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- Physik (4653) (remove)
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.
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.
Using 16 energy points of e+e− annihilation data collected in the vicinity of the J/ψ resonance with the BESIII detector and with a total integrated luminosity of around 100 pb−1, we study the relative phase between the strong and electromagnetic amplitudes of J/ψ decays. The relative phase between J/ψ electromagnetic decay and the continuum process (e+e− annihilation without the J/ψ resonance) is confirmed to be zero by studying the cross section lineshape of μ+μ− production. The relative phase between J/ψ strong and electromagnetic decays is then measured to be (84.9 ± 3.6)◦ or (−84.7 ± 3.1)◦ for the 2(π+π−)π0 final state by investigating the interference pattern between the J/ψ decay and the continuum process. This is the first measurement of the relative phase between J/ψ strong and electromagnetic decays into a multihadron final state using the lineshape of the production cross section. We also study the production lineshape of the multihadron final state ηπ+π− with η → π+π−π0, which provides additional information about the phase between the J/ψ electromagnetic decay amplitude and the continuum process. Additionally, the branching fraction of J/ψ → 2(π+π−)π0 is measured to be (4.73 ± 0.44)% or (4.85 ± 0.45)%, and the branching fraction of J/ψ → ηπ+π− is measured to be (3.78 ± 0.68) × 10−4. Both of them are consistent with the world average values. The quoted uncertainties include both statistical and systematic uncertainties, which are mainly caused by the low statistics.
Bounding Dark Energy from the SPARC rotation curves: Data driven probe for galaxy virialization
(2024)
Dark Energy (DE) acts as a repulsive force that opposes gravitational attraction. Assuming galaxies maintain a steady state over extended periods, the estimated upper bound on DE studies its resistance to the attractive gravitational force from dark matter. Using the SPARC dataset, we fit the Navarro-Frenk-White (NFW) and Hernquist models to identify the most suitable galaxies for these models. Introducing the presence of DE in these galaxies helps establish the upper limit on its repulsive force. This upper bound on DE sits around ρ(<Λ)∼10−25~kg/m3, only two orders of magnitude higher than the one measured by Planck. We discuss the conditions for detecting DE in different systems and show the consistency of the upper bound from galaxies to other systems. The upper bound is of the same order of magnitude as ρ200=200ρc for both dark matter profiles. We also address the implications for future measurements on that upper bound and the condition for detecting the impact of Λ on galactic scales.
Determining the phase structure of Quantum Chromodynamics (QCD) and its Equation of State (EOS) at densities and temperatures realized inside neutron stars and their mergers is a long-standing open problem. The holographic V-QCD framework provides a model for the EOS of dense and hot QCD, which describes the deconfinement phase transition between a dense baryonic and a quark matter phase. We use this model in fully general relativistic hydrodynamic (GRHD) simulations to study the formation of quark matter and the emitted gravitational wave signal of binary systems that are similar to the first ever observed neutron star merger event GW170817.
Using an 𝑒+𝑒− collision data sample with a total integrated luminosity of 3.19 fb−1 collected with the BESIII detector at a center-of-mass energy of 4.178 GeV, the branching fraction of the inclusive decay of the 𝐷+𝑠 meson to final states including at least three charged pions is measured for the first time to be ℬ(𝐷+𝑠→𝜋+𝜋+𝜋−𝑋)=(32.81±0.35stat±0.63syst)%. In this measurement the charged pions from 𝐾0𝑆 meson decays are excluded. The partial branching fractions of 𝐷+𝑠→𝜋+𝜋+𝜋−𝑋 are also measured as a function of the 𝜋+𝜋+𝜋− invariant mass.
The process e+e−→Σ+Σ¯− is studied from threshold up to 3.04 GeV/c2 via the initial-state radiation technique using data with an integrated luminosity of 12.0 fb−1, collected at center-of-mass energies between 3.773 and 4.258 GeV with the BESIII detector at the BEPCII collider. The pair production cross sections and the effective form factors of Σ are measured in eleven Σ+Σ¯− invariant mass intervals from threshold to 3.04 GeV/c2. The results are consistent with the previous results from Belle and BESIII. Furthermore, the branching fractions of the decays J/ψ→Σ+Σ¯− and ψ(3686)→Σ+Σ¯− are determined and the obtained results are consistent with the previous results of BESIII.
The process 𝑒+𝑒−→Σ+¯Σ− is studied from threshold up to 3.04 GeV/𝑐2 via the initial-state radiation technique using data with an integrated luminosity of 12.0 fb−1, collected at center-of-mass energies between 3.773 and 4.258 GeV with the BESIII detector at the BEPCII collider. The pair production cross sections and the effective form factors of Σ are measured in eleven Σ+¯Σ− invariant mass intervals from threshold to 3.04 GeV/𝑐2. The results are consistent with the previous results from Belle and BESIII. Furthermore, the branching fractions of the decays 𝐽/𝜓→Σ+¯Σ− and 𝜓(3686)→Σ+¯Σ− are determined and the obtained results are consistent with the previous results of BESIII.
The main focus of this thesis is the application of the nonperturbative Functional Renormalization Group (FRG) to the study of low-energies effective models for Quantum Chromodynamics (QCD). The study of effective field theories and models is crucial for our understanding of physics, especially when we deal with fundamental interaction theories like QCD. In particular, the ultimate goal is the understanding of the critical properties of these models in such a way that we can have an insight on the actual critical phenomena of QCD, with a special focus on its chiral phase transition. The choice of the FRG method derives from the fact that it belongs to the class of functional non-perturbative methods and has also the advantage of linking physics at different energy scales. These features make FRG perfectly compatible with the task of studying non-perturbative phenomena and in particular phase transitions, like the ones expected for strongly interacting matter. However, the functional nature of the FRG approach and of the Wetterich equation has a consequence that its exact resolution is hardly possible, and an ansatz for the effective action is generally needed. In this work we choose to adopt the local-potential approximation (LPA), which prescribes to stop at zeroth order in the expansion in derivative operators of the quantum effective action, including only the quantum effective potential. In this work we exploited the key observation that the FRG flow equation can be cast, for specific models and truncation schemes, in the form of an advection-diffusion, possibly with a source term. This type of equation belongs to the class of problems faced in the context of viscous hydrodynamics. Therefore, an innovative approach to the solution of the FRG flow equation consists in the choice of a method developed specifically for the resolution of this class of hydrodynamic equations. In particular, the Kurganov-Tadmor finite-volume scheme is adopted. Throughout this work we apply this scheme to the study of different physical systems, showing the reliability and the flexibility of this approach.
In the first part of the thesis, we discuss the well-known O(N) model, using the hydrodynamic formulation to solve the FRG flow equation in the LPA truncation. We focus on the study of the critical behaviour of the system and calculate the corresponding critical exponents. Particular attention is given to the error estimation in the extraction of critical exponents, which is a needed and not widely explored aspect. The results are well compatible with others in the literature, obtained with different perturbative and nonperturbative methods, which validates the procedure. In the second part of the thesis, we introduce the quark-meson model as a low-energy effective model for QCD, with a specific focus on its chiral symmetry-breaking pattern and the subsequent dynamical quark-mass generation. The LPA flow equation is of the advection-diffusion type, with an extra source contribution which is due to the inclusion of fermionic degrees of freedom. We thus adopt the developed numerical techniques to derive the phase diagram of the model, which is in agreement with the one obtained with other techniques in the literature.
We also follow another possible way for the study of the critical properties of the quark-meson model: the so-called thermodynamic geometry. This approach is based on the interpretation of the parameter space of the system as a differential manifold. One can then obtain relevant information about the phase transitions from the Ricci scalar. We studied the chiral crossover investigating the behavior of the Ricci scalar up to the critical point, featuring a peaking behavior in the presence of the crossover. We then repeated this analysis in the chiral limit, where the phase transition is expected to be of second order. Via this geometric technique it is possible to have a different view on the chiral phase transition of QCD. This is the case since this approach is based on the calculation of quantities which are influenced by higher-order momenta of the thermodynamic potential, thus allowing for a more comprehensive analysis of the phase transition.
Finally, we exploit the numerical advancement to face the issue of the regulator choice in the FRG calculations. This is one of the most delicate issues which arise when using approximations to solve the FRG flow equation and deserves extensive investigation. In particular, we performed a vacuum parameter study and used the RG consistency requirement to determine the impact of the choice of the regulator on the physical observables and on the phase diagram of the model. Via this study we develop a systematic method to comparison the results obtained via different regulators. We show the importance of the choice of an appropriate UV cutoff in the determination of UV-independent IR observables and, consequently, the impact on the latter that the truncation of the effective average action and the choice of the regulator have.
In response to pathogen infection, gasdermin (GSDM) proteins form membrane pores that induce a host cell death process called pyroptosis1–3. Studies of human and mouse GSDM pores reveal the functions and architectures of 24–33 protomers assemblies4–9, but the mechanism and evolutionary origin of membrane targeting and GSDM pore formation remain unknown. Here we determine a structure of a bacterial GSDM (bGSDM) pore and define a conserved mechanism of pore assembly. Engineering a panel of bGSDMs for site-specific proteolytic activation, we demonstrate that diverse bGSDMs form distinct pore sizes that range from smaller mammalian-like assemblies to exceptionally large pores containing >50 protomers. We determine a 3.3 Å cryo-EM structure of a Vitiosangium bGSDM in an active slinky-like oligomeric conformation and analyze bGSDM pores in a native lipid environment to create an atomic-level model of a full 52-mer bGSDM pore. Combining our structural analysis with molecular dynamics simulations and cellular assays, we define a stepwise model of GSDM pore assembly and demonstrate that pore formation is driven by local unfolding of membrane-spanning β-strand regions and pre-insertion of a covalently bound palmitoyl into the target membrane. These results yield insights into the diversity of GSDM pores found in nature and the function of an ancient post-translational modification in enabling a programmed host cell death process.
In response to pathogen infection, gasdermin (GSDM) proteins form membrane pores that induce a host cell death process called pyroptosis1–3. Studies of human and mouse GSDM pores reveal the functions and architectures of 24–33 protomers assemblies4–9, but the mechanism and evolutionary origin of membrane targeting and GSDM pore formation remain unknown. Here we determine a structure of a bacterial GSDM (bGSDM) pore and define a conserved mechanism of pore assembly. Engineering a panel of bGSDMs for site-specific proteolytic activation, we demonstrate that diverse bGSDMs form distinct pore sizes that range from smaller mammalian-like assemblies to exceptionally large pores containing >50 protomers. We determine a 3.3 Å cryo-EM structure of a Vitiosangium bGSDM in an active slinky-like oligomeric conformation and analyze bGSDM pores in a native lipid environment to create an atomic-level model of a full 52-mer bGSDM pore. Combining our structural analysis with molecular dynamics simulations and cellular assays, our results support a stepwise model of GSDM pore assembly and suggest that a covalently bound palmitoyl can leave a hydrophobic sheath and insert into the membrane before formation of the membrane-spanning β-strand regions. These results reveal the diversity of GSDM pores found in nature and explain the function of an ancient post-translational modification in enabling programmed host cell death.
By analyzing 𝑒+𝑒− annihilation data with an integrated luminosity of 2.93 fb−1 collected at the center-of-mass energy √𝑠=3.773 GeV with the BESIII detector, we present the first absolute measurements of the branching fractions of twenty Cabibbo-suppressed hadronic 𝐷0(+) decays involving multiple pions. The highest four branching fractions obtained are ℬ(𝐷0→𝜋+𝜋−𝜋0) = (1.343±0.013stat±0.016syst)%, ℬ(𝐷0→𝜋+𝜋−2𝜋0) = (1.002±0.019stat±0.024syst)%, ℬ(𝐷+→2𝜋+𝜋−𝜋0) = (1.165±0.021stat±0.021syst)%, and ℬ(𝐷+→2𝜋+𝜋−2𝜋0) = (1.074±0.040stat±0.030syst)%. The 𝐶𝑃 asymmetries for the six decays with highest signal yields are also determined and found to be compatible with zero.
By analyzing e+e− annihilation data with an integrated luminosity of 2.93 fb−1 collected at the center-of-mass energy s√= 3.773 GeV with the BESIII detector, we present the first absolute measurements of the branching fractions of twenty Cabibbo-suppressed hadronic D0(+) decays involving multiple pions. The largest four branching fractions obtained are B(D0→π+π−π0) = >(1.343±0.013stat±0.016syst)%, B(D0→π+π−2π0) = (0.998±0.019stat±0.024syst)%, B(D+→2π+π−π0)
(1.174±0.021stat±0.021syst)%, and B(D+→2π+π−2π0) = (1.074±0.040stat±0.030syst)%. The CP asymmetries for the six decays with highest event yields are also determined.
Using a sample of (448.1±2.9)×106 𝜓(3686) decays collected with the BESIII detector at BEPCII, we report an observation of Ξ− transverse polarization with a significance of 7.3𝜎 in the decay 𝜓(3686)→Ξ− ¯Ξ+ (Ξ−→Λ𝜋−, ¯Ξ+→¯Λ𝜋+, Λ→𝑝𝜋−, ¯Λ→¯𝑝𝜋+). The relative phase of the electric and magnetic form factors is determined to be ΔΦ=(0.667±0.111±0.058) rad. This is the first measurement of the relative phase for a 𝜓(3686) decay into a pair of Ξ−¯Ξ+ hyperons. The Ξ− decay parameters (𝛼Ξ−, 𝜙Ξ−) and their conjugates (𝛼¯Ξ+, 𝜙¯Ξ+), the angular-distribution parameter 𝛼𝜓, and the strong-phase difference 𝛿𝑝−𝛿𝑠 for Λ𝜋− scattering are measured to be consistent with previous BESIII results.
Luminosities and energies of e⁺e⁻ collision data taken between √s=4.61 GeV and 4.95 GeV at BESIII
(2022)
From December 2019 to June 2021, the BESIII experiment collected about 5.85 fb−1 of data at center-of-mass energies between 4.61 GeV and 4.95 GeV. This is the highest collision energy BEPCII has reached so far. The accumulated e+e− annihilation data samples are useful for studying charmonium(-like) states and charmed-hadron decays. By adopting a novel method of analyzing the production of Λ+cΛ¯−c pairs in e+e− annihilation, the center-of-mass energies are measured with a precision of ∼0.6 MeV. Integrated luminosities are measured with a precision of better than 1\% by analyzing the events of large-angle Bhabha scattering. These measurements provide important inputs to the analyses based on these data samples.
The production cross section of inclusive isolated photons has been measured by the ALICE experiment at the CERN LHC in pp collisions at centre-of-momentum energy of s√=13 TeV collected during the LHC Run 2 data-taking period. The measurement is performed by combining the measurements of the electromagnetic calorimeter EMCal and the central tracking detectors ITS and TPC, covering a pseudorapidity range of |ηγ|<0.67 and a transverse momentum range of 7<pγT<200 GeV/c. The result extends to lower pγT and xγT=2pγT/s√ ranges, the lowest xγT of any isolated photon measurements to date, extending significantly those measured by the ATLAS and CMS experiments towards lower pγT at the same collision energy with a small overlap between the measurements. The measurement is compared with next-to-leading order perturbative QCD calculations and the results from the ATLAS and CMS experiments as well as with measurements at other collision energies. The measurement and theory prediction are in agreement with each other within the experimental and theoretical uncertainties.
Alternating acquisition of background and sample spectra is often employed in conventional Fourier-transform infrared spectroscopy or ultraviolet–visible spectroscopy for accurate background subtraction. For example, for solvent background correction, typically a spectrum of a cuvette with solvent is measured and subtracted from a spectrum of a cuvette with solvent and solute. Ultrafast spectroscopies, though, come with many peculiarities that make the collection of well-matched, subtractable background and sample spectra challenging. Here, we present a demountable split-sample cell in combination with a modified Lissajous scanner to overcome these challenges. It allows for quasi-simultaneous measurements of background and sample spectra, mitigating the effects of drifts of the setup and maintaining the beam and sample geometry when swapping between background and sample measurements. The cell is moving between subsequent laser shots to refresh the excited sample volume. With less than 45 μl of solution for 150 μm optical thickness, sample usage is economical. Cell assembly is a key step and covered in an illustrated protocol.
Using about 23 fb−1 of data collected with the BESIII detector operating at the BEPCII storage ring, a precise measurement of the 𝑒+𝑒−→𝜋+𝜋−𝐽/𝜓 Born cross section is performed at center-of-mass energies from 3.7730 to 4.7008 GeV. Two structures, identified as the 𝑌(4220) and the 𝑌(4320) states, are observed in the energy-dependent cross section with a significance larger than 10𝜎. The masses and widths of the two structures are determined to be (𝑀,Γ)=(4221.4±1.5±2.0 MeV/𝑐2,41.8±2.9±2.7 MeV) and (𝑀,Γ)=(4298±12±26 MeV/𝑐2,127±17±10 MeV), respectively. A small enhancement around 4.5 GeV with a significance about 3𝜎, compatible with the 𝜓(4415), might also indicate the presence of an additional resonance in the spectrum. The inclusion of this additional contribution in the fit to the cross section affects the resonance parameters of the 𝑌(4320) state.
Observation of ηc(2S) → 3(π⁺π⁻) and measurements of χcJ → 3(π⁺π⁻) in ψ(3686) radiative transitions
(2022)
The hadronic decay 𝜂𝑐(2𝑆)→3(𝜋+𝜋−) is observed with a statistical significance of 9.3 standard deviations using (448.1±2.9)×106 𝜓(3686) events collected by the BESIII detector at the BEPCII collider. The measured mass and width of 𝜂𝑐(2𝑆) are (3643.4±2.3 (stat)±4.4 (syst)) MeV/𝑐2 and (19.8±3.9 (stat)±3.1 (syst)) MeV, respectively, which are consistent with the world average values within two standard deviations. The product branching fraction ℬ[𝜓(3686)→𝛾𝜂𝑐(2𝑆)]×ℬ[𝜂𝑐(2𝑆)→3(𝜋+𝜋−)] is measured to be (9.2±1.0 (stat)±1.2 (syst))×10−6. Using ℬ[𝜓(3686)→𝛾𝜂𝑐(2𝑆)]=(7.0+3.4−2.5)×10−4, we obtain ℬ[𝜂𝑐(2𝑆)→3(𝜋+𝜋−)]=(1.31±0.15 (stat)±0.17 (syst) (+0.64−0.47) (extr))×10−2, where the third uncertainty is from ℬ[𝜓(3686)→𝛾𝜂𝑐(2𝑆)]. We also measure the 𝜒𝑐𝐽→3(𝜋+𝜋−) (𝐽=0, 1, 2) decays via 𝜓′→𝛾𝜒𝑐𝐽 transitions. The branching fractions are ℬ[𝜒𝑐0→3(𝜋+𝜋−)]=(2.080±0.006 (stat)±0.068 (syst))×10−2, ℬ[𝜒𝑐1→3(𝜋+𝜋−)]=(1.092±0.004 (stat)±0.035 (syst))×10−2, and ℬ[𝜒𝑐2→3(𝜋+𝜋−)]=(1.565±0.005 (stat)±0.048 (syst))×10−2.
Observation of ηc(2S) → 3(π⁺π⁻) and measurements of χcJ → 3(π⁺π⁻) in ψ(3686) radiative transitions
(2022)
The hadronic decay ηc(2S)→3(π+π−) is observed with a statistical significance of 9.3 standard deviations using (448.1±2.9)×106 ψ(3686) events collected by the BESIII detector at the BEPCII collider. The measured mass and width of ηc(2S) are (3643.4±2.3(stat.)±4.4(syst.)) MeV/c2 and (19.8±3.9(stat.)±3.1(syst.)) MeV, respectively, which are consistent with the world average values within two standard deviations. The product branching fraction B[ψ(3686)→γηc(2S)]×B[ηc(2S)→3(π+π−)] is measured to be (9.2±1.0(stat.)±0.9(syst.))×10−6. Using B[ψ(3686)→γηc(2S)]=(7.0+3.4−2.5)×10−4, we obtain B[ηc(2S)→3(π+π−)]=(1.31±0.15(stat.)±0.13(syst.)(+0.64−0.47)(extr))×10−2, where the third uncertainty is from B[ψ(3686)→γηc(2S)]. We also measure the χcJ→3(π+π−) (J=0,1,2) decays via ψ(3686)→γχcJ transitions. The branching fractions are B[χc0→3(π+π−)]=(2.080±0.006(stat.)±0.068(syst.))×10−2, B[χc1→3(π+π−)]=(1.092±0.004(stat.)±0.035(syst.))×10−2, and B[χc2→3(π+π−)]=(1.565±0.005(stat.)±0.048(syst.))×10−2.
Observation of ηc(2S) → 3(π⁺π⁻) and measurements of χcJ → 3(π⁺π⁻) in ψ(3686) radiative transitions
(2022)
The hadronic decay ηc(2S)→3(π+π−) is observed with a statistical significance of 9.3 standard deviations using (448.1±2.9)×106 ψ(3686) events collected by the BESIII detector at the BEPCII collider. The measured mass and width of ηc(2S) are (3643.4±2.3(stat.)±4.4(syst.)) MeV/c2 and (19.8±3.9(stat.)±3.1(syst.)) MeV, respectively, which are consistent with the world average values within two standard deviations. The product branching fraction B[ψ(3686) → γηc(2S)]×B[ηc(2S)→3(π+π−)] is measured to be (9.2±1.0(stat.)±0.9(syst.))×10−6. Using B[ψ(3686)→γηc(2S)]=(7.0+3.4−2.5)×10−4, we obtain B[ηc(2S)→3(π+π−)]=(1.31±0.15(stat.)±0.13(syst.)(+0.64−0.47)(extr))×10−2, where the third uncertainty is from B[ψ(3686)→γηc(2S)]. We also measure the χcJ→3(π+π−) (J=0,1,2) decays via ψ(3686)→γχcJ transitions. The branching fractions are B[χc0→3(π+π−)]=(2.080±0.006(stat.)±0.068(syst.))×10−2, B[χc1→3(π+π−)]=(1.092±0.004(stat.)±0.035(syst.))×10−2, and B[χc2→3(π+π−)]=(1.565±0.005(stat.)±0.048(syst.))×10−2.
The absolute branching fraction of the decay Λc(2625)+→Λ+cπ+π− is measured for the first time to be (50.7±5.0stat.±4.9syst.)% with 368.48 pb−1 of e+e− collision data collected by the BESIII detector at the center-of-mass energies of s√=4.918 and 4.950 GeV. This result is lower than the naive prediction of 67\%, obtained from isospin symmetry, by more than 2σ, thereby indicating that the novel mechanism referred to as the \textit{threshold effect}, proposed for the strong decays of Λc(2595)+, also applies to Λc(2625)+. This measurement is necessary to obtain the coupling constants for the transitions between s-wave and p-wave charmed baryons in heavy hadron chiral perturbation theory. In addition, we search for the decay Λc(2595)+→Λ+cπ+π−. No significant signal is observed, and the upper limit on its branching fraction is determined to be 80.8\% at the 90\% confidence level.
Using a sample of (10.09 ± 0.04) × 109 J/ψ decays collected with the BESIII detector, partial wave analyses of the decay J/ψ → γK0SK0Sπ0 are performed within the K0SK0Sπ0 invariant mass region below 1.6 GeV/c2. The covariant tensor amplitude method is used in both mass independent and mass dependent approaches. Both analysis approaches exhibit dominant pseudoscalar and axial vector components, and show good consistency for the other individual components. Furthermore, the mass dependent analysis reveals that the K0SK0 Sπ0 invariant mass spectrum for the pseudoscalar component can be well described with two isoscalar resonant states using relativistic Breit-Wigner model, i.e., the η(1405) with a mass of 1391.7±0.7+11.3 −0.3 MeV/c 2 and a width of 60.8±1.2+5.5 −12.0 MeV, and the η(1475) with a mass of 1507.6±1.6+15.5−32.2 MeV/c2 and a width of 115.8±2.4 +14.8 −10.9 MeV. The first and second uncertainties are statistical and systematic, respectively. Alternate models for the pseudoscalar component are also tested, but the description of the K0SK0Sπ0invariant mass spectrum deteriorates significantly.
We report a measurement of the cross section for the process e+e−→π+π−J/ψ around the X(3872) mass in search for the direct formation of e+e−→X(3872) through the two-photon fusion process. No enhancement of the cross section is observed at the X(3872) peak and an upper limit on the product of electronic width and branching fraction of X(3872)→π+π−J/ψ is determined to be Γee×B(X(3872)→π+π−J/ψ)<7.5×10−3eV at 90% confidence level under an assumption of total width of 1.19±0.21 MeV. This is an improvement of a factor of about 17 compared to the previous limit. Furthermore, using the latest result of B(X(3872)→π+π−J/ψ), an upper limit on the electronic width Γee of X(3872) is obtained to be <0.32eV at the 90% confidence level.
A measurement of the CP-even fraction of the decay D0→π+π−π+π− is performed with a quantum-correlated ψ(3770)→DD¯ data sample collected by the BESIII experiment, corresponding to an integrated luminosity of 2.93 fb−1. Using a combination of CP eigenstates, D→π+π−π0 and D→K0S,Lπ+π− as tagging modes, the CP-even fraction is measured to be F4π+=0.735±0.015±0.005, where the first uncertainty is statistical and the second is systematic. This is the most precise determination of this quantity to date. It provides valuable model-independent input for the measurement of the CKM angle γ with B±→DK± decays, and for time-dependent studies of CP violation and mixing in the D0-D¯0 system.
A measurement of the 𝐶𝑃-even fraction of the decay 𝐷0→𝜋+𝜋−𝜋+𝜋− is performed with a quantum-correlated 𝜓(3770)→𝐷¯𝐷 data sample collected by the BESIII experiment, corresponding to an integrated luminosity of 2.93 fb−1. Using a combination of 𝐶𝑃 eigenstates, 𝐷→𝜋+𝜋−𝜋0 and 𝐷→𝐾0𝑆,𝐿𝜋+𝜋− as tagging modes, the 𝐶𝑃-even fraction is measured to be 𝐹4𝜋+=0.735±0.015±0.005, where the first uncertainty is statistical and the second is systematic. This is the most precise determination of this quantity to date. It provides valuable model-independent input for the measurement of the angle 𝛾 of the Cabibbo-Kobayashi-Maskawa matrix with 𝐵±→𝐷𝐾± decays, and for time-dependent studies of 𝐶𝑃 violation and mixing in the 𝐷0−¯𝐷0 system.
Using a data sample of (448.1±2.9)×106 𝜓(3686) decays collected at an 𝑒+𝑒− center-of-mass energy of 3.686 GeV by the BESIII detector at Beijing Electron Positron Collider II, we report an observation of the hindered electromagnetic Dalitz decay 𝜓(3686)→𝑒+𝑒−𝜂𝑐 with a significance of 7.9𝜎. The branching fraction is determined to be ℬ(𝜓(3686)→𝑒+𝑒−𝜂𝑐)=(3.77±0.40stat±0.18syst)×10−5, agreeing well with the prediction of the vector meson dominance model. This is the first measurement of the electromagnetic Dalitz transition between the 𝜓(3686) and the 𝜂𝑐, which provides new insight into the electromagnetic properties of this decay, and offers new opportunities to measure the absolute branching fractions of 𝜂𝑐 decays.
Lattice QCD investigation of a doubly-bottom b̄b̄ud tetraquark with quantum numbers I(JP) = 0(1⁺)
(2019)
We use lattice QCD to investigate the spectrum of the ¯𝑏¯𝑏𝑢𝑑 four-quark system with quantum numbers 𝐼(𝐽𝑃)=0(1+). We use five different gauge-link ensembles with 2+1 flavors of domain-wall fermions, including one at the physical pion mass, and treat the heavy ¯𝑏 quark within the framework of lattice nonrelativistic QCD. Our work improves upon previous similar computations by considering in addition to local four-quark interpolators also nonlocal two-meson interpolators and by performing a Lüscher analysis to extrapolate our results to infinite volume. We obtain a binding energy of (−128±24±10) MeV, corresponding to the mass (10476±24±10) MeV, which confirms the existence of a ¯𝑏¯𝑏𝑢𝑑 tetraquark that is stable with respect to the strong and electromagnetic interactions.
We present our recent results on antiheavy-antiheavy-light-light tetraquark systems using lattice QCD. Our study of the b¯b¯us four-quark system with quantum numbers JP=1+ and the b¯c¯ud four-quark systems with I(JP)=0(0+) and I(JP)=0(1+) utilizes scattering operators at the sink to improve the extraction of the low-lying energy levels. We found a bound state for b¯b¯us with Ebind,b¯b¯us=(−86±22±10)MeV, but no indication for a bound state in both b¯c¯ud channels. Moreover, we show preliminary results for b¯b¯ud with I(JP)=0(1+), where we used scattering operators both at the sink and the source. We found a bound state and determined its infinite-volume binding energy with a scattering analysis, resulting in Ebind,b¯b¯ud=(−103±8)MeV.
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.
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 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
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.
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 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.
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 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 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 pure contributions 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 genuine properties of the excess need further exploration with more statistics.
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.
In this work we investigate the existence of bound states for doubly heavy tetraquark systems Q¯Q¯′qq′ in a full lattice-QCD computation, where heavy bottom quarks are treated in the framework of non-relativistic QCD. We focus on three systems with quark content b¯b¯ud, b¯b¯us and b¯c¯ud. We show evidence for the existence of b¯b¯ud and b¯b¯us bound states, while no binding appears to be present for b¯c¯ud. For the bound four-quark states we also discuss the importance of various creation operators and give an estimate of the meson-meson and diquark-antidiquark percentages.
In this work we investigate the existence of bound states for doubly heavy tetraquark systems Q¯Q¯′qq′ in a full lattice-QCD computation, where heavy bottom quarks are treated in the framework of non-relativistic QCD. We focus on three systems with quark content b¯b¯ud, b¯b¯us and b¯c¯ud. We show evidence for the existence of b¯b¯ud and b¯b¯us bound states, while no binding appears to be present for b¯c¯ud. For the bound four-quark states we also discuss the importance of various creation operators and give an estimate of the meson-meson and diquark-antidiquark percentages.
This thesis is concerned with the investigation of static and dynamic properties of quantum Heisenberg paramagnets in the absence of a magnetic field and therefore for vanishing magnetization. For this purpose a new formulation of the spin functional renormalization group (SFRG) is employed. The first manifestations of the SFRG were developed by Krieg and Kopietz, motivated by the FRG approach to ordinary field theories and the older works of Vaks, Larkin and Pikin on diagrammatic methods for spin operators.
The main idea is to study quantum spin systems by considering the evolution of correlation functions under a continuous deformation of the interaction between magnetic moments, starting from a solvable limit. This leads to nonperturbative results for quantities like the spin-spin correlation function. After a basic introduction to the phenomena and concomitant problems discussed in this thesis, a detailed description of the SFRG method in its initial formulation is given in the second chapter. We start with the generating functional of connected imaginary-time spin-correlation functions GΛ [h], for which an exact flow equation is derived. A particular issue, already pointed out by Krieg and Kopietz, arises here, namely the singular non-interacting limit of its subtracted Legendre transform ΓΛ [m]. As a consequence the initial condition of that functional does not have a proper series expansion in powers of m. This prevents us from working directly within a pure one-particle irreducible (1-PI) parametrization of the correlation functions, as is often done in the context of field theories. Thus motivated, we develop a workaround explicitly tailored to paramagnets, which provides us with a functional that has a well-behaved Legendre transform. The new approach is based on a different treatment of fluctuations at zero and finite frequencies, analogous to a previous hybrid formulation for the symmetry-broken phase. Certain properties, considered to be highly relevant for isotropic paramagnets, as well as previous observations, already made in the study of simpler spin systems like the Ising model, serve as additional justifications for choosing this construction.
In the third chapter our new method is assessed by calculating the dynamic susceptibility G(k, iω) and thus the dynamic structure factor S(k, ω) in the symmetric phase. For this purpose an approximate integral equation for the dynamic polarization function Π̃(k, iω) was derived. This equation results from a truncation of the hierarchy of flow equations and contains static quantities, that are assumed to be known from another source. Our first application is the high-temperature limit T → ∞ in d ≤ 3 dimensions. Salient features, believed to be part of the spin dynamics in isotropic Heisenberg magnets are also exhibited by our solution, like (anomalous) diffusion in a suitable hydrodynamic limit. Moreover we obtain the same order of magnitude for the diffusion coefficient D as in experiments and other theoretical calculations. Other aspects do not entirely agree with previous approaches.
Afterwards we continue by investigating systems close to the critical point Tc. Dynamic scaling forms for Π̃(k, iω) and S(k, ω), which, like spin diffusion, are postulated on the basis of quite general physical arguments, are reproduced. Agreement of the line-shapes 2with neutron scattering experiments at T = Tc is found to be satisfying, with deviations for ω → 0, that may be attributed to the simplicity of the approximation, like at infinite temperature.
Finally, we focus our attention on the thermodynamic properties of isotropic Heisenberg paramagnets by calculating the static susceptibility G(k). For this purpose we employ simple truncation schemes of the flow equations for the static self-energy ΣΛ (k) and four-spin vertex ΓΛ , together with a basic ansatz for the dynamic polarization Π̃(k, iω) in quantum systems. As a result we obtain transition temperatures Tc of three-dimensional nonfrustrated magnets within an accuracy of 5 percent compared to established benchmark values from Quantum Monte Carlo and high temperature expansion series. We conclude this chapter by giving an outlook on the application of our method to frustrated systems, which may require a combined non-trivial calculation of static and dynamic properties.
Search for the lepton number violating decay Σ⁻ → pe⁻e⁻ and the rare inclusive decay Σ⁻ → Σ⁺X
(2021)
Using a data sample of (1310.6±7.0)×106 𝐽/𝜓 events taken with the BESIII detector at the center-of-mass energy of 3.097 GeV, we search for the first time for the lepton number violating decay Σ−→𝑝𝑒−𝑒− and the rare inclusive decay Σ−→Σ+𝑋, where 𝑋 denotes any possible particle combination. The Σ− candidates are tagged in 𝐽/𝜓→¯Σ(1385)+Σ− decays. No signal candidates are found, and the upper limits on the branching fractions at the 90% confidence level are determined to be ℬ(Σ−→𝑝𝑒−𝑒−)<6.7×10−5 and ℬ(Σ−→Σ+𝑋)<1.2×10−4.
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.
Using 6.32 fb−1 of 𝑒+𝑒− collision data collected by the BESIII detector at the center-of-mass energies between 4.178 and 4.226 GeV, an amplitude analysis of the 𝐷+𝑠→𝐾0𝑆𝐾−𝜋+𝜋+ decays is performed for the first time to determine the intermediate-resonant contributions. The dominant component is the 𝐷+𝑠→𝐾*(892)+¯𝐾*(892)0 decay with a fraction of (40.6±2.9stat±4.9sys)%. Our results of the amplitude analysis are used to obtain a more precise measurement of the branching fraction of the 𝐷+𝑠→𝐾0𝑆𝐾−𝜋+𝜋+ decay, which is determined to be (1.46±0.05stat±0.05sys)%.
Using a total of 5.25 fb−1 of e+e− collision data with center-of-mass energies from 4.236 to 4.600 GeV, we report the first observation of the process e+e− → ηψ(2S) with a statistical significance of 4.9 standard deviations. The data sets were collected by the BESIII detector operating at the BEPCII storage ring. We measure the yield of events integrated over center-of-mass energies and also present the energy dependence of the measured cross section.
The decays D → K−π+π+π− and D → K−π+π 0 are studied in a sample of quantum-correlated DD¯ pairs produced through the process e+e− → ψ(3770) → DD¯, exploiting a data set collected by the BESIII experiment that corresponds to an integrated luminosity of 2.93 fb−1 . Here D indicates a quantum superposition of a D0 and a D¯ 0 meson. By reconstructing one neutral charm meson in a signal decay, and the other in the same or a different final state, observables are measured that contain information on the coherence factors and average strong-phase differences of each of the signal modes. These parameters are critical inputs in the measurement of the angle γ of the Unitarity Triangle in B− → DK− decays at the LHCb and Belle II experiments. The coherence factors are determined to be RK3π = 0.52+0.12−0.10 and RKππ0 = 0.78 ± 0.04, with values for the average strong-phase differences that are δ K3π D = (167+31−19)◦ and δKππ0D = (196+14−15◦ , where the uncertainties include both statistical and systematic contributions. The analysis is re-performed in four bins of the phase-space of the D → K−π+π+π− to yield results that will allow for a more sensitive measurement of γ with this mode, to which the BESIII inputs will contribute an uncertainty of around 6◦.
We report new measurements of the branching fraction ℬ(𝐷+𝑠→ℓ+𝜈), where ℓ+ is either 𝜇+ or 𝜏+(→𝜋+¯𝜈𝜏), based on 6.32 fb−1 of electron-positron annihilation data collected by the BESIII experiment at six center-of-mass energy points between 4.178 and 4.226 GeV. Simultaneously floating the 𝐷+𝑠→𝜇+𝜈𝜇 and 𝐷+𝑠→𝜏+𝜈𝜏 components yields ℬ(𝐷+𝑠→𝜏+𝜈𝜏)=(5.21±0.25±0.17)×10−2, ℬ(𝐷+𝑠→𝜇+𝜈𝜇)=(5.35±0.13±0.16)×10−3, and the ratio of decay widths 𝑅=Γ(𝐷+𝑠→𝜏+𝜈𝜏)Γ(𝐷+𝑠→𝜇+𝜈𝜇)=9.73+0.61−0.58±0.36, where the first uncertainties are statistical and the second systematic. No evidence of 𝐶𝑃 asymmetry is observed in the decay rates 𝐷±𝑠→𝜇±𝜈𝜇 and 𝐷±𝑠→𝜏±𝜈𝜏: 𝐴𝐶𝑃(𝜇±𝜈)=(−1.2±2.5±1.0)% and 𝐴𝐶𝑃(𝜏±𝜈)=(+2.9±4.8±1.0)%. Constraining our measurement to the Standard Model expectation of lepton universality (𝑅=9.75), we find the more precise results ℬ(𝐷+𝑠→𝜏+𝜈𝜏)=(5.22±0.10±0.14)×10−2 and 𝐴𝐶𝑃(𝜏±𝜈𝜏)=(−0.1±1.9±1.0)%. Combining our results with inputs external to our analysis, we determine the 𝑐→¯𝑠 quark mixing matrix element, 𝐷+𝑠 decay constant, and ratio of the decay constants to be |𝑉𝑐𝑠|=0.973±0.009±0.014, 𝑓𝐷+𝑠=249.9±2.4±3.5 MeV, and 𝑓𝐷+𝑠/𝑓𝐷+=1.232±0.035, respectively.