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DOE OSTI2026

Slow Quasiparticle Dynamics and Anyonic Statistics in a Fractional Quantum Hall Fabry-Pérot Interferometer

Anyons are two-dimensional particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, their exchange statistics can be measured in the edge-state Fabry-Pérot interferometer, wherein the presence of 𝑁 𝑞⁢𝑝 localized anyons contributes a phase 𝑁 𝑞⁢𝑝⁢ 𝜃 𝑎 to the interference pattern where 𝜃 𝑎 is twice the exchange phase. Here we report the observation of large, hysteretic phase jumps in a monolayer graphene Fabry-Pérot interferometer at 𝜈 = 1/3. When the filling factor is increased from 𝜈 < 1/3 toward the center of the plateau, we observe phase slips with magnitude Δ⁢𝜃 ≈ 2⁢𝜋/3, consistent with the addition of individual quasiparticles to the interferometer bulk. These phase slips occur as instantaneous jumps in the interference signal, with intervals between the jumps indicating quasiparticle equilibration times exceeding 20 min. We use this long timescale to investigate the effect of changes in interferometer area 𝐴 𝐼 and 𝑁 𝑞⁢𝑝 independently at fixed magnetic field, revealing a striking memory effect in the phase slip magnitude. In particular, as the 𝜈 =1/3 plateau is approached from higher filling, we observed phase slips with Δ⁢𝜃 significantly larger than 2⁢𝜋/3 over the same range of gate voltage where quantized jumps are seen for increasing 𝜈. We discuss this asymmetry in terms of bulk-edge coupling of quasiparticles localized near the edge or in the bulk, and argue that this effect can be qualitatively reconciled with theoretical expectations for strongly interacting quasiparticles in the presence of weak disorder and strongly nonequilibrium charge dynamics. Besides providing a replication of interferometric measurements sensitive to 𝜃 𝑎 , our results highlight the key role played by charge dynamics on signatures of the anyon phase, and demonstrate that fractional quasiparticles can be indefinitely localized in nonequilibrium configurations.

anyons↗

DOE OSTI2025

Measurement of the 𝐷 0 →𝐾 − ⁢𝜋 + ⁢𝑒 + ⁢𝑒 − branching fraction and search for 𝐷 0 → 𝜋 + ⁢𝜋 − ⁢𝑒 + ⁢𝑒 − and 𝐷 0 →𝐾 + ⁢𝐾 − ⁢𝑒 + ⁢𝑒 − decays at Belle

We present a study of the rare charm meson decays 𝐷 0 →𝐾 + ⁢𝐾 − ⁢𝑒 + ⁢𝑒 − , 𝜋 + ⁢𝜋 − ⁢𝑒 + ⁢𝑒 − , and 𝐾 − ⁢𝜋 + ⁢𝑒 + ⁢𝑒 − using a 942 fb −1 dataset collected by the Belle detector at the KEKB asymmetric-energy 𝑒 + ⁢𝑒 − collider. We identify 𝐷 0 candidates via the charge of the pion from 𝐷* + →𝐷 0 ⁢𝜋 + decays and normalize the branching fractions to 𝐷 0 → 𝐾 − ⁢𝜋 + ⁢𝜋 − ⁢𝜋 + decays. The branching fraction for decay 𝐷 0 → 𝐾 − ⁢𝜋 + ⁢𝑒 + ⁢𝑒 − is measured to be (39.6 ± 4.5 (stat) ± 2.9 (syst)) × 10 −7 , with the dielectron mass in the 𝜌/𝜔 mass region 675 < 𝑚 𝑒⁢𝑒 < 875 MeV/⁢𝑐 2 . We also search for 𝐷 0 → ℎ − ⁡ℎ (′)+ ⁡𝑒 + ⁢𝑒 − (ℎ (′) = 𝐾, 𝜋) decays with the dielectron mass near the 𝜂 and 𝜙 resonances, and away from these resonances for the 𝐾 + ⁢𝐾 − ⁢𝑒 + ⁢𝑒 − and 𝜋 + ⁢𝜋 − ⁢𝑒 + ⁢𝑒 − modes. For these modes, we find no significant signals and set 90% confidence level upper limits on their branching fractions at the 𝒪⁡(10 −7 ) level.

branching fraction↗

DOE OSTI2020

Interplay between fractional quantum Hall liquid and crystal phases at low filling

The nature of the state at low Landau-level filling factors has been a long-standing puzzle in the field of the fractional quantum Hall effect (FQHE). While theoretical calculations suggest that a crystal is favored at filling factors $\nu$≲1/6, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $\nu$ 1/7, 2/11, 2/13, 3/19, 1/9, 2/15, and 2/17, which belong to the standard sequences $\nu$ =n/(6n ± 1) and $\nu$=n/(8n ± 1). To address this paradox, we investigate the nature of some of the low-$\nu$ states, specifically $\nu$= 1/7, 2/13, and 1/9, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. Finally, this suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Measurement of branching fractions of Λ$^+_c$ → p⁢K$^0_S$K$^0_S$ and Λ$^+_c$ → p⁢K$^0_S$⁢η at Belle

We present a study of a singly Cabibbo-suppressed decay Λ$^+_c$ → p⁢K$^0_S$K$^0_S$ and a Cabibbo-favored decay Λ$^+_c$ → p⁢K$^0_S$⁢η based on 980 fb -1 of data collected by the Belle detector, operating at the KEKB energy-asymmetric e + ⁢e - collider. We measure their branching fractions relative to Λ$^+_c$ → p⁢K$^0_S$: $\mathscr{B}$(Λ$^+_c$ → p⁢K$^0_S$K$^0_S$)/$\mathscr{B}$(Λ$^+_c$ → p⁢K$^0_S$) = (1.48 ± 0.08 ± 0.04) × 10 -2 and $\mathscr{B}$(Λ$^+_c$ → p⁢K$^0_S$η)/$\mathscr{B}$(Λ$^+_c$ → p⁢K$^0_S$) = (2.73 ± 0.06 ± 0.13) × 10 -1 . Combining with the world average $\mathscr{B}$(Λ$^+_c$ → p⁢K$^0_S$), we have the absolute branching fractions, $\mathscr{B}$(Λ$^+_c$ → p⁢K$^0_S$K$^0_S$) = (2.35 ± 0.12 ± 0.07 ± 0.12) × 10 -4 and $\mathscr{B}$(Λ$^+_c$ → p⁢K$^0_S$η) = (4.35 ± 0.10 ± 0.20 ± 0.22) × 10 -3 . The first and second uncertainties are statistical and systematic, respectively, while the third ones arise from the uncertainty on $\mathscr{B}$(Λ$^+_c$ → p⁢K$^0_S$). The mode Λ$^+_c$ → p⁢K$^0_S$K$^0_S$ is observed for the first time and has a statistical significance of >10σ. The branching fraction of Λ$^+_c$ → p⁢K$^0_S$η has been measured with a threefold improvement in precision over previous results and is found to be consistent with the world average.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Anderson Localization in the Fractional Quantum Hall Effect

The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor ν=n/(2n+1) has a striking quantitative correspondence to the localization of a single electron in the (n+1)th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation, these results can be extended to situations where a finite density of quasiparticles is present.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

First Measurement of the B + → π + π 0 π 0 Branching Fraction and C P Asymmetry

We study B + → π + π 0 π 0 using 711 fb -1 of data collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e + e - collider. Here we measure an inclusive branching fraction of (19.0 ±1.5 ±1.4)×10 -6 and an inclusive CP asymmetry of (9.2 ±6.8 ±0.7)%, where the first uncertainties are statistical and the second are systematic, and a B + → ρ(770) + π 0 branching fraction of (11.2 ± 1.1 ± 0.9 $^{+0.8}_{-1.6}$)× 10 -6 , where the third uncertainty is due to possible interference with B + → ρ(1450) + π 0 . We present the first observation of a structure around 1 GeV/c 2 in the π 0 π 0 mass spectrum, with a significance of 6.4σ, and measure a branching fraction to be (6.9 ±0.9 ±0.6) × 10 -6 . We also report a measurement of local CP asymmetry in this structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Targeted Particle Fractionation Technologies: Proof of Concept

Most methods of particle-size analysis involve particle fractionation which, is often done by filtration or the use of screens. This paper provides proof of concept testing for new in-pipe particle fractionation technologies that can be used at laboratory to industrial scales. These technologies are extensions of recent advancements in bump arrays as well as testing of new inline angled-to-the-flow slats, and advanced boycott-based Avalanche separation technologies. Experiments were conducted for three targeted particle fractionation technologies to evaluate the in-pipe removal of oversized sands in Newtonian slurries prior to the introduction of bump arrays. The mesofluidic system uses an array of staggered posts as configured in a bump array for Newtonian slurry conditions. The methods and results of these experiments are described in this paper. This information could be applied in most industrial and laboratory systems to rapidly remove oversized particles from a flowing slurry.

slurry, solids removal, particle fractionation, bu↗

DOE OSTI2020

Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models

In this work, we consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by the fractional power $s\in(0,1)$, are studied. Furthermore, in order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a parametric model order reduction approach. Major difficulties arise since the kernels are not affine in the parameters, singular, and discontinuous. Moreover, the spatial regularity of the solutions depends on the varying fractional power $s$. To address this, we derive regularity and differentiability results with respect to $\delta$ and $s$, which are of independent interest for other applications such as optimization and parameter identification. We then use these results to construct affine approximations of the kernels by local polynomials. Finally, we certify the method by providing reliable a posteriori error estimators, which account for all approximation errors, and support the theoretical findings by numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Oxidation of Dissolved Tetravalent Selenium by Birnessite: Se Isotope Fractionation and the Effects of pH and Birnessite Structure

Redox reactions control the mobility and bioavailability of selenium (Se) in biogeochemical systems, both modern and ancient. Se isotope ratio measurements (e.g., 82 Se/ 76 Se) have been developed to enhance understanding of biogeochemical transformations and transport of Se. Stable isotope ratios of many elements are known to be powerful indicators of redox reactions, and shifts in 82 Se/ 76 Se have been observed for Se reduction reactions. However, Se isotope shifts caused by naturally relevant oxidation reactions have not been published. Here, we report Se isotope fractionation factors for oxidation of Se(IV) by birnessite. Experiments were conducted at pH = 4.0 and 5.5, with two types of birnessite of contrasting composition at two concentrations of suspended birnessite. The results are consistent with a single 82 Se/ 76 Se fractionation factor, for all times during all experiments, of 0.99767 (±0.0035 2 s.d.). Expressed as ε, the fractionation is 2.33‰ (±0.08‰).

58 GEOSCIENCES↗

DOE OSTI2021

Hierarchical Fractional Advection-Dispersion Equation (FADE) to Quantify Anomalous Transport in River Corridor over a Broad Spectrum of Scales: Theory and Applications

Fractional calculus-based differential equations were found by previous studies to be promising tools in simulating local-scale anomalous diffusion for pollutants transport in natural geological media (geomedia), but efficient models are still needed for simulating anomalous transport over a broad spectrum of scales. This study proposed a hierarchical framework of fractional advection-dispersion equations (FADEs) for modeling pollutants moving in the river corridor at a full spectrum of scales. Applications showed that the fixed-index FADE could model bed sediment and manganese transport in streams at the geomorphologic unit scale, whereas the variable-index FADE well fitted bedload snapshots at the reach scale with spatially varying indices. Further analyses revealed that the selection of the FADEs depended on the scale, type of the geomedium (i.e., riverbed, aquifer, or soil), and the type of available observation dataset (i.e., the tracer snapshot or breakthrough curve (BTC)). When the pollutant BTC was used, a single-index FADE with scale-dependent parameters could fit the data by upscaling anomalous transport without mapping the sub-grid, intermediate multi-index anomalous diffusion. Pollutant transport in geomedia, therefore, may exhibit complex anomalous scaling in space (and/or time), and the identification of the FADE’s index for the reach-scale anomalous transport, which links the geomorphologic unit and watershed scales, is the core for reliable applications of fractional calculus in hydrology.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2000

Nonbiological fractionation of iron isotopes

Laboratory experiments demonstrate that iron isotopes can be chemically fractionated in the absence of biology. Isotopic variations comparable to those seen during microbially mediated reduction of ferrihydrite are observed. Fractionation may occur in aqueous solution during equilibration between inorganic iron complexes. These findings provide insight into the mechanisms of iron isotope fractionation and suggest that nonbiological processes may contribute to iron isotope variations observed in sediments.

NASA Discipline Exobiology↗

NASA NTRS2015

Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

Atmospheric Turbulence Modeling↗

DOE OSTI2023

Kernel Buffer Volume Fraction Margin of the AGR Designed Fuel Particle

Modeling results used to assess the fuel performance of the TRISO-coated fuel particles as a function of kernel/buffer volume fraction include SiC tangential stress, formation of the buffer/IPyC gap, particle temperature profile, internal particle pressure, fission gas released from the kernel, probability of fuel particle failure, and fission product diffusion. These results were evaluated at two burnup levels and irradiation temperatures to bound expected steady-state irradiation conditions. In general, increasing the kernel/buffer volume fraction increases the SiC stress and subsequently the failure probability of a fuel particle when compared to the AGR designed particle. There was little impact on the fission product diffusion through the particle as the kernel/buffer volume fraction increased.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Evaluation of the Sum-of-Fractions Methodology for Water and Polyethylene Moderated Systems

Sum-of-Fractions is a method intended to assure a subcritical margin for aqueous solutions and slurries of fissionable isotopes. The method indicates that a system is subcritical if the sum of the ratios of the mass of each isotope in a mixture to its individual minimum subcritical mass limit is less than or equal to one. The basis of the Sum-of Fractions has historically been derived from allowances given in ANSI/ANS-8.15-1981. However, the allowance was removed in ANSI/ANS-8.15-2014 due to a lack of technical basis. A methodology was developed to assess the validity of using the Sum-of-Fractions for water or polyethylene moderated systems for the following nuclides: 232 U, 233 U, 234 U, 235 U, 237 Np, 236 Pu, 238 Pu, 239 Pu, 240 Pu, 241 Pu, 242 Pu, 241 Am, 242 mAm, 243 Am, 242 Cm, 243 Cm, 244 Cm, 245 Cm, 246 Cm, 247 Cm, 249 Cf, and 251 Cf. The methodology uses available benchmark data for mixtures of 233 U, 235 U, and 239 Pu to establish the calculational margin, and a mass limit reduction to establish the margin of subcriticality. Water or polyethylene moderated and reflected mixtures containing the nuclides are evaluated with SCALE 6.2.4. Including the calculational margin, subcritical mass limits for each nuclide were computed for optimally water or polyethylene moderated and fully reflected systems. These masses were used to create nuclide mixtures in which the sum of the mass to subcritical mass limit ratios is one. The various nuclide mixtures were modeled over a range of moderation and demonstrate the k eff does not exceed the calculational margin. For additional assurance of subcriticality, a significant mass reduction is applied to each computed minimum critical mass of the nuclides without adequate benchmark data consistent with the method in ANSI/ANS-8.15-2014.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2023

Efficient Fast Fractionation of Biomass Using a Diol-Based Deep Eutectic Solvent for Facilitating Enzymatic Hydrolysis and Obtaining High-Quality Lignin

Current DES pretreatment is often performed under relatively severe conditions with high temperature, long time, and high DES usage. This work studied a short-time diol DES (deep eutectic solvent) pretreatment under mild conditions to fractionate the bamboo, facilitate enzymatic hydrolysis, and obtain high-quality lignin. At an optimized condition of 130 °C for only 10 min, lignin and xylan removal reached 61.34% and 84.15 %, with residual glucan showing a ~90% enzymatic hydrolysis yield. Equally important, the dissolved lignin could be readily recovered with 97.51% yield, exhibiting 96.65 % β-O-4 preservation. The fractionation and lignin protection mechanisms were unveiled by XRD, FTIR, cellulose-DP, 2D HSQC NMR, 31 P NMR and GPC analysis. Finally, this study highlighted that short-time fractionation of bamboo can be achieved by a diol-based DES which is an ideal strategy to upgrade the lignocellulose biomass for high enzymatic hydrolysis yields and high-quality lignin stream.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Measurements of the branching fraction ratio $$ \mathcal{B}\left(\phi \to {\mu}^{+}{\mu}^{-}\right)/\mathcal{B}\left(\phi \to {\textrm{e}}^{+}{\textrm{e}}^{-}\right) $$ with charm meson decays

Abstract Measurements of the branching fraction ratio$$ \mathcal{B}\left(\phi \to {\mu}^{+}{\mu}^{-}\right)/\mathcal{B}\left(\phi \to {e}^{+}{e}^{-}\right) $$ B ϕ → μ + μ − / B ϕ → e + e − with$$ {D}_s^{+}\to {\pi}^{+}\phi $$ D s + → π + ϕ andD + → π + ϕdecays, denoted$$ {R}_{\phi \pi}^s $$ R ϕπ s and$$ {R}_{\phi \pi}^d $$ R ϕπ d , are presented. The analysis is performed using a dataset corresponding to an integrated luminosity of 5.4 fb −1 ofppcollision data collected with the LHCb experiment. The branching fractions are normalised with respect to theB + →K + J/ψ(→e + e − ) andB + →K + J/ψ(→μ + μ − ) decay modes. The combination of the results yields$$ {R}_{\phi \pi}=1.022\pm 0.012\left(\textrm{stat}\right)\pm 0.048\left(\textrm{syst}\right). $$ R ϕπ = 1.022 ± 0.012 stat ± 0.048 syst . The result is compatible with previous measurements of theϕ→ℓ + ℓ − branching fractions and predictions based on the Standard Model.

Physics↗

DOE OSTI2020

Measurement of quark- and gluon-like jet fractions using jet charge in PbPb and pp collisions at 5.02 TeV

The momentum-weighted sum of the electric charges of particles inside a jet, known as jet charge, is sensitive to the electric charge of the particle initiating the parton shower. This paper presents jet charge distributions in $ \sqrt{s_{\mathrm{NN}}} $ = 5.02 TeV lead-lead (PbPb) and proton-proton (pp) collisions recorded with the CMS detector at the LHC. These data correspond to integrated luminosities of 404 μb$^{−1}$ and 27.4 pb$^{−1}$ for PbPb and pp collisions, respectively. Leveraging the sensitivity of the jet charge to fundamental differences in the electric charges of quarks and gluons, the jet charge distributions from simulated events are used as templates to extract the quark- and gluon-like jet fractions from data. The modification of these jet fractions is examined by comparing pp and PbPb data as a function of the overlap of the colliding Pb nuclei (centrality). This measurement tests the color charge dependence of jet energy loss due to interactions with the quark-gluon plasma. No significant modification between different centrality classes and with respect to pp results is observed in the extracted quark- and gluon-like jet fractions.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Precise measurements of branching fractions for $ {\mathrm{D}}_{\mathrm{s}}^{+} $ meson decays to two pseudoscalar mesons

We measure the branching fractions for seven $D$$^{+}_{s}$ two-body decays to pseudo-scalar mesons, by analyzing data collected at √s = 4.178 ~ 4.226 GeV with the BESIII detector at the BEPCII collider. The branching fractions are determined to be $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({D}_s^{+}\to {K}^{+}\eta \hbox{'}\right)=\left(2.68\pm 0.17\pm 0.17\pm 0.08\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to \eta \hbox{'}{\pi}^{+}\right)=\left(37.8\pm 0.4\pm 2.1\pm 1.2\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}\eta \right)=\left(1.62\pm 0.10\pm 0.03\pm 0.05\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to \eta {\pi}^{+}\right)=\left(17.41\pm 0.18\pm 0.27\pm 0.54\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}{K}_S^0\right)=\left(15.02\pm 0.10\pm 0.27\pm 0.47\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}_S^0{\pi}^{+}\right)=\left(1.109\pm 0.034\pm 0.023\pm 0.035\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}{\pi}^0\right)=\left(0.748\pm 0.049\pm 0.018\pm 0.035\right)\times {10}^{-3},\end{array}} $$ B D s + → K + η ' = 2.68 ± 0.17 ± 0.17 ± 0.08 × 10 - 3 , B D s + → η ' π + = 37.8 ± 0.4 ± 2.1 ± 1.2 × 10 - 3 , B D s + → K + η = 1.62 ± 0.10 ± 0.03 ± 0.05 × 10 - 3 , B D s + → η π + = 17.41 ± 0.18 ± 0.27 ± 0.54 × 10 - 3 , B D s + → K + K S 0 = 15.02 ± 0.10 ± 0.27 ± 0.47 × 10 - 3 , B D s + → K S 0 π + = 1.109 ± 0.034 ± 0.023 ± 0.035 × 10 - 3 , B D s + → K + π 0 = 0.748 ± 0.049 ± 0.018 ± 0.035 × 10 - 3 , where the first uncertainties are statistical, the second are systematic, and the third are from external input branching fraction of the normalization mode $ {D}_s^{+} $ D s + → K + K - π + . Precision of our measurements is significantly improved compared with that of the current world average values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗