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Yi. Ding

Publications and source records attributed to Yi. Ding.

At least 19 recordsLinked to original sources

Study of $K_{S}^{0}$-$K_{L}^{0}$ asymmetry in the decays $D^0 \to K_{S}^{0}\omega $ and $D^0 \to K_{L}^{0} \omega $

Based on $e^+ e^-$ annihilation data corresponding to an integrated luminosity of 7.93~$fb^{-1}$ collected at a center-of-mass energy of 3.773 GeV with the BESIII detector at the BEPCII collider, the absolute branching fractions of the decays $D^0 \to K_{S}^{0} \omega$ and $D^0 \to K_{L}^{0} \omega $ are measured to be $(11.79 \pm 0.19 \pm 0.26 \pm 0.47) \times 10^{-3}$ and ($10.84 \pm 0.14 \pm 0.23 \pm 0.44) \times 10^{-3}$, respectively. The $K_{S}^{0}- K_{L}^{0}$ branching-fraction asymmetry of these two decays is $R(D^0,K_{S,L}^{0} \omega) = \frac{\mathcal{B}(D^0 \to K_{S}^{0} \omega) - \mathcal{B}(D^0 \to K_{L}^{0}\omega )}{\mathcal{B}(D^0 \to K_{S}^{0} \omega) + \mathcal{B}(D^0 \to K_{L}^{0} \omega)} =(4.2 \pm 1.0 \pm 0.9 \pm 2.8)\%$. Here, the first uncertainties are statistical, the second systematic, and the third arise from the interference between $D^0 \to K_{S,L}^{0} \omega$ and the non-resonant $D^0 \to \pi^+ \pi^- \pi^0 K_{S,L}^{0}$ processes.

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Observation of $\psi(3686)\to p K^- K_S^0 \bar \Xi^0+c.c.$

Using a sample of $(2.712 \pm 0.014) \times 10^{9}$ $\psi(3686)$ events collected with the BESIII detector, the decay of $\psi(3686)\to p K^- K_S^0 \bar \Xi^0+c.c.$ is observed for the first time with a statistical significance of $11.5\sigma$. The branching fraction of this decay is measured to be $(2.84\pm 0.40\pm 0.25) \times 10^{-6}$, where the first and second uncertainties are statistical and systematic, respectively. This measurement extends the experimental information on rare multi-strange $\psi(3686)$ decays and provides an experimental reference for future studies of related decay modes.

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Evidence for $\eta_{c}(2S)\to p\bar{p}\pi^{+}\pi^{-}\pi^{0}$ and observation of $\chi_{cJ} \to p\bar{p}\pi^{+}\pi^{-}\pi^{0}$

Using $(2.712\pm0.014)\times 10^9$ $\psi(3686)$ events collected by the BESIII detector at the BEPCII collider, the $\psi(3686) \to \gamma p\bar{p}\pi^+\pi^-\pi^0$ process is investigated. Evidence for the decay of $\eta_{c}(2S)\to p\bar{p}\pi^{+}\pi^{-}\pi^{0}$ is found with a signal significance of 3.3$\sigma$. The product of branching fractions of $\mathcal{B}[\psi(3686)\to \gamma \eta_{c}(2S)]\times\mathcal{B}[\eta_{c}(2S)\to p\bar{p}\pi^{+}\pi^{-}\pi^{0}]$ 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 $\chi_{cJ} \to p\bar{p}\pi^+\pi^-\pi^0$$~(J=0,1,2)$ are observed, and their branching fractions are measured to be $\mathcal{B}(\chi_{c0}\to p\bar{p}\pi^{+}\pi^{-}\pi^{0})=(4.79\pm 0.01\pm0.40) \times 10^{-3}$, $\mathcal{B}(\chi_{c1}\to p\bar{p}\pi^{+}\pi^{-}\pi^{0})=(2.13\pm 0.01\pm0.17) \times 10^{-3}$, and $\mathcal{B}(\chi_{c2}\to p\bar{p}\pi^{+}\pi^{-}\pi^{0})=(3.72\pm 0.01\pm0.29) \times 10^{-3}$, respectively. Furthermore, the branching fractions for the intermediate processes $\chi_{cJ}\to p\bar{p}\omega$ are updated with significantly improved precision: $\mathcal{B}(\chi_{c0}\to p\bar{p}\omega)=(5.76\pm0.01\pm0.42)\times10^{-4}$, $\mathcal{B}(\chi_{c1}\to p\bar{p}\omega)=(1.85\pm0.01\pm0.13)\times10^{-4}$, and $\mathcal{B}(\chi_{c2}\to p\bar{p}\omega)=(4.51\pm0.01\pm0.33)\times10^{-4}$, respectively.

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First measurements of the branching fractions of $J/\psi$ and $\psi(3686) \to \Sigma^{0} \bar{\Sigma}^{0}\eta$

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

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Measurement of Born Cross Section for $e^+e^-\to K_S^0\bar{\Xi}^+\Sigma^-+\rm{c.c.}$ at $\sqrt{s} = 3.51-4.95$ GeV

Using $e^+e^-$ collision data collected with the BESIII detector at the BEPCII collider corresponding to a total integrated luminosity of 44~fb$^{-1}$, we present the first measurement of the Born cross sections for the process $e^+e^-\to K_S^0\bar{\Xi}^+\Sigma^-+\rm{c.c.}$ at 56 center-of-mass energies from 3.510 to 4.951~GeV. By fitting the dressed cross sections of $e^+e^-\to K_S^0\bar{\Xi}^+\Sigma^-+\rm{c.c.}$ with the assumption of a power-law function plus a charmonium(-like) resonance, i.e. $\psi(3770)$, $\psi(4040)$, $\psi(4160)$, $Y(4230)$, $Y(4360)$, $\psi(4415)$, {\it Y}(4500), $Y(4660)$, and {\it Y}(4710), no significant signal of any charmonium(-like) state decaying into the $K_S^0\bar{\Xi}^+\Sigma^-+\rm{c.c.}$ is observed. Upper limits on the product of the electronic width and branching fraction at the 90\% confidence level are given for each resonance. Combining this result with the previous measurement of the isospin-symmetric process $e^+e^-\to K^{-} \bar{\Xi}^{+} \Sigma^{0} + \rm{c.c.}$, the ratio of the Born cross sections, $R=\sigma^{B}(e^+e^-\to K_S^0\bar{\Xi}^+\Sigma^-+\rm{c.c.})/$$\sigma^{B}(e^+e^-\to K^-\bar{\Xi}^+\Sigma^0+\rm{c.c.})$, is found to be approximately 1.

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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 $10.09\times10^{9}$ $J/\psi$ 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 $10.09\times10^{9}$ $J/\psi$ events collected at BESIII to analyze the reaction $e^+e^-\rightarrow J/\psi \rightarrow p\bar{p}$. This allows the first determination of the sine of the relative phase between the proton psionic form factors, $\sin\Delta\Phi=-0.20\pm0.34_{\textrm{stat}}\pm0.11_{\textrm{syst}}$. 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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Observation of $\psi(3770)\to p\bar p$ and Measurement of Electromagnetic Form Factors of Proton at $\sqrt{s} = 3.510-4.946$ GeV

We search for possible charmonium(-like) states decaying into the $p\bar{p}$ final state by studying the Born cross sections of the $e^+e^-\to p\bar{p}$ reaction, and we determine the proton electromagnetic form factors by analyzing the proton angular distribution. The measurement is performed using a sample of $e^+e^-$ collision data collected at 47 center-of-mass energies from 3.510 to 4.946 GeV, corresponding to an integrated luminosity of 26 fb$^{-1}$, recorded by the BESIII detector collected at the BEPCII collider. The decay $\psi(3770)\to p\bar{p}$ is observed with a significance of 6.6$\sigma$ including systematic uncertainties. Furthermore, a structure near 4.2 GeV is observed with significances of $4.6\sigma$ or $4.8\sigma$ for the $\psi(4160)$ or $Y(4230)$ hypotheses including systematic uncertainties, respectively; these interpretations cannot presently be distinguished. In addition, the moduli of the form factor ratios $|G_{E}/G_{M}|$ and of the magnetic form factors $|G_{M}|$ are extracted by analyzing the proton polar angle distribution with higher precision at large time-like squared momentum transfer. These results provide important experimental insights into both the decay mechanisms of charmonium(-like) states in the open charm region and the internal structure of proton.

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Measurement of Born cross sections for $e^+e^-\to p\bar p$ at $\sqrt{s} =3.510-4.946$ GeV

We report a measurement of the Born cross section and the effective form factor for the $e^+e^-\to p\bar{p}$ reaction at 47 center-of-mass energies between 3.510 and 4.946 GeV. The measurement is performed using the energy-scan technique and is based on data corresponding to an integrated luminosity of 26 fb\(^{-1}\) collected with the BESIII detector at the BEPCII collider. For the first time, the moduli of the electromagnetic form factor ratio $|G_{E}/G_{M}|$ and of the magnetic form factor $|G_{M}|$ are determined with high precision by analyzing the distribution of the polar angle of the proton at a large timelike momentum transfer. These results provide essential insights into the nature of charmonium(-like) states above the open-charm threshold and the dynamics underlying the proton electromagnetic form factors.

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Measurement of Born Cross Sections for $e^+e^- \to K^+\Xi^0\bar\Sigma^-$ at $\sqrt{s} = 3.51-4.95$ GeV and Observation of $\psi(3770) \to K^+\Xi^0\bar\Sigma^-$

Using 44.55 fb$^{-1}$ of $e^+e^-$ collision data collected by the BESIII detector at the BEPCII collider, we report the first measurement of the Born cross sections for the $e^+e^- \to K^+\Xi^0\bar\Sigma^-$ reaction at fifty-six center-of-mass energies between 3.51 and 4.95~GeV. A fit to the dressed cross sections reveals the first observation of the $\psi(3770) \to K^+\Xi^0\bar\Sigma^-$ process, with a statistical significance of 6.0$\sigma$ including systematic uncertainties. This result represents the first observation of charmless three-body baryonic decay of a vector charmonium state above the open-charm threshold. No significant signals for other charmonium(-like) states i.e., $\psi(4040)$, $\psi(4160)$, $Y(4230)$, $Y(4360)$, $\psi(4415)$, $Y(4500)$, $Y(4660)$ or $Y(4710)$ are observed, and the upper limits for the product of the branching fraction and the electronic partial width at the 90% confidence level for each assumed charmonium(-like) state are provided. Additionally, the ratios of Born cross sections between this work and the previous measurements of $e^+e^- \to K^{0}_{S}\bar\Xi^{-}\Sigma^-$ and $K^-\bar\Xi^+\bar\Sigma^0$ are provided, which can be used to validate theoretical predictions related to isospin symmetry.

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Study of $\phi\to K\bar{K}$ in the amplitude analysis of $D^{+}\to K_{S}^{0}K_{L}^{0}\pi^{+}$

We present the first amplitude analysis and branching fraction measurement of $D^{+} \rightarrow K_{S}^{0}K_{L}^{0}\pi^{+}$ decay. The analysis uses a dataset corresponding to an integrated luminosity of 20.3~$\rm fb^{-1}$, which was recorded at a center-of-mass energy 3.773~GeV by the BESIII detector. The measured branching fraction is $\mathcal{B}(D^{+} \rightarrow K_{S}^{0}K_{L}^{0}\pi^{+})=(5.780\pm0.085\pm 0.052)\times10^{-3}$, where the first uncertainty is statistical and the second is systematic. Using the known value of ${\cal B}(D^+ \to \phi \pi^+,\,\phi \to K^+K^-)$, we determine the relative branching fraction between $\phi \to K_{S}^0K_{L}^0$ and $\phi \to K^+K^-$ to be $\mathcal{B}(D^{+} \to \phi \pi^{+}, \phi \to K_{S}^0K_{L}^0)/\mathcal{B}(D^{+} \to \phi \pi^{+}, \phi \to K^+K^-)= 0.628\pm0.022\pm 0.015\pm0.017$, where the third uncertainty is related to $\mathcal{B}(D^{+} \to \phi \pi^{+}, \phi \to K^+K^-)$. This result is significantly lower than the previous world average and is consistent with the isospin expectation for the $\phi$ meson's coupling to charged and neutral kaon pairs.

hep-ex

Measurement of the Absolute Branching Fraction of Xi(1530)^{-} to (Xi pi)^{-} and Updated Measurement of the Branching Fraction of psi(3686) to anti-Xi^{+} Xi(1530)^{-} + c.c

Based on (2712.4+-14.3)*10^{6} psi(3686) events collected with the BESIII detector, the decays Xi(1530)^{-} to Xi^{0} pi^{-} and Xi(1530)^{-} to Xi^{-} pi^{0} are investigated jointly via the process psi(3686) to anti-Xi^{+} Xi(1530)^{-} + c.c. Under the assumption of isospin symmetry, the two decay modes are treated as fully correlated, and we report the first measurement of their absolute branching fractions. The results are B(Xi(1530)^{-} to Xi^{0} pi^{-})=(61.4+-4.5+-4.6)% and B(Xi(1530)^{-} to Xi^{-} pi^{0}) =(29.7+-2.2+-2.2)%. The combined branching fraction of the two decays is B(Xi(1530)^{-} to (Xi pi)^{-})=(91.1+-6.7+-6.8)%, with uncertainties accounting for the correlations between the two modes. Here, the first uncertainties are statistical, while the second are systematic. Additionally, we update the branching fraction of the decay psi(3686) to anti-Xi^{+} Xi(1530)^{-} + c.c. The updated measurement is B(psi(3686) to anti-Xi^{+} Xi(1530)^{-} + c.c.)=(8.67+-0.52+-0.58+-0.57)*10^{-6}, where the first uncertainty is statistical, the second is systematic related to event selection and the fit model, and the third is associated with the interference effect.

hep-ex

Observation of a Doubly-strange Hyperon $\Xi(1720)$ in $J/\psi\rightarrow{}K^{-}\Sigma^0\bar{\Xi}^{+}+c.c.$

Based on a sample of $(10087 \pm 44) \times 10^6$ $J/\psi$ events collected with the BESIII detector at BEPCII, we report the first observation of the decay $J/\psi \rightarrow K^- \Sigma^0 \bar{\Xi}^++c.c.$. A partial wave analysis is performed to investigate the involved excited states. In addition to the well-established $\Xi(1690)$, a new doubly-strange hyperon $\Xi(1720) $ is observed decaying to $K^- \Sigma^0$ with a mass of $1721.0 \pm 5.2_{\rm stat.} \pm 3.4_{\rm syst.} ~{\rm MeV}/c^2$ and a width of $31.3 \pm 18.3_{\rm stat.} \pm 15.4_{\rm syst.} ~{\rm MeV}$, with a statistical significance exceeding $10\sigma$. The spin-parity hypothesis testing across various quantum number configurations reveals that the spin-parity of $\Xi(1720)$ favors $J^P = {\frac{3}{2}}^+$. Furthermore, the branching fraction of $J/\psi \rightarrow K^- \Sigma^0 \bar{\Xi}^++c.c.$ is determined to be $(2.68 \pm 0.04_{\rm stat.} \pm 0.17_{\rm syst.}) \times 10^{-5}$.

hep-ex

Observation of the Exotic State $\pi_{1}(1600)$ in $\psi(2S)\rightarrow\gamma\chi_{c1},\chi_{c1}\rightarrow\pi^{+}\pi^{-}\eta'$

A partial wave analysis of the process $\psi(2S)\rightarrow\gamma\chi_{c1}, \chi_{c1}\rightarrow\pi^+\pi^-\eta^{\prime}$ is performed using $(2712.4\pm14.3)\times10^{6}$ $\psi(2S)$ events collected with the BESIII detector. An isovector state with exotic quantum numbers $J^{PC}=1^{-+}$, denoted as $\pi_{1}(1600)$, is observed for the first time in the charmonium decay of $\chi_{c1}\rightarrow\pi_{1}^{\pm}(1600)\pi^{\mp}$, $\pi_{1}^{\pm}(1600)\rightarrow\pi^{\pm}\eta^{\prime}$ with a statistical significance over $21\sigma$. Its mass and width are determined to be $1828 \pm 8 ({\rm stat})^{+11}_{-33}({\rm syst})~\mathrm{MeV}/c^2$ and $638 \pm 26 ({\rm stat})^{+35}_{-86}({\rm syst})~\mathrm{MeV}$, respectively, using a relativistic Breit-Wigner function with a mass-dependent width. The corresponding product of branching fractions is determined to be $\mathcal{B}\left[\chi_{c1}\rightarrow\pi_{1}(1600)^{\pm}\pi^{\mp} \right] \times \mathcal{B}\left[\pi_{1}(1600)^{\pm}\rightarrow\pi^{\pm}\eta^{\prime}\right] = \left( 4.30 \pm 0.14 ({\rm stat})^{+1.04}_{-1.03}({\rm syst})~ \right) \times 10^{-4}$.

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First Observation of \boldmath{$D^+ \to a_0(980)\rho$ and $D^+ \to a_0(980)^+ f_0(500)$} in \boldmath{$D^+ \to \pi^+\pi^+\pi^-\eta$ and $D^+ \to \pi^+\pi^0\pi^0\eta$} Decays

We perform the first amplitude analysis of the singly Cabibbo-suppressed decays $D^+ \to \pi^+ \pi^{+(0)} \pi^{-(0)} \eta$, using $e^+e^-$ collision data collected with the BESIII detector at the center-of-mass energy of 3.773\,GeV, corresponding to an integrated luminosity of 20.3 $\rm{fb}^{-1}$. The absolute branching fractions of the $D^+ \to \pi^+ \pi^+ \pi^- \eta$ and $D^+ \to \pi^+ \pi^0 \pi^0 \eta$ decays are measured to be $(3.20\pm0.06_{\text{stat.}}\pm0.03_{\text{syst.}})\times 10^{-3}$ and $(2.43 \pm 0.11_{\text{stat.}} \pm 0.04_{\text{syst.}}) \times 10^{-3}$, respectively. % , both achieving three times better precision than the current PDG values. The decay process $D^{+}\to a_0(980)^{+}f_0(500)$ is observed for the first time with an unexpectedly large branching fraction. Moreover, we observe the decays $D^+ \to a_0(980)^{+(0)} \rho(770)^{0(+)}$ and measure the ratio $r_{+/0} \equiv \frac{\mathcal{B}(D^+ \to a_0(980)^+ \rho(770)^0)}{\mathcal{B}(D^+ \to a_0(980)^0 \rho(770)^+)}$ for the first time to be $0.55\pm0.08_{\text{stat.}}\pm0.05_{\text{syst.}}$. These results offer a novel insight into our comprehension of the nature of the $a_0(980)$ and $f_0(500)$ states.

hep-ex

Measurement of the branching fractions of $\chi_{cJ} \to \pi^{+}\pi^{-}\pi^{0}\pi^{0}$ via $\psi(3686) \to \gamma\chi_{cJ}$

Using $(2712.4\pm14.3)\times 10^6$ $\psi(3686)$ events collected with the BESIII detector operating at BEPCII, the branching fractions of $\chi_{cJ}\to\pi^+\pi^-\pi^0\pi^0$ ($J=0,~1,~2$) are measured via the radiative transition $\psi(3686)\to\gamma\chi_{cJ}$. The results are $\mathcal{B}(\chi_{c0} \to \pi^{+}\pi^{-}\pi^{0}\pi^{0}) = (3.10 \pm 0.01 \pm 0.14) \times 10^{-2}$, $\mathcal{B}(\chi_{c1} \to \pi^{+}\pi^{-}\pi^{0}\pi^{0}) = (1.16 \pm 0.01 \pm 0.05) \times 10^{-2}$, and $\mathcal{B}(\chi_{c2} \to \pi^{+}\pi^{-}\pi^{0}\pi^{0}) = (1.92 \pm 0.01 \pm 0.08) \times 10^{-2}$, where the first uncertainties are statistical and the second systematic. The dominant intermediate states are found to be $\chi_{cJ}\to\rho^+\rho^-$. These results supersede the previous most precise measurements and provide significantly improved precision.

hep-ex

Measurement of the CKM angle $\gamma$ in $B^{\pm} \rightarrow D(\rightarrow K^{0}_{\rm S} h^{\prime+}h^{\prime-})h^{\pm}$ decays with a novel approach

A measurement of the CKM angle $\gamma$ and related strong-phase parameters is performed using a novel, model-independent approach in ${B^{\pm}\rightarrow D(\rightarrow K^{0}_{\rm S} h^{\prime+}h^{\prime-}) h^{\pm}}$ decays, where $h^{(\prime)} \equiv \pi, K$. The analysis uses a joint data sample of electron-positron collisions collected by the BESIII experiment at the Beijing Electron-Positron Collider II during 2010--2011 and 2021--2022, corresponding to an integrated luminosity of 8 fb$^{-1}$, and proton-proton collisions collected by the LHCb experiment at the Large Hadron Collider during 2011--2018, corresponding to an integrated luminosity of 9 fb$^{-1}$. The two datasets are analyzed simultaneously by applying per-event weights based on the amplitude variation over the $D$-decay phase space to enhance the sensitivity to $C\!P$-violating observables. The CKM angle $\gamma$ is determined to be $\gamma = (71.3\pm 5.0)^{\circ}$, which constitutes the most precise single measurement to date.

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Precise measurement of the CKM angle $\gamma$ with a novel approach

A measurement of the CKM angle $\gamma$ is performed by applying a novel, unbinned, model-independent approach to datasets of electron-positron collisions collected by the BESIII experiment and proton-proton collisions by the LHCb experiment, corresponding to integrated luminosities of 8 fb$^{-1}$ and 9 fb$^{-1}$, respectively. The $C\!P$-violating phase $\gamma$ is determined from ${B^{\pm}\rightarrow D(\rightarrow K_{\rm S}^{0} h^{\prime+}h^{\prime-}) h^{\pm}}$ decays in LHCb data, where $h^{(\prime)}$ is either a pion or kaon, while the corresponding strong-phase parameters are measured using doubly tagged ${D\rightarrow K_{\rm S/L}^0 h^{\prime+} h^{\prime-}}$ decays in the quantum-correlated $D\overline{D}$ system present in BESIII data. A joint fit to both datasets, which allows for a simultaneous determination of the associated $C\!P$-violating observables and strong-phase parameters, yields ${\gamma = (71.3\pm 5.0)^{\circ}}$. The result is the most precise to date and consistent with previous measurements and world averages.

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