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BESIII Collaboration

Publications and source records attributed to BESIII Collaboration.

At least 37 records · Page 2Linked to original sources

Measurement of inelastic scattering $Λ(\overlineΛ)+p\toΣ^{0}(\overlineΣ^{0})+p$ via $e^+e^-\to J/ψ\toΛ\overlineΛ$

Using a sample of $(10087\pm44)\times10^{6}$ $J/ψ$ events collected with the BESIII detector, we investigate the inelastic scattering processes $Λ+p\toΣ^{0}+p$ and $\overlineΛ+p\to\overlineΣ^{0}+p$, exploiting hyperons from $J/ψ\toΛ\overlineΛ$ decays as an effective beam and the beam-pipe materials as targets. The processes $Λ+{}^{9}\mathrm{Be}\toΣ^{0}+p+{}^{8}\mathrm{Li}$ and $\overlineΛ+{}^{9}\mathrm{Be}\to\overlineΣ^{0}+p+{}^{8}\mathrm{Li}$ are measured at a hyperon momentum of $1.074~\mathrm{GeV}/c$, with cross sections of $(10.1\pm1.4_{\rm stat}\pm0.7_{\rm syst})$ mb and $(1.7\pm0.6_{\rm stat}\pm0.4_{\rm syst})$ mb, respectively. Under the assumption of surface-dominated hyperon-nucleus scattering, these measurements are used to extract the corresponding proton-target cross sections. Independently, direct measurements using the hydrogen component of the beam-pipe oil yield $(3.2\pm1.1_{\rm stat}\pm0.5_{\rm syst})$ mb for $Λ+p\toΣ^{0}+p$ and $(1.5\pm0.5_{\rm stat}\pm0.1_{\rm syst})$ mb for $\overlineΛ+p\to\overlineΣ^{0}+p$, consistent with the indirect determinations. The combined cross sections are $(4.7\pm0.7)$ mb and $(1.1\pm0.3)$ mb, respectively. The $\overlineΛ+p\to\overlineΣ^{0}+p$ signal constitutes the first evidence for anti-hyperon inelastic scattering with baryonic final states, with a significance of $3.1σ$. The pronounced difference between the $Λp$ and $\overlineΛp$ inelastic scattering cross sections provides new experimental constraints on hyperon-nucleon and anti-hyperon-nucleon interactions.

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Observation of the $X(2370)$ in $J/ψ\rightarrowγK^{0}_{S}K^{0}_{S}π^{0}$ and $J/ψ\rightarrowγπ^{0}π^{0}η$

Based on $(10087\pm44)\times10^{6}$ $J/ψ$ events collected with the BESIII detector, the $J/ψ\rightarrowγK^{0}_{S}K^{0}_{S}π^{0}$ and $J/ψ\rightarrowγπ^{0}π^{0}η$ processes are studied. The $X(2370)$ is observed in both the $K^{0}_{S}K^{0}_{S}π^{0}$ and $π^{0}π^{0}η$ invariant mass spectra, with statistical significances greater than $14σ$ and $20σ$, respectively. By combining measurements from these processes with those from the previously reported $J/ψ\rightarrowγK^{0}_{S}K^{0}_{S}η^{\prime}$ process, the mass and width of the $X(2370)$ are determined to be $2359^{+13}_{-14}~\text{MeV}/c^{2}$ and $170^{+44}_{-29}~\text{MeV}$, respectively. In addition, the decay $X(2370)\to a_{0}(980)^{0}π^{0}$ with $a_{0}(980)^{0}\to π^{0}η$ is observed with a statistical significance exceeding $9σ$. The properties of the $X(2370)$\textemdash decay pattern similarities to that of $η_{c}$, are consistent with those of a pseudoscalar glueball.

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Production and Decay Dynamics of the Charmed Baryon $Λ_c^+$ in $e^+e^-$ Annihilations near Threshold

The study of the charmed baryons is crucial for investigating the strong and weak interactions in the standard model and for gaining insights into the internal structure of baryons. In an $e^+e^-$ experiment the lightest charmed baryon, $Λ_c^+$, can be produced in pairs through the single-photon annihilation process. This process can be described by two complex electromagnetic form factors. The presence of a nonzero relative phase between these form factors gives rise to a transverse polarization of the charmed baryon and provides additional constraints on the dynamic parameters in the decays. In this article, we present the first observation of the transverse polarization of $Λ_{c}^{+}$ in the reaction $e^+e^- \to Λ_c^{+}\barΛ_c^-$, based on $6.4~\text{fb}^{-1}$ of $e^{+}e^{-}$ annihilation data collected at center-of-mass energies between $4600$~MeV and $4951$~MeV with the BESIII detector. The decay asymmetry parameters in the decays $Λ_c^+ \to pK_S^0$, $Λπ^+$, $Σ^0π^+$, and $Σ^+π^0$ are simultaneously extracted from the joint angular distributions. By independently extracting the above parameters for the process and its $C\!P$-conjugate counterpart, we derive both the strong and weak phase differences between different partial waves, and test several $C\!P$ observables. The obtained results fully demonstrate the feasibility of exploiting transverse polarization at electron-positron colliders to search for $C\!P$-violating effects, opening up a new avenue for exploring $C\!P$ violation in the charmed baryon sector.

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Observation of the $χ_{cJ}$ decays into $pK^{-}\barΛη+\mathrm{c.c.}$

By analyzing $(2712.4 \pm 14.3) \times 10^{6}$ $ψ(3686)$ events collected with the BESIII detector operating at the BEPCII collider, the decays $χ_{cJ} \to pK^{-}\barΛη+ \mathrm{c.c.}$ ($J=0,1,2$) are observed for the first time, with statistical significances exceeding $5σ$ for all three $χ_{cJ}$ states. The measured branching fractions are $\mathcal{B}(χ_{c0} \to pK^{-}\barΛη+ \mathrm{c.c.}) = (5.3 \pm 0.7 \pm 0.5) \times 10^{-5}$, $\mathcal{B}(χ_{c1} \to pK^{-}\barΛη+ \mathrm{c.c.}) = (9.8 \pm 0.6 \pm 0.6) \times 10^{-5}$, and $\mathcal{B}(χ_{c2} \to pK^{-}\barΛη+ \mathrm{c.c.}) = (9.3 \pm 0.6 \pm 0.6) \times 10^{-5}$, where the first uncertainties are statistical and the second are systematic. Structures consistent with the known hyperon resonances $Λ(1520)$ and $\barΛ(1690)$ are seen in the $pK^{-}$ and $\barΛη$ invariant mass spectra, respectively. The reported branching fractions include both resonant and non-resonant contributions. These results provide new experimental information on hadronic decays of $P$-wave charmonium states and contribute to the understanding of baryon production and hadronization dynamics in the nonperturbative QCD regime.

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Evidence for $η_{c}(2S)\to p\bar{p}π^{+}π^{-}π^{0}$ and observation of $χ_{cJ} \to p\bar{p}π^{+}π^{-}π^{0}$

Using $(2.712\pm0.014)\times 10^9$ $ψ(3686)$ events collected by the BESIII detector at the BEPCII collider, the $ψ(3686) \to γp\bar{p}π^+π^-π^0$ process is investigated. Evidence for the decay of $η_{c}(2S)\to p\bar{p}π^{+}π^{-}π^{0}$ is found with a signal significance of 3.3$σ$. The product of branching fractions of $\mathcal{B}[ψ(3686)\to γη_{c}(2S)]\times\mathcal{B}[η_{c}(2S)\to p\bar{p}π^{+}π^{-}π^{0}]$ is determined to be $(3.4\pm0.5\pm0.8) \times 10^{-6}$, where the first uncertainty is statistical and the second systematic. The hadronic decays of $χ_{cJ} \to p\bar{p}π^+π^-π^0$$~(J=0,1,2)$ are observed, and their branching fractions are measured to be $\mathcal{B}(χ_{c0}\to p\bar{p}π^{+}π^{-}π^{0})=(4.79\pm 0.01\pm0.40) \times 10^{-3}$, $\mathcal{B}(χ_{c1}\to p\bar{p}π^{+}π^{-}π^{0})=(2.13\pm 0.01\pm0.17) \times 10^{-3}$, and $\mathcal{B}(χ_{c2}\to p\bar{p}π^{+}π^{-}π^{0})=(3.72\pm 0.01\pm0.29) \times 10^{-3}$, respectively. Furthermore, the branching fractions for the intermediate processes $χ_{cJ}\to p\bar{p}ω$ are updated with significantly improved precision: $\mathcal{B}(χ_{c0}\to p\bar{p}ω)=(5.76\pm0.01\pm0.42)\times10^{-4}$, $\mathcal{B}(χ_{c1}\to p\bar{p}ω)=(1.85\pm0.01\pm0.13)\times10^{-4}$, and $\mathcal{B}(χ_{c2}\to p\bar{p}ω)=(4.51\pm0.01\pm0.33)\times10^{-4}$, respectively.

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Measurement of branching fractions of $D^+_s\to K^0_SK^0_S π^+π^0$ and $D^+_s\to K^0_S K^+π^0π^0$

By analyzing $e^+e^-$ collision data corresponding to an integrated luminosity of 7.33~fb$^{-1}$ collected with the BESIII detector at center-of-mass energies ranging from 4.128 to 4.226~GeV, we report the observations of the hadronic decays $D^+_s\to K^0_SK^0_Sπ^+π^0$ and $D^+_s\to K^0_S K^+π^0π^0$. Their decay branching fractions are determined to be ${\mathcal B}(D^+_s\to K^0_SK^0_S π^+π^0)=(4.08\pm0.46_{\rm stat}\pm0.45_{\rm syst})\times 10^{-3}$ and ${\mathcal B}(D^+_s\to K^0_S K^+π^0π^0)=(3.32\pm0.64_{\rm stat}\pm0.31_{\rm syst})\times 10^{-3}$, where the first uncertainties are statistical and the second are systematic.

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Amplitude Analysis of Singly Cabibbo-Suppressed Decay $Λ^{+}_{c}\to p K^{+} K^{-}$

Using a sample of $e^{+}e^{-}$ annihilation data corresponding to an integrated luminosity of 4.4 $\rm{fb}^{-1}$ collected with the BESIII detector at the BEPCII collider and produced at center-of-mass energies from $4600$ to $4698~\rm{MeV}$, an amplitude analysis is performed of the singly Cabibbo-suppressed decay $Λ^{+}_{c}\to pK^{+}K^{-}$. The branching fractions of $Λ^{+}_{c}\to pϕ(1020)$, $pf_{0}(980)$, $Λ(1405)K^{+}$, and $Λ(1670)K^{+}$ are measured, where the latter two modes are decays that are observed for the first time. At the same time, with the detection efficiency based on the results of the amplitude analysis, the branching fraction of $Λ^{+}_{c}\to pK^{+}K^{-}$ is updated to be $(9.94\pm0.65_{\text{stat.}}\pm0.50_{\text{syst.}})\times10^{-4}$, which is consistent with the current world average value within one standard deviation. The result supersedes the previous BESIII measurement with precision improved by approximately a factor of 1.5.

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Measurement of Branching Fraction and Transition Magnetic Moment of the Hyperon Dalitz Decay $Σ^0 \rightarrow Λe^+e^-$

Based on a data sample of 10 billion $J/ψ$ events collected with the BESIII detector operating at the BEPCII collider, the Dalitz decay $Σ^0 \rightarrow Λe^+e^-$ is studied experimentally for the first time. The $Σ^0$ hyperons are produced through the process $J/ψ\rightarrow Σ^0\barΣ^0$ and analyzed using a double-tag method. The absolute branching fraction is measured to be $\mathcal{B}(Σ^0 \rightarrow Λe^+e^-) = (6.34 \pm 0.25_{\rm stat.} \pm 0.23_{\rm syst.}) \times 10^{-3}$. This result shows a $2σ$ discrepancy from the theoretical calculation quoted in the PDG, where the uncertainties are statistical and systematic, respectively. In addition to the branching fraction, the transition magnetic moment $μ$ is determined to be $(1.74 \pm 0.03_{\rm stat.} \pm 0.09_{\rm syst.})\,μ_N$, where $μ_N=e/(2m_p)$ represents the nucleon magnetic moment, providing valuable insight into the intrinsic structure of the $Σ^0$ hyperon.

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First measurements of the branching fractions of $J/ψ$ and $ψ(3686) \to Σ^{0} \barΣ^{0}η$

Based on $(10087 \pm 44) \times 10^6$ $J/ψ$ and $(2712 \pm 14) \times 10^6$ $ψ(3686)$ events collected with the BESIII detector at the BEPCII collider, the hadronic decays $J/ψ\to Σ^{0} \barΣ^{0} η$ and $ψ(3686) \to Σ^{0} \barΣ^{0} η$ are observed for the first time. The corresponding branching fractions are measured to be $\mathcal{B}(J/ψ\to Σ^{0} \barΣ^{0}η)= (7.5 \pm 0.3 \pm 0.8) \times 10^{-5}$ and $\mathcal{B}(ψ(3686) \to Σ^{0} \barΣ^{0}η)= (1.3\pm 0.1 \pm 0.1) \times 10^{-5}$, respectively, where the first uncertainties are statistical, and the second systematic. The ratio $\text{Q} \approx \frac{\mathcal{B}(ψ(3686) \to Σ^{0} \barΣ^{0} η)}{\mathcal{B}(J/ψ\to Σ^{0} \barΣ^{0} η)}$ is determined to be $(17.3 \pm 1.5 \pm 1.7)\%$, which is con sistent with the 12\%-rule within 3.0$σ$.~No significant intermediate states or threshold enhancements are observed in the $Σ^0$($\barΣ^{0}$)$η$ and $Σ^0$$\barΣ^{0}$ invariant mass spectra.

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High-precision measurement of the space-like $η^\prime$ transition form factor

Using a data sample corresponding to an integrated luminosity of $20.3\ \text{fb}^{-1}$, collected with the BESIII detector at a center-of-mass energy of $3.773\ \text{GeV}$ at the BEPCII collider, we report a precision measurement of the product $Q^2|F(Q^2)|$, where $F(Q^2)$ is the single-virtual space-like transition form factor of the $η'$ meson and $Q^2$ is the squared momentum transfer of the tagged virtual photon. The transition form factor is extracted from the differential Born cross section of the two-photon fusion processes $e^+e^- \to e^+e^-γγ^* \to e^+e^-η^\prime$ using a single-tag technique, where only one scattered lepton is detected. The measurement covers $Q^2 \in [0.1, 6.0]$ GeV$^2$, achieving unprecedented precision, better than $3.0\%$ for $Q^2 < 1.5$ GeV$^2$, and providing the first direct determination at $Q^2 < 0.3$ GeV$^2$.

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Observation of $Λ^+_c\to nπ^+η$ and search for $Λ^+_c\to na_0(980)^+$

By analysing 6.1 ${\rm fb}^{-1}$ of data collected at center-of-mass energies between $\sqrt{s}=4.600$ and 4.843 $\rm GeV$ with the BESIII detector at the BEPCII collider, we observe the decay $Λ_c^+\to nπ^+η$ for the first time with a statistical significance of $9.5σ$. The ratio of branching fractions $\mathcal{B}(Λ_c^+\to nπ^+η)/\mathcal{B}(Λ_c^+\to Λπ^+η)$ is measured to be $0.155\pm0.031_{\rm stat.}\pm0.012_{\rm syst.}$ Taking the world average of $\mathcal{B}(Λ_c^+\to Λπ^+η)$ as reference, the absolute branching fraction is calculated to be $\mathcal{B}(Λ_c^+\to nπ^+η)=(2.94\pm0.59_{\rm stat.}\pm0.23_{\rm syst.}\pm0.13_{\rm ref.})\times10^{-3}$. The intermediate process $Λ_c^+\to na_0(980)^+$ is also searched for in the $π^+η$ invariant mass spectrum. Since no significant signal is found, the upper limit on $\mathcal{B}(Λ_c^+\to na_0(980)^+)\times\mathcal{B}(a_0(980)^+\toπ^+η)$ is set to $8.4\times10^{-4}$ at 90\% confidence level. A sophisticated deep learning approach using a Transformer-based architecture is employed to distinguish signals from prevalent hadronic backgrounds, complemented by thorough validation and systematic uncertainty quantification.

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Search for the charged lepton flavour violating decay $η'\to eμ$

Based on $(8998\pm40)\times10^6$ $J/ψ$ events collected in $e^+e^-$ collisions at $\sqrt{s} = 3.097$ GeV with the BESIII detector, we present a search for the charged lepton flavour violating decay $η'\to eμ$ with $J/ψ\toγη'$. No significant signal is observed, and an upper limit on its decay branching fraction is set to be $6.3\times10^{-7}$ at the 90% confidence level, improving the previous best result by nearly three orders of magnitude.

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Observation of a Charged Charmoniumlike Structure in $e^+e^-\rightarrow D^0D^-π^++c.c.$

We present a partial wave analysis of the process $e^+e^- \rightarrow D^0 D^- π^++c.c.$ using a data sample collected with the BESIII detector at a center-of-mass energy of 4682~MeV. A charged structure, referred to as the $X(3790)^-$ near the $D^0D^-$ mass threshold with a significance of $5.3σ$, which includes systematic uncertainties and the look-elsewhere effect. Assuming a Flatté description of the structure, the quantum numbers of the $X(3790)^-$ are found to be $J^{P}=1^{-}$, and its mass and coupling strength to the $D^0D^-$ channel are determined to be $(3794.7 \pm 6.0 \pm 8.7)$~MeV/$c^2$ and $(1.6 \pm 0.2 \pm 0.2)$~GeV, respectively, where the first uncertainties are statistical and the second systematic. In addition, we also report measurements of the masses and widths of the $D_{2}^{*}(2460)$, $D_{1}^{*}(2600)$, and $D_{1}^{*}(2760)$ charmed mesons.

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First energy scan measurement of $e^{+}e^{-}\to K^{+}K^{-}$ around the $ψ(2S)$ resonance

We report the precise energy scan measurement of the cross section lineshape of $ψ(2S)\to K^{+}K^{-}$. The analysis is based on $e^{+}e^{-}$ collision data corresponding to an integrated luminosity of 495~pb$^{-1}$ collected with the BESIII detector at BEPCII. By analyzing the cross section line-shape, we extract the relative phase $Φ$ between the strong and electromagnetic amplitudes of the $ψ(2S)$ resonance, a fundamental parameter in charmonium physics, based on the assumption that the relative phase between the electromagnetic amplitude of the $ψ(2S)$ resonance and the continuum is zero. Two distinct solutions for the branching fraction $\mathcal{B}$ of $ψ(2S)\to K^{+}K^{-}$ are observed: a constructive interference solution with $\mathcal{B}=(7.49\pm0.41)\times10^{-5}$ and $Φ=(110.1 \pm6.7)^\circ$, and a destructive interference solution with $\mathcal{B}=(10.94\pm0.48)\times10^{-5}$ and $Φ=(-106.8\pm5.7)^\circ$. A significant correlation between $Φ$ and $\mathcal{B}$ is established, demonstrating that interference effects must be taken into account in the $ψ(2S)$ branching fraction measurements. Additionally, the first results for both the $ψ(2S)$ strong form factor, which characterizes the strong coupling between $ψ(2S)$ and $K^{+}K^{-}$, and the energy-dependent electromagnetic form factor of the charged kaon in this energy region are reported.

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Precision measurements of semleptonic decays $D^0 \to π^-\ell^+ν_\ell$ and $D^+ \to π^0\ell^+ν_\ell$ ($\ell =e,μ$)

The branching fractions of $D^0\to π^-e^+ν_e$, $D^0\to π^-μ^+ν_μ$, $D^+\to π^0e^+ν_e$, and $D^+\to π^0μ^+ν_μ$ are measured to be $(2.950\pm0.017_{\rm stat.}\pm 0.017_{\rm syst.})\times10^{-3}$, $(2.817\pm0.037_{\rm stat.}\pm 0.019_{\rm syst.})\times10^{-3}$, $(3.622\pm0.034_{\rm stat.}\pm 0.018_{\rm syst.})\times10^{-3}$, and $(3.507\pm0.043_{\rm stat.}\pm 0.026_{\rm syst.})\times10^{-3}$ using $e^+e^-$ collision data with an integrated luminosity of 20.3 fb$^{-1}$ collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. The partial decay rates of these four decays are measured with the best precision to date and their forward-backward asymmetries are determined for the first time. By performing a simultaneous fit to these results, the product of the hadronic transition form factor $f^{D\toπ}_+(0)$ and the modulus of the $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ is given by $f^{D\toπ}_+(0)|V_{cd}|=0.1425\pm0.0005_{\rm stat.}\pm0.0003_{\rm syst.}$. Taking the $|V_{cd}|$ provided by the standard model global fit and the $f^{D\toπ}_+(0)$ calculated from the lattice quantum chromodynamics as input, we obtain $f^{D\toπ}_+(0)=0.6339\pm0.0024_{\rm stat.}\pm0.0014_{\rm syst.}$ and $|V_{cd}|=0.2262\pm0.0008_{\rm stat.}\pm0.0005_{\rm syst.}\pm0.0018_{\rm LQCD.}$, respectively. The reported results have the best precision to date. We also search for the scalar current contribution in the $c\to d \ell^+ν_{\ell}$ transition and determine Re$(C_S^μ)=$ $0.022 \pm 0.023_{\rm stat.}\pm 0.003_{\rm syst.}$ and $|{\rm Im}(C_S^μ)|=0.000 \pm $ $0.038_{\rm stat.} \pm 0.012_{\rm syst.}$. In addition, the lepton flavor universality is tested with the ratios of the decay rates between semimuonic and semielectronic decays in full and several $\ell^+ν_\ell$ four-momentum transfer ranges.

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Precision Measurement of Decay Dynamics in $D^{0(+)}\to π^{-(0)}\ell^+ν_\ell$

The branching fractions of $D^0\to π^-e^+ν_e$, $D^0\to π^-μ^+ν_μ$, $D^+\to π^0e^+ν_e$, and $D^+\to π^0μ^+ν_μ$ are precisely measured, using 20.3 fb$^{-1}$ of $e^+e^-$ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. The ratios of the decay widths between muon and positron channels are examined in full, across several four-momentum transfer ranges of $\ell^+ν_{\ell}$. No lepton flavor universality violation is found in the current data. From a simultaneous fit to the precisely measured partial decay rates and the first measured forward-backward asymmetries of these four decays, the product of the hadronic transition form factor, $f^{D\toπ}_+(0)$, and the modulus of the $c\to d$ quark mixing element, $|V_{cd}|$, is measured with unprecedented precision to be $f^{D\toπ}_+(0)|V_{cd}|=0.1425\pm0.0005_{\rm stat.}\pm0.0003_{\rm syst.}$. Taking the value of $|V_{cd}|$ from the standard model global fit and $f^{D\toπ}_+(0)$ derived by the lattice quantum chromodynamics calculation as input, we obtain $f^{D\toπ}_+(0)=0.1425\pm0.0005_{\rm stat.}\pm0.0003_{\rm syst.}$ and $|V_{cd}|=0.2262\pm0.0008_{\rm stat.}\pm0.0005_{\rm syst.}\pm0.0018_{\rm LQCD.}$, respectively. The precision of each result is a factor of 2-3 better than the previous best measurements. Additionally, the real and imaginary parts of the scalar current contribution in the $c\to d \ell^+ν_{\ell}$ transition are measured for the first time to be Re $(C_S^μ)=$ $0.022 \pm 0.023_{\rm stat.}\pm 0.003_{\rm syst.}$ and $|\mathrm{Im} (C_S^μ)|=0.000 \pm 0.038_{\rm stat.}\pm 0.012_{\rm syst.}$.

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Proof of principle for nucleon polarization measurement at BESIII

A novel technique for measuring the spin polarization of final-state nucleons in a general-purpose spectrometer is validated. Using $10.09\times10^{9}$ $J/ψ$ events at BESIII, the asymmetry of polarized proton scattering on detector support material is measured, and is consistent with the expected value. This proves that a general-purpose spectrometer can be utilized as a large-acceptance polarimeter, providing the spin polarization in addition to the conventional four-momentum information of the final-state particles. With this technique, physics capabilities are enhanced for existing and future facilities in particle and nuclear physics.

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First Measurement of the Relative Phase between Proton Psionic Form Factors

The relative phase between the time-like form factors of the proton is a crucial observable for a complete understanding of its internal structure, yet it has remained unmeasured due to the formidable experimental challenge of determining the final-state polarization or having available polarized beams. With a novel technique that measures polarization via secondary scattering on spectrometer material, we use $10.09\times10^{9}$ $J/ψ$ events collected at BESIII to analyze the reaction $e^+e^-\rightarrow J/ψ\rightarrow p\bar{p}$. This allows the first determination of the sine of the relative phase between the proton psionic form factors, $\sinΔΦ=-0.20\pm0.34_{\textrm{stat}}\pm0.11_{\textrm{syst}}$. This result provides the first direct insight into the complex dynamics of proton formation, and offers valuable new information to constrain theoretical models of nucleon structure.

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