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Using an 𝑒+𝑒− collision data sample of 2.93 fb−1 collected at a center-of-mass energy of 3.773 GeV by the BESIII detector at BEPCII, we report the observation of 𝐷0→𝑎0(980)−𝑒+𝜈𝑒 and evidence for 𝐷+→𝑎0(980)0𝑒+𝜈𝑒 with significances of 6.4𝜎 and 2.9𝜎, respectively. The absolute branching fractions are determined to be ℬ(𝐷0→𝑎0(980)−𝑒+𝜈𝑒)×ℬ(𝑎0(980)−→𝜂𝜋−) = [1.33+0.33−0.29(stat)±0.09(syst)]×10−4 and ℬ(𝐷+→𝑎0(980)0𝑒+𝜈𝑒)×ℬ(𝑎0(980)0→𝜂𝜋0)=[1.66+0.81
−0.66(stat)±0.11(syst)]×10−4. This is the first time the 𝑎0(980) meson has been measured in a 𝐷0 semileptonic decay, which would open one more interesting page in the investigation of the nature of the puzzling 𝑎0(980) states.
The processes 𝑒+𝑒−→𝐷+ 𝑠𝐷𝑠1(2460)−+c.c. and 𝑒+𝑒−→𝐷*+ 𝑠𝐷𝑠1(2460)−+c.c. are studied for the first time using data samples collected with the BESIII detector at the BEPCII collider. The Born cross sections of 𝑒+𝑒−→𝐷+ 𝑠𝐷𝑠1(2460)−+c.c. at nine center-of-mass energies between 4.467 GeV and 4.600 GeV and those of 𝑒+𝑒−→𝐷*+ 𝑠𝐷𝑠1(2460)−+c.c. at √𝑠=4.590 GeV and 4.600 GeV are measured. No obvious charmonium or charmoniumlike structure is seen in the measured cross sections.
We report an amplitude analysis and branching fraction measurement of D+s→K+K−π+ decay using a data sample of 3.19 fb−1 recorded with BESIII detector at a center-of-mass energy of 4.178 GeV.
We perform a model-independent partial wave analysis in the low K+K− mass region to determine the K+K− S-wave lineshape, followed by an amplitude analysis of our very pure high-statistics sample.
The amplitude analysis provides an accurate determination of the detection efficiency allowing us to measure the branching fraction B(D+s→K+K−π+)=(5.47±0.08stat±0.13sys)%.
The cross section of the process e+e−→K+K− is measured at a number of center-of-mass energies s√ from 2.00 to 3.08 GeV with the BESIII detector at the Beijing Electron Positron Collider (BEPCII). The results provide the best precision achieved so far. A resonant structure around 2.2 GeV is observed in the cross section line shape. A Breit-Wigner fit yields a mass of M=2239.2±7.1±11.3~and a width of Γ=139.8±12.3±20.6 MeV, where the first uncertainties are statistical and the second ones are systematic. In addition, the time-like electromagnetic form factor of the kaon is determined at the individual center-of-mass energy points.
Search for the reaction channel e⁺e⁻ → ηcηπ⁺π⁻ at center-of-mass energies from 4.23 to 4.60 GeV
(2021)
Using data collected with the BESIII detector operating at the Beijing Electron Positron Collider, we search for the process 𝑒+𝑒−→𝜂𝑐𝜂𝜋+𝜋−. The search is performed using five large datasets recorded at center-of-mass energies of 4.23, 4.26, 4.36, 4.42, and 4.60 GeV. The 𝜂𝑐 meson is reconstructed in 16 exclusive decay modes. No signal is observed in the 𝜂𝑐 mass region at any center-of-mass energy. The upper limits on the reaction cross sections are determined to be 6.2, 10.8, 27.6, 22.6 and 23.7 pb at the 90% confidence level at the center-of-mass energies listed above.
Using a sample of 106 million 𝜓(3686) decays, 𝜓(3686)→𝛾𝜒𝑐𝐽(𝐽=0,1,2) and 𝜓(3686)→𝛾𝜒𝑐𝐽,𝜒𝑐𝐽→𝛾𝐽/𝜓(𝐽=1,2) events are utilized to study inclusive 𝜒𝑐𝐽→anything, 𝜒𝑐𝐽→hadrons, and 𝐽/𝜓→anything distributions, including distributions of the number of charged tracks, electromagnetic calorimeter showers, and 𝜋0s, and to compare them with distributions obtained from the BESIII Monte Carlo simulation. Information from each Monte Carlo simulated decay event is used to construct matrices connecting the detected distributions to the input predetection “produced” distributions. Assuming these matrices also apply to data, they are used to predict the analogous produced distributions of the decay events. Using these, the charged particle multiplicities are compared with results from MARK I. Further, comparison of the distributions of the number of photons in data with those in Monte Carlo simulation indicates that G-parity conservation should be taken into consideration in the simulation.
The process 𝑒+𝑒−→𝜙𝜂′ has been studied for the first time in detail using data sample collected with the BESIII detector at the BEPCII collider at center of mass energies from 2.05 to 3.08 GeV. A resonance with quantum numbers 𝐽𝑃𝐶=1−− is observed with mass 𝑀=(2177.5±4.8(stat)±19.5(syst))MeV/𝑐2 and width Γ=(149.0±15.6(stat)±8.9(syst)) MeV with a statistical significance larger than 10𝜎, including systematic uncertainties. If the observed structure is identified with the 𝜙(2170), then the ratio of partial width between the 𝜙𝜂′ by BESIII and 𝜙𝜂 by BABAR is (ℬ𝑅𝜙𝜂Γ𝑅𝑒𝑒)/(ℬ𝑅𝜙𝜂′Γ𝑅𝑒𝑒)=0.23±0.10(stat)±0.18(syst), which is smaller than the prediction of the 𝑠¯𝑠𝑔 hybrid models by several orders of magnitude.
Using a 3.19 fb−1 data sample collected at an 𝑒+𝑒− center-of-mass energy of 𝐸cm=4.178 GeV with the BESIII detector, we measure the branching fraction of the leptonic decay 𝐷+𝑠→𝜇+𝜈𝜇 to be ℬ𝐷+𝑠→𝜇+𝜈𝜇=(5.49±0.16stat±0.15syst)×10−3. Combining our branching fraction with the masses of the 𝐷+𝑠 and 𝜇+ and the lifetime of the 𝐷+𝑠, we determine 𝑓𝐷+𝑠|𝑉𝑐𝑠|=246.2±3.6stat±3.5syst MeV. Using the 𝑐→𝑠 quark mixing matrix element |𝑉𝑐𝑠| determined from a global standard model fit, we evaluate the 𝐷+𝑠 decay constant 𝑓𝐷+𝑠=252.9±3.7stat±3.6syst MeV. Alternatively, using the value of 𝑓𝐷+𝑠 calculated by lattice quantum chromodynamics, we find |𝑉𝑐𝑠|=0.985±0.014stat±0.014syst. These values of ℬ𝐷+𝑠→𝜇+𝜈𝜇, 𝑓𝐷+𝑠|𝑉𝑐𝑠|, 𝑓𝐷+𝑠 and |𝑉𝑐𝑠| are each the most precise results to date.
We report an amplitude analysis and branching fraction measurement of D+s→K+K−π+ decay using a data sample of 3.19 fb−1 recorded with BESIII detector at a center-of-mass energy of 4.178 GeV.
We perform a model-independent partial wave analysis in the low K+K− mass region to determine the K+K− S-wave lineshape,
followed by an amplitude analysis of our very pure high-statistics sample.
The amplitude analysis provides an accurate determination of the detection efficiency allowing us to measure the branching fraction B(D+s→K+K−π+)=(5.47±0.08stat±0.13sys)%.
The Born cross sections for the process e+e−→η′π+π− at different center-of-mass energies between 2.00 and 3.08~GeV are reported with improved precision from an analysis of data samples collected with the BESIII detector operating at the BEPCII storage ring. An obvious structure is observed in the Born cross section line shape. Fit as a Breit-Wigner resonance, it has a statistical significance of 6.3σ and a mass and width of M=(2108±46±25)~MeV/c2 and Γ=(138±36±30)~MeV, where the uncertainties are statistical and systematic, respectively. These measured resonance parameters agree with the measurements of BABAR in e+e−→η′π+π− and BESIII in e+e−→ωπ0 within two standard deviations.
Using a data sample of 448.1×106 𝜓(3686) events collected at √𝑠=3.686 GeV with the BESIII detector at the Beijing Electron-Positron Collider II, we search for the rare decay 𝐽/𝜓→𝜙𝑒+𝑒− via 𝜓(3686)→𝜋+𝜋−𝐽/𝜓. No signal events are observed and the upper limit on the branching fraction is set to be ℬ(𝐽/𝜓→𝜙𝑒+𝑒−)<1.2×10−7 at the 90% confidence level, which is still about one order of magnitude higher than the Standard Model prediction.
By analyzing a data sample corresponding to an integrated luminosity of 2.93 fb−1 collected at a center-of-mass energy of 3.773 GeV with By analyzing a data sample corresponding to an integrated luminosity of 2.93 fb−1 collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we measure for the first time the absolute branching fraction of the 𝐷+→𝜂𝜇+𝜈𝜇 decay to be ℬ𝐷+→𝜂𝜇+𝜈𝜇=(10.4±1.0stat±0.5syst)×10−4. Using the world averaged value of ℬ𝐷+→𝜂𝑒+𝜈𝑒, the ratio of the two branching fractions is determined to be ℬ𝐷+→𝜂𝜇+𝜈𝜇/ℬ𝐷+→𝜂𝑒+𝜈𝑒=0.91±0.13(stat+syst), which agrees with the theoretical expectation of lepton flavor universality within uncertainty. By studying the differential decay rates in five four-momentum transfer intervals, we obtain the product of the hadronic form factor 𝑓𝜂+(0) and the 𝑐→𝑑 Cabibbo-Kobayashi-Maskawa matrix element |𝑉𝑐𝑑| to be 𝑓𝜂+(0)|𝑉𝑐𝑑|=0.087±0.008stat±0.002syst. Taking the input of |𝑉𝑐𝑑| from the global fit in the standard model, we determine 𝑓𝜂+(0)=0.39±0.04stat±0.01syst. On the other hand, using the value of 𝑓𝜂+(0) calculated in theory, we find |𝑉𝑐𝑑| = 0.242±0.022stat±0.006syst±0.033theory.
Using 2.93 fb−1 of 𝑒+𝑒− collision data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, the first observation of the doubly Cabibbo-suppressed decay 𝐷+→𝐾+𝜋+𝜋−𝜋0 is reported. After removing decays that contain narrow intermediate resonances, including 𝐷+→𝐾+𝜂, 𝐷+→𝐾+𝜔, and 𝐷+→𝐾+𝜙, the branching fraction of the decay 𝐷+→𝐾+𝜋+𝜋−𝜋0 is measured to be (1.13±0.08stat±0.03syst)×10−3. The ratio of branching fractions of 𝐷+→𝐾+𝜋+𝜋−𝜋0 over 𝐷+→𝐾−𝜋+𝜋+𝜋0 is found to be (1.81±0.15)%, which corresponds to (6.28±0.52)tan4𝜃𝐶, where 𝜃𝐶 is the Cabibbo mixing angle. This ratio is significantly larger than the corresponding ratios for other doubly Cabibbo-suppressed decays. The asymmetry of the branching fractions of charge-conjugated decays 𝐷±→𝐾±𝜋±𝜋∓𝜋0 is also determined, and no evidence for 𝐶𝑃 violation is found. In addition, the first evidence for the 𝐷+→𝐾+𝜔 decay, with a statistical significance of 3.3𝜎, is presented and the branching fraction is measured to be ℬ(𝐷+→𝐾+𝜔) = (5.7+2.5−2.1stat±0.2syst)×10−5.
he process e+e−→pK0Sn¯K−+c.c. and its intermediate processes are studied for the first time, using data samples collected with the BESIII detector at BEPCII at center-of-mass energies of 3.773, 4.008, 4.226, 4.258, 4.358, 4.416, and 4.600 GeV, with a total integrated luminosity of 7.4 fb−1. The Born cross section of e+e−→pK0Sn¯K−+c.c. is measured at each center-of-mass energy, but no significant resonant structure in the measured cross-section line shape between 3.773 and 4.600 GeV is observed. No evident structure is detected in the pK−, nK0S, pK0S, nK+, pn¯, or K0SK− invariant mass distributions except for Λ(1520). The Born cross sections of e+e−→Λ(1520)n¯K0S+c.c. and e+e−→Λ(1520)p¯K++c.c. are measured, and the 90\% confidence level upper limits on the Born cross sections of e+e−→Λ(1520)Λ¯(1520) are determined at the seven center-of-mass energies.
We report an amplitude analysis and branching fraction measurement of 𝐷+
𝑠→𝐾+𝐾−𝜋+ decay using a data sample of 3.19 fb−1 recorded with BESIII detector at a center-of-mass energy of 4.178 GeV. We perform a model-independent partial wave analysis in the low 𝐾+𝐾− mass region to determine the 𝐾+𝐾− S-wave line shape, followed by an amplitude analysis of our very pure high-statistics sample. With the detection efficiency based on the amplitude analysis results, the absolute branching fraction is measured to be ℬ(𝐷+𝑠→𝐾+𝐾−𝜋+)=(5.47±0.08stat±0.13sys)%.
Using a sample of 1.31×109 𝐽/𝜓 events collected with the BESIII detector, we perform a study of 𝐽/𝜓→𝛾𝜂𝜂𝜂′ to search for the 𝑋(2370) and 𝜂𝑐 in the 𝜂𝜂𝜂′ invariant mass distribution. No significant signal for the 𝑋(2370) is observed, and we set an upper limit for the product branching fraction of ℬ(𝐽/𝜓→𝛾𝑋(2370)·ℬ(𝑋(2370)→𝜂𝜂𝜂′)<9.2×10−6 at the 90% confidence level. A clear 𝜂𝑐 signal is observed for the first time, yielding a product branching fraction of ℬ(𝐽/𝜓→𝛾𝜂𝑐)·ℬ(𝜂𝑐→𝜂𝜂𝜂′)=(4.86±0.62(stat)±0.45(sys))×10−5.
Observation of η′ → π⁺π⁻μ⁺μ⁻
(2021)
Using (1310.6±7.0)×106 𝐽/𝜓 events acquired with the BESIII detector at the BEPCII storage rings, the decay 𝜂′→𝜋+𝜋−𝜇+𝜇− is observed for the first time with a significance of 8𝜎 via the process 𝐽/𝜓→𝛾𝜂′. We measure the branching fraction of 𝜂′→𝜋+𝜋−𝜇+𝜇− to be ℬ(𝜂′→𝜋+𝜋−𝜇+𝜇−)=(1.97±0.33(stat)±0.19(syst))×10−5, where the first and second uncertainties are statistical and systematic, respectively
Measurement of cross sections for e⁺e⁻ → μ⁺μ⁻ at center-of-mass energies from 3.80 to 4.60 GeV
(2020)
The observed cross sections for 𝑒+𝑒−→𝜇+𝜇− at energies from 3.8 to 4.6 GeV are measured using data samples taken with the BESIII detector operated at the BEPCII collider. We measure the muonic widths and determine the branching fractions of the charmonium states 𝜓(4040), 𝜓(4160), and 𝜓(4415) decaying to 𝜇+𝜇−, as well as making a first determination of the phase of the amplitudes. In addition, we observe evidence for a structure in the dimuon cross section near 4.220 GeV/𝑐2, which we denote as 𝑆(4220). Analyzing a coherent sum of amplitudes yields eight solutions, one of which gives a mass of 𝑀𝑆(4220) = 4216.7±8.9±4.1 MeV/𝑐2, a total width of Γtot S(4220) = 47.2±22.8±10.5 MeV, and a muonic width of Γ𝜇𝜇 𝑆(4220) = 1.53±1.26±0.54 keV, where the first uncertainties are statistical and the second systematic. The eight solutions give the central values of the mass, total width, muonic width to be, respectively, in the range from 4212.8 to 4219.4 MeV/𝑐2, from 36.4 to 49.6 MeV, and from 1.09 to 1.53 keV. The statistical significance of the 𝑆(4220) signal is 3.9𝜎. Correcting the total dimuon cross section for radiative effects yields a statistical significance for this structure of 8.1𝜎.
An amplitude analysis of the 𝐾𝑆𝐾𝑆 system produced in radiative 𝐽/𝜓 decays is performed using the (1310.6±7.0)×106 𝐽/𝜓 decays collected by the BESIII detector. Two approaches are presented. A mass-dependent analysis is performed by parametrizing the 𝐾𝑆𝐾𝑆 invariant mass spectrum as a sum of Breit-Wigner line shapes. Additionally, a mass-independent analysis is performed to extract a piecewise function that describes the dynamics of the 𝐾𝑆𝐾𝑆 system while making minimal assumptions about the properties and number of poles in the amplitude. The dominant amplitudes in the mass-dependent analysis include the 𝑓0(1710), 𝑓0(2200), and 𝑓′2(1525). The mass-independent results, which are made available as input for further studies, are consistent with those of the mass-dependent analysis and are useful for a systematic study of hadronic interactions. The branching fraction of radiative 𝐽/𝜓 decays to 𝐾𝑆𝐾𝑆 is measured to be (8.1±0.4)×10−4, where the uncertainty is systematic and the statistical uncertainty is negligible.
Observation of a near-threshold structure in the K⁺ recoil-mass spectra in e⁺e⁻ → K⁺(Dₛ⁻D*⁰+Dₛ*⁻D⁰)
(2021)
We report a study of the processes of 𝑒+𝑒−→𝐾+𝐷−𝑠𝐷*0 and 𝐾+𝐷*−𝑠𝐷0 based on 𝑒+𝑒− annihilation samples collected with the BESIII detector operating at BEPCII at five center-of-mass energies ranging from 4.628 to 4.698 GeV with a total integrated luminosity of 3.7 fb−1. An excess of events over the known contributions of the conventional charmed mesons is observed near the 𝐷−𝑠𝐷*0 and 𝐷*−𝑠𝐷0 mass thresholds in the 𝐾+ recoil-mass spectrum for events collected at √𝑠=4.681 GeV. The structure matches a mass-dependent-width Breit-Wigner line shape, whose pole mass and width are determined as (3982.5+1.8
−2.6±2.1) MeV/𝑐2 and (12.8+5.3−4.4±3.0) MeV, respectively. The first uncertainties are statistical and the second are systematic. The significance of the resonance hypothesis is estimated to be 5.3 𝜎 over the contributions only from the conventional charmed mesons. This is the first candidate for a charged hidden-charm tetraquark with strangeness, decaying into 𝐷−𝑠𝐷*0 and 𝐷*−𝑠𝐷0. However, the properties of the excess need further exploration with more statistics.
We report new measurements of the cross sections for the production of Dbar D final states at the ψ(3770) resonance. Our data sample consists of an integrated luminosity of 2.93 fb−1 of e+e− annihilation data produced by the BEPCII collider and collected and analyzed with the BESIII detector. We exclusively reconstruct three D0 and six D+ hadronic decay modes and use the ratio of the yield of fully reconstructed Dbar D events ("double tags") to the yield of all reconstructed D or bar D mesons ("single tags") to determine the number of D0bar D0 and D+D− events, benefiting from the cancellation of many systematic uncertainties. Combining these yields with an independent determination of the integrated luminosity of the data sample, we find the cross sections to be σ(e+e− → D0bar D0) nb and σ(e+e− → D+D−) = (2.830 ± 0.011 ± 0.026) nb, where the uncertainties are statistical and systematic, respectively.
Using 10.1 × 109 J/ψ events produced by the Beijing Electron Positron Collider (BEPCII) at a center-of-mass energy √s = 3.097 GeV and collected with the BESIII detector, we present a search for the rare semi-leptonic decay J/ψ → D−e+νe + c.c. No excess of signal above background is observed, and an upper limit on the branching fraction B(J/ψ → D−e +νe + c.c.) < 7.1 × 10−8 is obtained at 90% confidence level. This is an improvement of more than two orders of magnitude over the previous best limit.
We study the hadronic decays of Λ+c to the final states Σ+η and Σ+η′, using an e+e− annihilation data sample of 567 pb−1 taken at a center-of-mass energy of 4.6 GeV with the BESIII detector at the BEPCII collider. We find evidence for the decays Λ+c→Σ+η and Σ+η′ with statistical significance of 2.5σ and 3.2σ, respectively. Normalizing to the reference decays Λ+c→Σ+π0 and Σ+ω, we obtain the ratios of the branching fractions B(Λ+c→Σ+η)B(Λ+c→Σ+π0) and B(Λ+c→Σ+η′)B(Λ+c→Σ+ω) to be 0.35±0.16±0.03 and 0.86±0.34±0.07, respectively. The upper limits at the 90\% confidence level are set to be B(Λ+c→Σ+η)B(Λ+c→Σ+π0)<0.58 and B(Λ+c→Σ+η′)B(Λ+c→Σ+ω)<1.2. Using BESIII measurements of the branching fractions of the reference decays, we determine B(Λ+c→Σ+η)=(0.41±0.19±0.05)% (<0.68%) and B(Λ+c→Σ+η′)=(1.34±0.53±0.21)% (<1.9%). Here, the first uncertainties are statistical and the second systematic. The obtained branching fraction of Λ+c→Σ+η is consistent with the previous measurement, and the branching fraction of Λ+c→Σ+η′ is measured for the first time.
We study the electromagnetic Dalitz decay 𝐽/𝜓→𝑒+𝑒−𝜂 and search for dielectron decays of a dark gauge boson (𝛾′) in 𝐽/𝜓→𝛾′𝜂 with the two 𝜂 decay modes 𝜂→𝛾𝛾 and 𝜂→𝜋+𝜋−𝜋0 using (1310.6±7.0)×106 𝐽/𝜓 events collected with the BESIII detector. The branching fraction of 𝐽/𝜓→𝑒+𝑒−𝜂 is measured to be (1.43±0.04(stat)±0.06(syst))×10−5, with a precision that is improved by a factor of 1.5 over the previous BESIII measurement. The corresponding dielectron invariant mass dependent modulus square of the transition form factor is explored for the first time, and the pole mass is determined to be Λ=2.84±0.11(stat)±0.08(syst) GeV/𝑐2. We find no evidence of 𝛾′ production and set 90% confidence level upper limits on the product branching fraction ℬ(𝐽/𝜓→𝛾′𝜂)×ℬ(𝛾′→𝑒+𝑒−) as well as the kinetic mixing strength between the standard model photon and 𝛾′ in the mass range of 0.01≤𝑚𝛾′≤2.4 GeV/𝑐2.
The Born cross sections for the process e+e−→η′π+π− at different center-of-mass energies between 2.00 and 3.08 GeV are reported with improved precision from an analysis of data samples collected with the BESIII detector operating at the BEPCII storage ring. An obvious structure is observed in the Born cross section line shape. Fit as a Breit-Wigner resonance, it has a statistical significance of 6.3σ and a mass and width of M=(2111±43±25)~MeV/c2 and Γ=(135±34±30)~MeV, where the uncertainties are statistical and systematic, respectively. These measured resonance parameters agree with the measurements of BABAR in e+e−→η′π+π− and BESIII in e+e−→ωπ0 within two standard deviations.
The rare decay 𝜂′→𝜋+𝜋−𝑒+𝑒− is studied using a sample of 1.3×109 𝐽/𝜓 events collected with the BESIII detector at BEPCII in 2009 and 2012. The branching fraction is measured with improved precision to be (2.42±0.05stat±0.08syst)×10−3. Due to the inclusion of new data, this result supersedes the last BESIII result on this branching fraction. In addition, the 𝐶𝑃-violating asymmetry in the angle between the decay planes of the 𝜋+𝜋−-pair and the 𝑒+𝑒−-pair is investigated. A measurable value would indicate physics beyond the standard model; the result is 𝒜𝐶𝑃=(2.9±3.7stat±1.1syst)%, which is consistent with the standard model expectation of no 𝐶𝑃-violation. The precision is comparable to the asymmetry measurement in the 𝐾0𝐿→𝜋+𝜋−𝑒+𝑒− decay where the observed (14±2)% effect is driven by a standard model mechanism.
Using a sample of 4.48×108 ψ(3686) events collected with the BESIII detector at the BEPCII collider, we study the two-photon decays of the pseudoscalar mesons π0, η, η′, η(1405), η(1475), η(1760), and X(1835) in J/ψ radiative decays using ψ(3686)→π+π−J/ψ events. The π0, η and η′ mesons are clearly observed in the two-photon mass spectra, and the branching fractions are determined to be B(J/ψ→γπ0→3γ)=(3.57±0.12±0.16)×10−5, B(J/ψ→γη→3γ)=(4.42±0.04±0.18)×10−4, and B(J/ψ→γη′→3γ)=(1.26±0.02±0.05)×10−4, where the first errors are statistical and the second systematic. No clear signal for η(1405), η(1475), η(1760) or X(1835) is observed in the two-photon mass spectra, and upper limits at the 90% confidence level on the product branching fractions are obtained.
Using a data sample of 448.1×106 ψ(3686) events collected at s√= 3.686 GeV with the BESIII detector at the BEPCII, we search for the rare decay J/ψ→ϕe+e− via ψ(3686)→π+π−J/ψ. No signal events are observed and the upper limit on the branching fraction is set to be B(J/ψ→ϕe+e−)<1.2×10−7 at the 90\% confidence level, which is still about one order of magnitude higher than the Standard Model prediction.
We report an amplitude analysis and branching fraction measurement of D+s→K+K−π+ decay using a data sample of 3.19 fb−1 recorded with BESIII detector at a center-of-mass energy of 4.178 GeV.
We perform a model-independent partial wave analysis in the low K+K− mass region to determine the K+K− S-wave lineshape, followed by an amplitude analysis of our very pure high-statistics sample.
The amplitude analysis provides an accurate determination of the detection efficiency allowing us to measure the branching fraction B(D+s→K+K−π+)=(5.47±0.08stat±0.13sys)%.
We report a study of the processes of e+e−→K+(D−sD∗0+D∗−sD0) based on e+e− annihilation samples collected with the BESIII detector operating at BEPCII at five center-of-mass energies ranging from 4.628 to 4.698 GeV with a total integrated luminosity of 3.7 fb−1. An excess over the known contributions of the conventional charmed mesons is observed near the D−sD∗0 and D∗−sD0 mass thresholds in the K+ recoil-mass spectrum for events collected at s√=4.681 GeV. The structure matches a mass-dependent-width Breit-Wigner line shape, whose pole mass and width are determined as (3982.5+1.8−2.6±2.1) MeV/c2 and (12.8+5.3−4.4±3.0) MeV, respectively. The first uncertainties are statistical and the second are systematic. The significance of the resonance hypothesis is estimated to be 5.3 σ over the contributions only from the conventional charmed mesons. This is the first candidate of the charged hidden-charm tetraquark with strangeness, decaying into D−sD∗0 and D∗−sD0. However, the properties of the excess need further exploration with more statistics.
We report on new measurements of Cabibbo-suppressed semileptonic D+s decays using 3.19 fb−1 of e+e− annihilation data sample collected at a center-of-mass energy of 4.178~GeV with the BESIII detector at the BEPCII collider. Our results include branching fractions B(D+s→K0e+νe)=(3.25±0.38(stat.)±0.16(syst.))×10−3 and B(D+s→K∗0e+νe)=(2.37±0.26(stat.)±0.20(syst.))×10−3 which are much improved relative to previous measurements, and the first measurements of the hadronic form-factor parameters for these decays. For D+s→K0e+νe, we obtain f+(0)=0.720±0.084(stat.)±0.013(syst.), and for D+s→K∗0e+νe, we find form-factor ratios rV=V(0)/A1(0)=1.67±0.34(stat.)±0.16(syst.) and r2=A2(0)/A1(0)=0.77±0.28(stat.)±0.07(syst.).
Using a data sample with an integrated luminosity of 2.93 fb−1 taken at the center-of-mass energy of 3.773 GeV, we search for the Majorana neutrino (𝜈𝑚) in the lepton number violating decays 𝐷→𝐾𝜋𝑒+𝑒+. No significant signal is observed, and the upper limits on the branching fraction at the 90% confidence level are set to be ℬ(𝐷0→𝐾−𝜋−𝑒+𝑒+)<2.8×10−6, ℬ(𝐷+→𝐾0𝑆𝜋−𝑒+𝑒+)<3.3×10−6 and ℬ(𝐷+→𝐾−𝜋0𝑒+𝑒+)<8.5×10−6. The Majorana neutrino is searched for with different mass assumptions ranging from 0.25 to 1.0 GeV/𝑐2 in the decays 𝐷0→𝐾−𝑒+𝜈𝑚,𝜈𝑚→𝜋−𝑒+ and 𝐷+→𝐾0𝑆𝑒+𝜈𝑚,𝜈𝑚→𝜋−𝑒+, and the upper limits on the branching fraction at the 90% confidence level are at the level of 10−7∼10−6, depending on the mass of the Majorana neutrino. The constraints on the mixing matrix element |𝑉𝑒𝜈𝑚|2 are also evaluated.
Using a low background data sample of 9.7×105 𝐽/𝜓→𝛾𝜂′, 𝜂′→𝛾𝜋+𝜋− events, which are 2 orders of magnitude larger than those from the previous experiments, recorded with the BESIII detector at BEPCII, the decay dynamics of 𝜂′→𝛾𝜋+𝜋− are studied with both model-dependent and model-independent approaches. The contributions of 𝜔 and the 𝜌(770)−𝜔 interference are observed for the first time in the decays 𝜂′→𝛾𝜋+𝜋− in both approaches. Additionally, a contribution from the box anomaly or the 𝜌(1450) resonance is required in the model-dependent approach, while the process specific part of the decay amplitude is determined in the model-independent approach.
he Born cross sections for the process 𝑒+𝑒−→𝜂′𝜋+𝜋− at different center-of-mass energies between 2.00 and 3.08 GeV are reported with improved precision from an analysis of data samples collected with the BESIII detector operating at the BEPCII storage ring. An obvious structure is observed in the Born cross section line shape. Fit as a Breit-Wigner resonance, it has a statistical significance of 6.3𝜎 and a mass and width of 𝑀=(2111±43±25) MeV/𝑐2 and Γ=(135±34±30) MeV, where the uncertainties are statistical and systematic, respectively. These measured resonance parameters agree with the measurements of BABAR in 𝑒+𝑒−→𝜂′𝜋+𝜋− and BESIII in 𝑒+𝑒−→𝜔𝜋0 within two standard deviations.
We report the first observation of the semimuonic decay 𝐷+→𝜔𝜇+𝜈𝜇 using an 𝑒+𝑒− collision data sample corresponding to an integrated luminosity of 2.93 fb−1 collected with the BESIII detector at a center-of-mass energy of 3.773 GeV. The absolute branching fraction of the 𝐷+→𝜔𝜇+𝜈𝜇 decay is measured to be ℬ𝐷+→𝜔𝜇+𝜈𝜇=(17.7±1.8stat±1.1syst)×10−4. Its ratio with the world average value of the branching fraction of the 𝐷+→𝜔𝑒+𝜈𝑒 decay probes lepton flavor universality and it is determined to be ℬ𝐷+→𝜔𝜇+𝜈𝜇/ℬPDG 𝐷+→𝜔𝑒+𝜈𝑒=1.05±0.14, in agreement with the standard model expectation within one standard deviation.
A partial-wave analysis of the decay 𝐽/𝜓→𝐾+𝐾−𝜋0 has been made using (223.7±1.4)×106 𝐽/𝜓 events collected with the BESIII detector in 2009. The analysis, which is performed within the isobar-model approach, reveals contributions from 𝐾*2(1430)±, 𝐾*2(1980)± and 𝐾*4(2045)± decaying to 𝐾±𝜋0. The two latter states are observed in 𝐽/𝜓 decays for the first time. Two resonance signals decaying to 𝐾+𝐾− are also observed. These contributions cannot be reliably identified and their possible interpretations are discussed. The measured branching fraction 𝐵(𝐽/𝜓→𝐾+𝐾−𝜋0) of (2.88±0.01±0.12)×10−3 is more precise than previous results. Branching fractions for the reported contributions are presented as well. The results of the partial-wave analysis differ significantly from those previously obtained by BESII and BABAR.
Cross sections of the process 𝑒+𝑒−→𝜋0𝜋0𝐽/𝜓 at center-of-mass energies between 3.808 and 4.600 GeV are measured with high precision by using 12.4 fb−1 of data samples collected with the BESIII detector operating at the BEPCII collider facility. A fit to the measured energy-dependent cross sections confirms the existence of the charmoniumlike state 𝑌(4220). The mass and width of the 𝑌(4220) are determined to be (4220.4±2.4±2.3) MeV/𝑐2 and (46.2±4.7±2.1) MeV, respectively, where the first uncertainties are statistical and the second systematic. The mass and width are consistent with those measured in the process 𝑒+𝑒−→𝜋+𝜋−𝐽/𝜓. The neutral charmonium-like state 𝑍𝑐(3900)0 is observed prominently in the 𝜋0𝐽/𝜓 invariant-mass spectrum, and, for the first time, an amplitude analysis is performed to study its properties. The spin-parity of 𝑍𝑐(3900)0 is determined to be 𝐽𝑃=1+, and the pole position is (3893.1±2.2±3.0)−𝑖(22.2±2.6±7.0) MeV/𝑐2, which is consistent with previous studies of electrically charged 𝑍𝑐(3900)±. In addition, cross sections of 𝑒+𝑒− → 𝜋0𝑍𝑐(3900)0 → 𝜋0𝜋0𝐽/𝜓 are extracted, and the corresponding line shape is found to agree with that of the 𝑌(4220).
Based on an 𝑒+𝑒− collision data sample corresponding to an integrated luminosity of 567 pb−1 taken at the center-of-mass energy of √𝑠=4.6 GeV with the BESIII detector, we measure the absolute branching fraction of the inclusive decay Λ+𝑐→Λ+𝑋 to be ℬ(Λ+𝑐→Λ+𝑋)=(38.2+2.8−2.2±0.9)% using the double-tag method, where 𝑋 refers to any possible final state particles. In addition, we search for direct 𝐶𝑃 violation in the charge asymmetry of this inclusive decay for the first time, and obtain 𝒜𝐶𝑃≡[ℬ(Λ+𝑐→Λ+𝑋)−ℬ(¯Λ−𝑐 → ¯Λ+𝑋)]/[ℬ(Λ+𝑐→Λ+𝑋)+ℬ(¯Λ−𝑐 → ¯Λ+𝑋)]=(2.1+7.0−6.6±1.6)%, a statistically limited result with no evidence of 𝐶𝑃 violation.
The decay 𝐽/𝜓→𝛾𝛾𝜙 is studied using a sample of 1.31×109 𝐽/𝜓 events collected with the BESIII detector. Two structures around 1475 MeV/𝑐2 and 1835 MeV/𝑐2 are observed in the 𝛾𝜙 invariant mass spectrum for the first time. With a fit on the 𝛾𝜙 invariant mass, which takes into account the interference between the two structures, and a simple analysis of the angular distribution, the structure around 1475 MeV/𝑐2 is found to favor an assignment as the 𝜂(1475) and the mass and width for the structure around 1835 MeV/𝑐2 are consistent with the 𝑋(1835). The statistical significances of the two structures are 13.5𝜎 and 6.3𝜎, respectively. The results indicate that both 𝜂(1475) and 𝑋(1835) contain a sizeable 𝑠¯𝑠 component.
The Born cross sections for the process e+e−→η′π+π− at different center-of-mass energies between 2.00 and 3.08~GeV are reported with improved precision from an analysis of data samples collected with the BESIII detector operating at the BEPCII storage ring. An obvious structure is observed in the Born cross section line shape. Fit as a Breit-Wigner resonance, it has a statistical significance of 6.3σ and a mass and width of M=(2108±46±25)~MeV/c2 and Γ=(138±36±30)~MeV, where the uncertainties are statistical and systematic, respectively. These measured resonance parameters agree with the measurements of BABAR in e+e−→η′π+π− and BESIII in e+e−→ωπ0 within two standard deviations.
We report an amplitude analysis and branching fraction measurement of D+s→K+K−π+ decay using a data sample of 3.19 fb−1 recorded with BESIII detector at a center-of-mass energy of 4.178 GeV.
We perform a model-independent partial wave analysis in the low K+K− mass region to determine the K+K− S-wave lineshape, followed by an amplitude analysis of our very pure high-statistics sample.
The amplitude analysis provides an accurate determination of the detection efficiency allowing us to measure the branching fraction B(D+s→K+K−π+)=(5.47±0.08stat±0.13sys)%.
Using a data sample of 𝑒+𝑒− collisions corresponding to an integrated luminosity of 567 pb−1 collected at a center-of-mass energy of √𝑠=4.6 GeV with the BESIII detector, we measure the absolute branching fraction of the inclusive semileptonic Λ+𝑐 decay with a double-tag method. We obtain ℬ(Λ+𝑐→𝑋𝑒+𝜈𝑒)=(3.95±0.34±0.09)%, where the first uncertainty is statistical and the second systematic. Using the known Λ+𝑐 lifetime and the charge-averaged semileptonic decay width of nonstrange charmed mesons (𝐷0 and 𝐷+), we obtain the ratio of the inclusive semileptonic decay widths Γ(Λ+𝑐→𝑋𝑒+𝜈𝑒)/¯Γ(𝐷→𝑋𝑒+𝜈𝑒)=1.26±0.12.
Using a data sample of 448.1×106 𝜓(3686) events collected with the BESIII detector operating at the BEPCII, we perform search for the hadronic transition ℎ𝑐→𝜋+𝜋−𝐽/𝜓 via 𝜓(3686)→𝜋0ℎ𝑐. No signals of the transition are observed, and the upper limit on the product branching fraction ℬ(𝜓(3686)→𝜋0ℎ𝑐)ℬ(ℎ𝑐→𝜋+𝜋−𝐽/𝜓) at the 90% confidence level (C.L.) is determined to be 2.0×10−6. This is the most stringent upper limit to date.
We measure the Born cross sections of the process 𝑒+𝑒−→𝐾+𝐾−𝐾+𝐾− at center-of-mass (c.m.) energies, √𝑠, between 2.100 and 3.080 GeV. The data were collected using the BESIII detector at the BEPCII collider. An enhancement at √𝑠=2.232 GeV is observed, very close to the 𝑒+𝑒−→Λ¯Λ production threshold. A similar enhancement at the same c.m. energy is observed in the 𝑒+𝑒−→𝜙𝐾+𝐾− cross section. The energy dependence of the 𝐾+𝐾−𝐾+𝐾− and 𝜙𝐾+𝐾− cross sections differs significantly from that of 𝑒+𝑒−→𝜙𝜋+𝜋−.
Using 𝑒+𝑒−→Λ+𝑐¯Λ−𝑐 production from a 567 pb−1 data sample collected by BESIII at 4.6 GeV, a full angular analysis is carried out simultaneously on the four decay modes of Λ+𝑐→𝑝𝐾0𝑆, Λ𝜋+, Σ+𝜋0, and Σ0𝜋+. For the first time, the Λ+𝑐 transverse polarization is studied in unpolarized 𝑒+𝑒− collisions, where a nonzero effect is observed with a statistical significance of 2.1𝜎. The decay asymmetry parameters of the Λ+𝑐 weak hadronic decays into 𝑝𝐾0𝑆, Λ𝜋+, Σ+𝜋0 and Σ0𝜋+ are measured to be 0.18±0.43(stat)±0.14(syst), −0.80±0.11(stat)±0.02(syst), −0.57±0.10(stat)±0.07(syst), and −0.73±0.17(stat)±0.07(syst), respectively. In comparison with previous results, the measurements for the Λ𝜋+ and Σ+𝜋0 modes are consistent but with improved precision, while the parameters for the 𝑝𝐾0𝑆 and Σ0𝜋+ modes are measured for the first time.
Using 2.93 fb−1 of 𝑒+𝑒− annihilation data collected at a center-of-mass energy √𝑠=3.773 GeV with the BESIII detector operating at the BEPCII collider, we search for the semileptonic 𝐷0(+) decays into a 𝑏1(1235)−(0) axial-vector meson for the first time. No significant signal is observed for either charge combination. The upper limits on the product branching fractions are ℬ𝐷0→𝑏1(1235)−𝑒+𝜈𝑒·ℬ𝑏1(1235) −→ 𝜔𝜋−<1.12×10−4 and ℬ𝐷+→𝑏1(1235)0𝑒+𝜈𝑒·ℬ𝑏1(1235)0→𝜔𝜋0<1.75×10−4 at the 90% confidence level.
The Born cross sections of the e+e− → D*+D*− and e+e− → D*+D− processes are measured using e+e− collision data collected with the BESIII experiment at center-of-mass energies from 4.085 to 4.600 GeV, corresponding to an integrated luminosity of 15.7 fb−1. The results are consistent with and more precise than the previous measurements by the Belle, Babar and CLEO collaborations. The measurements are essential for understanding the nature of vector charmonium and charmonium-like states.
We measure the inclusive semielectronic decay branching fraction of the D+s meson. A double-tag technique is applied to e+e− annihilation data collected by the BESIII experiment at the BEPCII collider, operating in the center-of-mass energy range 4.178–4.230 GeV. We select positrons fromD+s→Xe+νe with momenta greater than 200 MeV/c and determine the laboratory momentum spectrum, accounting for the effects of detector efficiency and resolution. The total positron yield and semielectronic branching fraction are determined by extrapolating this spectrum below the momentum cutoff. We measure the D+s semielectronic branching fraction to be(6.30±0.13(stat.)±0.09(syst.)±0.04(ext.))%, showing no evidence for unobserved exclusive semielectronic modes. We combine this result with external data taken from literature to determine the ratio of the D+s and D0 semielectronic widths, Γ(D+s→Xe+νe)Γ(D0→Xe+νe)=0.790±0.016(stat.)±0.011(syst.)±0.016(ext.). Our results are consistent with and more precise than previous measurements.
Using 448.1 × 106 ψ(3686) decays collected with the BESIII detector at the BEPCII e+e− storage rings, the branching fractions and angular distributions of the decays χcJ → Ξ−Ξ¯¯¯¯+ and Ξ0Ξ¯¯¯¯0 (J = 0, 1, 2) are measured based on a partial-reconstruction technique. The decays χc1 → Ξ0Ξ¯¯¯¯0 and χc2 → Ξ0Ξ¯¯¯¯0 are observed for the first time with statistical significances of 7σ and 15σ, respectively. The results of this analysis are in good agreement with previous measurements and have significantly improved precision.
Using a data sample of e+e− collision data corresponding to an integrated luminosity of 2.93 fb−1 collected with the BESIII detector at a center-of-mass energy of s=3.773GeV, we search for the singly Cabibbo-suppressed decays D0→π0π0π0, π0π0η, π0ηη and ηηη using the double tag method. The absolute branching fractions are measured to be B(D0→π0π0π0)=(2.0±0.4±0.3)×10−4, B(D0→π0π0η)=(3.8±1.1±0.7)×10−4 and B(D0→π0ηη)=(7.3±1.6±1.5)×10−4 with the statistical significances of 4.8σ, 3.8σ and 5.5σ, respectively, where the first uncertainties are statistical and the second ones systematic. No significant signal of D0→ηηη is found, and the upper limit on its decay branching fraction is set to be B(D0→ηηη)<1.3×10−4 at the 90% confidence level.
In Ref. [1] the BESIII collaboration published a cross section measurement of the process e+e− → π+π− in the energy range between 600 and 900 MeV. In this corrigendum, we report a corrected evaluation of the statistical errors in terms of a fully propagated covariance matrix. The correction also yields a reduced statistical uncertainty for the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, which now reads as aππ,LO μ (600 − 900 MeV) = (368.2 ± 1.5stat ± 3.3syst) × 10−10. The central values of the cross section measurement and of aππ,LO μ , as well as the systematic uncertainties remain unchanged.
AIM: To evaluate and compare the effect of combined transarterial chemoembolization (TACE) and arterial administration of Bletilla striata (a Chinese traditional medicine against liver tumor) versus TACE alone for the treatment of hepatocellular carcinoma (HCC) in ACI rats.
METHODS: Subcapsular implantation of a solid Morris hepatoma 3 924A (2 mm3) in the liver was carried out in 30 male ACI rats. Tumor volume (V1) was measured by magnetic resonance imaging (MRI) on day 13 after implantation. The following different agents of interventional treatment were injected after retrograde catheterization via gastroduodenal artery (on day 14), namely, (A) TACE (0.1 mg mitomycin + 0.1 ml Lipiodol) + Bletilla striata (1.0 mg) (n=10); (B) TACE + Bletilla striata (1.0 mg) + ligation of hepatic artery (n=10), (C) TACE alone (control group, n=10). Tumor volume (V2) was assessed by MRI (on day 13 after treatment) and the tumor growth ratio (V2/V1) was calculated.
RESULTS: The mean tumor volume before (V1) and after (V2) treatment was 0.0355 cm3 and 0.2248 cm3 in group A, 0.0374 cm3 and 0.0573 cm3 in group B, 0.0380 cm3 and 0.3674 cm3 in group C, respectively. The mean ratio (V2/V1) was 6.2791 in group A, 1.5324 in group B and 9.1382 in group C. Compared with the control group (group C), group B showed significant inhibition of tumor growth (P<0.01), while group A did not (P>0.05). None of the animals died during implantation or in the postoperative period.
CONCLUSION: Combination of TACE and arterial administration of Bletilla striata plus ligation of hepatic artery is more effective than TACE alone in the treatment of HCC in rats.
Heart valve disease is a major clinical problem worldwide. Cardiac valve development and homeostasis need to be precisely controlled. Hippo signaling is essential for organ development and tissue homeostasis, while its role in valve formation and morphology maintenance remains unknown. VGLL4 is a transcription cofactor in vertebrates and we found it was mainly expressed in valve interstitial cells at the post-EMT stage and was maintained till the adult stage. Tissue specific knockout of VGLL4 in different cell lineages revealed that only loss of VGLL4 in endothelial cell lineage led to valve malformation with expanded expression of YAP targets. We further semi-knockout YAP in VGLL4 ablated hearts, and found hyper proliferation of arterial valve interstitial cells was significantly constrained. These findings suggest that VGLL4 is important for valve development and manipulation of Hippo components would be a potential therapy for preventing the progression of congenital valve disease.
The accurate knowledge of the groundwater storage variation (ΔGWS) is essential for reliable water resource assessment, particularly in arid and semi-arid environments (e.g., Australia, the North China Plain (NCP)) where water storage is significantly affected by human activities and spatiotemporal climate variations. The large-scale ΔGWS can be simulated from a land surface model (LSM), but the high model uncertainty is a major drawback that reduces the reliability of the estimates. The evaluation of the model estimate is then very important to assess its accuracy. To improve the model performance, the terrestrial water storage variation derived from the Gravity Recovery And Climate Experiment (GRACE) satellite mission is commonly assimilated into LSMs to enhance the accuracy of the ΔGWS estimate. This study assimilates GRACE data into the PCRaster Global Water Balance (PCR-GLOBWB) model. The GRACE data assimilation (DA) is developed based on the three-dimensional ensemble Kalman smoother (EnKS 3D), which considers the statistical correlation of all extents (spatial, temporal, vertical) in the DA process. The ΔGWS estimates from GRACE DA and four LSM simulations (PCR-GLOBWB, the Community Atmosphere Biosphere Land Exchange (CABLE), the Water Global Assessment and Prognosis Global Hydrology Model (WGHM), and World-Wide Water (W3)) are validated against the in situ groundwater data. The evaluation is conducted in terms of temporal correlation, seasonality, long-term trend, and detection of groundwater depletion. The GRACE DA estimate shows a significant improvement in all measures, notably the correlation coefficients (respect to the in situ data) are always higher than the values obtained from model simulations alone (e.g., ~0.15 greater in Australia, and ~0.1 greater in the NCP). GRACE DA also improves the estimation of groundwater depletion that the models cannot accurately capture due to the incorrect information of the groundwater demand (in, e.g., PCR-GLOBWB, WGHM) or the unavailability of a groundwater consumption routine (in, e.g., CABLE, W3). In addition, this study conducts the inter-comparison between four model simulations and reveals that PCR-GLOBWB and CABLE provide a more accurate ΔGWS estimate in Australia (subject to the calibrated parameter) while PCR-GLOBWB and WGHM are more accurate in the NCP (subject to the inclusion of anthropogenic factors). The analysis can be used to declare the status of the ΔGWS estimate, as well as itemize the possible improvements of the future model development.
Background: Alzheimer's disease is a common debilitating dementia with known heritability, for which 20 late onset susceptibility loci have been identified, but more remain to be discovered. This study sought to identify new susceptibility genes, using an alternative gene-wide analytical approach which tests for patterns of association within genes, in the powerful genome-wide association dataset of the International Genomics of Alzheimer's Project Consortium, comprising over 7 m genotypes from 25,580 Alzheimer's cases and 48,466 controls.
Principal findings: In addition to earlier reported genes, we detected genome-wide significant loci on chromosomes 8 (TP53INP1, p = 1.4×10−6) and 14 (IGHV1-67 p = 7.9×10−8) which indexed novel susceptibility loci.
Significance: The additional genes identified in this study, have an array of functions previously implicated in Alzheimer's disease, including aspects of energy metabolism, protein degradation and the immune system and add further weight to these pathways as potential therapeutic targets in Alzheimer's disease.