. G. Ferguson, V. Vakaryuk, R. Budakian, S. B. Chung, P. M. Goldbart, and Y. Maeno, Science 331, 186 (2011)), which suggests the presence of a half-flux-quantum (Φ 0 /2 = h/4e) state. Evidence for half flux quantum states, which can be viewed as coreless half vortices, was obtained in mesoscopic samples of Sr 2 RuO 4 in the torque magnetomitry measurements. However, the existence of such an important property has not been confirmed by any other independent measurement.

36 MATERIALS SCIENCE↗
NASA NTRS2001

Maternal reproductive experience enhances early postnatal outcome following gestation and birth of rats in hypergravity

A major goal of space life sciences research is to broaden scientific knowledge of the influence of gravity on living systems. Recent spaceflight and centrifugation studies demonstrate that reproduction and ontogenesis in mammals are amenable to study under gravitational conditions that deviate considerably from those typically experienced on Earth (1 x g). In the present study, we tested the hypothesis that maternal reproductive experience determines neonatal outcome following gestation and birth under increased (hyper) gravity. Primigravid and bigravid female rats and their offspring were exposed to 1.5 x g centrifugation from Gestational Day 11 either through birth or through the first postnatal week. On the day of birth, litter sizes were identical across gravity and parity conditions, although significantly fewer live neonates were observed among hypergravity-reared litters born to primigravid dams than among those born to bigravid dams (82% and 94%, respectively; 1.0 x g controls, 99%). Within the hypergravity groups, neonatal mortality was comparable across parity conditions from Postnatal Day 1 through Day 7, at which time litter sizes stabilized. Maternal reproductive experience ameliorated neonatal losses during the first 24 h after birth but not on subsequent days, and neonatal mortality was associated with changes in maternal care patterns. These results indicate that repeated maternal reproductive experience affords protection against neonatal losses during exposure to increased gravity. Differential mortality of neonates born to primigravid versus bigravid dams denotes gravitational load as one environmental mechanism enabling the expression of parity-related variations in birth outcome.

NASA Discipline Developmental Biology↗
DOE OSTI2019

A theory of R(D*, D) anomaly with right-handed currents

We present an ultraviolet complete theory for the R ( D * ) and R ( D ) anomaly in terms of a low mass W ± R gauge boson of a class of left-right symmetric models. These models, which are based on the gauge symmetry SU(3) c × SU(2) L × SU(2) R × U(1) B - L , utilize vector-like fermions to generate quark and lepton masses via a universal seesaw mechanism. A parity symmetric version as well as an asymmetric version are studied. A light sterile neutrino emerges naturally in this setup, which allows for new decay modes of B -meson via right-handed currents. We show that these models can explain R ( D * ) and R ( D ) anomaly while being consistent with LHC and LEP data as well as low energy flavor constraints arising from \( {K}_L-{K}_S,\kern0.5em {B}_{d,s}-{\overline{B}}_{d,s},\kern0.5em D-\overline{D} \) mixing, etc., but only for a limited range of the W R mass: 1.2 (1.8) TeV ≤ \( {M}_{W_R} \) ≤ 3 TeV for parity asymmetric (symmetric) Yukawa sectors. The ratio R ( D )/ R ( D * ) is predicted to be ≃ 1.16, which is the same as in the Standard Model. The light sterile neutrinos predicted by the model may be relevant for explaining the MiniBoone and LSND neutrino oscillation results. The parity symmetric version of the model provides a simple solution to the strong CP problem without relying on the axion. It also predicts an isospin singlet top partner with a mass M T = (1.5 - 2.5) TeV.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Predictive Dirac neutrino spectrum with strong CP solution in SU(5)L × SU(5)R unification

Abstract We develop a grand unified theory of matter and forces based on the gauge symmetry SU(5) L × SU(5) R with parity interchanging the two factor groups. Our main motivation for such a construction is to realize a minimal GUT embedding of left-right symmetric models that provide a parity solution to the strong CP problem without the axion. We show how the gauge couplings unify with an intermediate gauge symmetry SU(3) cL × SU(2) 2L × U(1) L × SU(5) R , and establish its consistency with proton decay constraints. The model correctly reproduces the observed fermion masses and mixings and leads tonaturally light Dirac neutrinoswith their Yukawa couplings suppressed by a factorM I /M G , the ratio of the intermediate scale to the GUT scale. We call this mechanism type II-Dirac seesaw. Furthermore, the model predictsδ CP = ±(130.4±1.2)° and$${m}_{{\nu }_{1}}$$= (4.8 – 8.4) meV for the Dirac CP phase and the lightest neutrino mass. We demonstrate how the model solves the strong CP problem via parity symmetry.

Physics↗
DOE OSTI2023

Search for direct production of winos and higgsinos in events with two same-charge leptons or three leptons in $pp$ collision data at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A search for supersymmetry targeting the direct production of winos and higgsinos is conducted in final states with either two leptons (e or μ) with the same electric charge, or three leptons. The analysis uses 139 fb -1 of pp collision data at $\sqrt{s}$ = 13 TeV collected with the ATLAS detector during Run 2 of the Large Hadron Collider. No significant excess over the Standard Model expectation is observed. Simplified and complete models with and without R-parity conservation are considered. In topologies with intermediate states including either Wh or WZ pairs, wino masses up to 525 GeV and 250 GeV are excluded, respectively, for a bino of vanishing mass. Higgsino masses smaller than 440 GeV are excluded in a natural R-parity-violating model with bilinear terms. Upper limits on the production cross section of generic events beyond the Standard Model as low as 40 ab are obtained in signal regions optimised for these models and also for an R-parity-violating scenario with baryon-number-violating higgsino decays into top quarks and jets. The analysis significantly improves sensitivity to supersymmetric models and other processes beyond the Standard Model that may contribute to the considered final states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A flavor of SO(10) unification with a spinor Higgs

We investigate Higgs Parity unification — a realization of SO(10) grand unification based on the Higgs Parity mechanism in which the Standard Model (SM) Higgs resides in a spinor representation. The theory has an intermediate left-right symmetric stage where the SU(2)R symmetry breaking scale is fixed by the vanishing of the SM Higgs quartic coupling. The strong CP problem is solved by parity. Gauge coupling unification successfully predicts αs(MZ) to within 1%. The spinor Higgs naturally leads to a seesaw origin for SM flavor observables. We identify a novel mechanism where large mixing of third generation fermions with additional heavy vector-like fermions accounts for the anarchical nature of the PMNS matrix and the lack of hierarchy in the neutrino mass spectrum, relative to the up-quarks. A fit to quark and lepton masses and mixings, with a minimal parameter set, predicts 1) A testable relation between the top quark mass and αs(MZ) which is about (1 – 2)σ from current best fit values, 2) The order of magnitude of the baryon asymmetry of the universe, via leptogenesis from second-generation right-handed neutrino decays. 3) The proton decay and the neutron EDM are likely observable in next generation experiments, and 4) A normal ordered neutrino mass spectrum where 0νββ decay and the mass of the lightest neutrino are out of reach of next generation experiments.

Baryo-and Leptogenesis↗
DOE OSTI2017

Hyperentanglement concentration of nonlocal two-photon six-qubit systems with linear optics

Hyperentanglement, the entangled states in the multiple degrees of freedom (DOFs) of a photon system simultaneously, has attracted much attention recently as it can increase the capacity of quantum communication largely. Here we present the first scheme for concentrating the nonlocal two-photon six-qubit systems entangled in polarization, spatial-mode, and time-bin DOFs with linear optics. We construct the parity-check gates for the quantum states of nonlocal photon systems in all the three DOFs with linear-optical elements. Fortunately, our parity-check gate for one DOF does not affect the quantum states in the other two DOFs, which makes our hyperentanglement concentration protocol (hyper-ECP) can be implemented conveniently for polarization–spatial–time-bin partially hyperentangled states. This hyper-ECP is practical as it requires only linear-optical elements, and it can be directly generalized to improve the entanglement of nonlocal multi-photon systems entangled in three DOFs in the long-distance high-capacity quantum communication. - Highlights: • A linear hyperentanglement concentration protocol is proposed for photon systems. • Parity-check gates on one degree of freedom (DOF) will not affect the other two DOFs. • Polarization, spatial-mode, and time-bin DOFs are manipulated with linear optics. • Nonlocal maximally hyperentangled two-photon six-qubit systems are obtained. • Entanglement of multiphoton systems in three DOFs can be improved with this method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Variability and predictors of serum perfluoroalkyl substance concentrations during pregnancy and early childhood

Highlights: • Few longitudinal studies have examined child perfluoroalkyl substance (PFAS) exposure. • Childhood PFAS concentrations increased from birth to age 3 and decreased by age 8. • Sociodemographic factors (income, race, parity) were associated with PFAS. • Breastfeeding was associated with high PFAS concentrations at ages 3 and 8 years. • Exposure may be higher during a potentially sensitive period of development. Exposure to poly- and perfluoroalkyl substances (PFAS), ubiquitous and persistent environmental contaminants, could be associated with adverse health outcomes, but there are limited longitudinal data assessing patterns and predictors of exposure during childhood. We quantified concentrations of eight different PFAS in sera collected from women during pregnancy and children at delivery and ages 3 and 8 years in 367 mother-child pairs enrolled in a prospective cohort from 2003 to 2006. In general, median childhood PFAS concentrations increased from birth to age 3 and then decreased by age 8. Maternal serum PFAS concentrations during pregnancy were strongly correlated with cord serum concentrations (0.76 < r < 0.94), but were weakly correlated with childhood concentrations (0.12 < r < 0.30). Several sociodemographic factors were associated with maternal PFAS concentrations, including income, race, and parity. In children, serum PFAS concentrations were associated with maternal age at delivery, race, parity, and child age. Breastfeeding duration was positively associated with childhood PFAS concentrations at ages 3 and 8 years. In addition, stain repellant use was associated with higher perfluorooctanoic acid and perfluorohexane sulfonic acid concentrations at age 8 years. Serum PFAS concentrations are higher during early childhood, a potentially sensitive period of development, and were highest among breastfed children.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Enhanced red emission induced by Tb{sup 3+} doping in europium-based molybdate phosphors

Graphical abstract: The introduction of Tb3+ significantly enhances the red emission of Eu3+ in europium-based molybdate phosphors. The enhanced red emission intensity is discussed by the relaxation of parity-forbidden selection rules of Eu3+ ions, whereas the contribution of Tb3+ → Eu3+ energy transfer is little in our case. - Highlights: • The introduction of Tb{sup 3+} significantly enhances the red emission of Eu{sup 3+} in europium-based molybdate phosphors. • At x = 0.02, the red-emitting intensity of LiEuMo{sub 2}O{sub 8} is enhanced by 30% under excitation at ultraviolet light 395 nm. • The enhanced red emission intensity is discussed by the relaxation of parity-forbidden selection rules of Eu{sup 3+} ions, whereas the contribution of Tb{sup 3+} → Eu{sup 3+} energy transfer is little in our case. - Abstract: A series of Tb{sup 3+}-doped europium-based molybdate red-emitting phosphors (LiEuMo{sub 2}O{sub 8}) were prepared by solid-state reaction method, their crystal structure and luminescence properties have been investigated by X-ray diffraction, micro-Raman spectra, diffuse reflectance spectra, photoluminescence and photoluminescence excitation spectra. Partial substitution of Li{sup +} by Tb{sup 3+} slightly distorts the host lattice, red-shifts the absorption edge of host and improves Eu{sup 3+} red-emitting intensity in LiEuMo{sub 2}O{sub 8} compound. The red-emitting intensity of LiEuMo{sub 2}O{sub 8} powder is enhanced by 30% at the doping level of 0.02 under excitation at 395 nm. In present study, we found that the contribution of Tb{sup 3+} → Eu{sup 3+} energy transfer to the enhanced Eu{sup 3+} emission is little since the Tb{sup 3+} ions are not responsive to the near ultraviolet (∼395 nm), the enhanced red emission is tentatively ascribed to the relaxation of parity-forbidden selection rules of Eu{sup 3+} ions. White light-emitting diodes are fabricated by using near ultraviolet light-emitting diode chips (∼395 nm) and the blends of the commercial blue, green and as-prepared red Li{sub 0.98}Tb{sub 0.02}EuMo{sub 2}O{sub 8} phosphor, the resulting white light-emitting diode shows a color-rendering index of 93.5, luminous efficacy of 14 lm/W and chromaticity coordinates of (0.292, 0.329).

36 MATERIALS SCIENCE↗
DOE OSTI2013

New insights into the nuclear structure in neutron-rich 112,114,115,116,117,118Pd

New level schemes of 112,114,115,116,117,118Pd are established by means of ?–?–??–?–?, ?–?–?–??–?–?–? and ?–?(0)?–?(0) measurements of prompt fission y rays from 252Cf using the Gammasphere multi-detector array. Spins/parities were assigned to levels based on ?–??–? angular correlation measurements, level systematics and decay patterns. In the even-N isotopes 112,114,116Pd, two sets of odd-parity bands were identified and extended with spins measured in each band. The odd-parity bands with large level staggerings were interpreted as disturbed chirality with less pronounced triaxial deformations in the Pd isotopes than observed in the chiral symmetry breaking 110,112Ru with maximum triaxiality. Onset of wobbling motion was identified from the sign of the signature splitting in the ? band of even–even 114Pd, and probably also in 116Pd, as first seen in the N=68N=68 isotone 112Ru. Maximal triaxiality in Ru and Pd isotopes is found to be reached for N=68N=68, 112Ru and 114Pd, 4 neutrons more than predicted in the theoretical calculations. The new data and TRS calculations allowed a systematic study of the band crossings in the even-N112,114,116Pd and odd-N115,117Pd isotopes. Now we find a new overall, more complex shape evolution than previously proposed from triaxial prolate in 110Pd via triaxial oblate in 112Pd to nearly oblate in 114,116Pd with a large change of the triaxial deformation parameter y toward nearly oblate in the (pi g 9/2)2 alignment in 114,115,116,117,118Pd, and triaxial-prolate–triaxial-oblate shape coexisting bands in 115Pd.

112,114,115,116,117,118Pd↗
DOE OSTI2018

Characterization of the 1S–2S transition in antihydrogen

In 1928, Dirac published an equation1 that combined quantum mechanics and special relativity. Negative-energy solutions to this equation, rather than being unphysical as initially thought, represented a class of hitherto unobserved and unimagined particles—antimatter. The existence of particles of antimatter was confirmed with the discovery of the positron2 (or anti-electron) by Anderson in 1932, but it is still unknown why matter, rather than antimatter, survived after the Big Bang. As a result, experimental studies of antimatter3,4,5,6,7, including tests of fundamental symmetries such as charge–parity and charge–parity–time, and searches for evidence of primordial antimatter, such as antihelium nuclei, have high priority in contemporary physics research. The fundamental role of the hydrogen atom in the evolution of the Universe and in the historical development of our understanding of quantum physics makes its antimatter counterpart—the antihydrogen atom—of particular interest. Current standard-model physics requires that hydrogen and antihydrogen have the same energy levels and spectral lines. The laser-driven 1S–2S transition was recently observed8 in antihydrogen. Here we characterize one of the hyperfine components of this transition using magnetically trapped atoms of antihydrogen and compare it to model calculations for hydrogen in our apparatus. We find that the shape of the spectral line agrees very well with that expected for hydrogen and that the resonance frequency agrees with that in hydrogen to about 5 kilohertz out of 2.5 × 1015 hertz. This is consistent with charge–parity–time invariance at a relative precision of 2 × 10-12—two orders of magnitude more precise than the previous determination8—corresponding to an absolute energy sensitivity of 2 ×10-20 GeV.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗