arXiv subjects

J. Fang

Publications and source records attributed to J. Fang.

At least 127 records · Page 7Linked to original sources

arXiv2026

Search for the radiative decays $D^0\to γ\bar K_1(1270)^0$ and $D^+\to γK_1(1270)^+$

A search for the radiative decays $D^0\to γ\bar K_1(1270)^0$ and $D^+\to γK_1(1270)^+$ is conducted using $20.3~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at the center-of-mass energy $\sqrt{s}=3.773$ GeV by the BESIII detector operating at the BEPCII collider. No significant signals are observed, and upper limits on the branching fractions of $D^0\to γ\bar K_1(1270)^0$ and $D^+\to γK_1(1270)^+$ at 90\% confidence level are determined to be $7.7\times10^{-4}$ and $3.9\times10^{-5}$, respectively. This represents the first test of the Vector Meson Dominance mechanism in the radiative decays of charmed mesons to axial-vector mesons.

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arXiv2026

Measurements of branching fractions of $Λ_{c}^{+}\toΣ^{0}K_{S}^{0}π^{+}$ and $Λ_{c}^{+}\toΣ^{0}K_{S}^{0}K^{+}$

Based on a data sample corresponding to an integrated luminosity of 6.4~fb$^{-1}$ of $e^+e^-$ annihilation and collected with the BESIII detector at 13 center-of-mass energy points ranging between 4.600~GeV and 4.950~GeV, we report the first observation of the singly Cabibbo-suppressed decay $Λ_c^+ \to Σ^0 K_S^0 π^+$ with a statistical significance of 5.9$σ$. The branching fraction is determined to be $\mathcal{B}(Λ_c^+ \to Σ^0 K_S^0 π^+) = (0.58 \pm 0.14_{\rm stat.} \pm 0.04_{\rm syst.}) \times 10^{-3}$. In addition, the decay $Λ_c^+\toΣ^0K_{S}^{0} K^+$ has also been investigated, and the first evidence for this decay is obtained with a statistical significance of 3.7$σ$.

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arXiv2026

Observation of $D_s^+ \to a_0(980)^+f_0(500)$ in the Amplitude Analysis of $D_s^+ \to π^+ π^0 π^0 η$

We report the first observation of the decay $D_s^+ \to π^+π^0π^0η$ in a data set corresponding to an integrated luminosity of 7.33 fb$^{-1}$, collected in $e^+e^-$ collisions by the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV. An unexpectedly large branching fraction $\mathcal{B}( D_s^+ \to a_0(980)^+ f_0(500), a_0(980)^+ \to π^+η, f_0(500)\to π^0π^0) = (0.98 \pm 0.16_{\rm{stat.}} \pm 0.22_{\rm{syst.}})\%$ is measured with a significance exceeding $10σ$, offering new constraints on the internal structure of light scalar mesons. The dominant intermediate process is $D_s^+ \to a_1(1260)^+η, a_1(1260)^+\to ρ(770)^+π^0$ with a branching fraction of $(1.77 \pm 0.21_{\rm stat.} \pm 0.12_{\rm syst.})\%$. The isospin symmetry has been validated to the decays of $a_1(1260)^+\to ρ(770)^0π^+$ and $a_1(1260)^+\to ρ(770)^+π^0$. Moreover, the measured $\mathcal{B}(D_s^+\to π^+π^0π^0η|_{\rm{non}-η^\prime})=(2.97 \pm 0.23_{\rm stat.} \pm 0.14_{\rm sys.})$ reduces the undetected $D_s^+ \to ηX$ decay branching fractions to (0.1 $\pm$ 3.1)\%.

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arXiv2026

Search for a massless particle beyond the Standard Model in the $Ξ^0\toΛ+ \text{invisible}$ decay

A search for a massless beyond-standard-model particle is performed in the decay $Ξ^{0}\toΛ+\text{invisible}$ using $(1.0087 \pm 0.0044)\times 10^{10}$ $J/ψ$ events collected with the BESIII detector at the BEPCII collider. No significant signal is observed and the upper limit on the branching fraction $\mathcal{B}(Ξ^{0}\toΛ+\text{invisible})$ is set to be $2.3 \times 10^{-4}$ at the $90\%$ confidence level. This is the first search for a flavor-changing neutral current process with missing energy in $Ξ^0$ decays. Throughout this paper, charge-conjugate processes are always implied.

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arXiv2026

First detection of ultra-high energy emission from gamma-ray binary LS I +61 303

We report the first detection of gamma-ray emission up to ultra-high-energy (UHE; $>$100 TeV) emission from the prototypical gamma-ray binary system LS I +61 303 using data from the Large High Altitude Air Shower Observatory (LHAASO). It is detected with significances of 9.2$σ$ in WCDA (1.4--30.5 TeV) and 6.2$σ$ in KM2A (25--267 TeV); in KM2A alone we identify 16 photon-like events above 100 TeV against an estimated 5.1 background events, corresponding to a 3.8$σ$ detection. These results provide compelling evidence of extreme particle acceleration in LS I +61 303. Furthermore, we observe orbital modulation at 3.9$σ$ confidence level, between 25 and 100 TeV, with a hint that the orbital modulation is energy-dependent. These features can be understood in a composite scenario in which leptonic and hadronic processes jointly contribute.

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arXiv2026

An improved measurement of $η^\prime\rightarrow e^{+}e^{-}ω$

Using a sample of $(10087 \pm 44) \times 10^{6}$ $J/ψ$ events collected with the BESIII detector, an improved measurement of the decay $η^{\prime}\rightarrow e^{+}e^{-}ω$, with $ω\rightarrowπ^{+}π^{-}π^{0}$ and $π^{0}\rightarrowγγ$ is performed. The branching fraction is determined to be $\mathcal{B}(η^{\prime}\rightarrow e^{+}e^{-}ω) = (1.79 \pm 0.09 \pm 0.12) \times 10^{-4}$, where the first uncertainty is statistical and the second is systematic. This result is consistent with the previous measurement and is obtained with significantly improved precision. Furthermore, the first measurement of the transition form factor cutoff parameter for this decay is reported, with $Λ^{-1} = (2.92 \pm 0.83 \pm 0.15)~\text{GeV}^{-1}$. These measurements provide valuable input for understanding the internal structure of the $η^{\prime}$ meson and testing theoretical models.

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arXiv2026

Evidence of cosmic-ray acceleration up to sub-PeV energies in the supernova remnant IC 443

Supernova remnants (SNRs) have been considered as the primary contributors to cosmic rays (CRs) in our Galaxy. However, the maximum energy of particles that can be accelerated by shocks of SNRs is uncertain, and SNRs' contribution to CRs around PeV energies is unclear. In this study, we present observations of high-energy $γ$-ray emission from the SNR IC 443 using the Large High Altitude Air Shower Observatory (LHAASO). The morphological analysis reveals a pointlike source whose location and spectrum are consistent with those of the Fermi-LAT-detected compact source with $π^0$-decay signature, and a more extended source that is associated with a newly discovered Fermi source. The spectrum of the point source can be described by a power-law function with an index of $\sim3.0$, extending beyond $\sim 30$ TeV without apparent cutoff. Assuming a hadronic origin of the $γ$-ray emission, the $95\%$ lower limit of accelerated protons reaches about 300 TeV. The extended source might be associated with IC 443, SNR G189.6+3.3 or the putative pulsar wind nebula CXOU J061705.3+222127, and can be explained by either a hadronic or a leptonic model with particles reaching hundreds of TeV. These LHAASO results provide compelling evidence that sub-PeV CRs can be accelerated efficiently by shocks of SNRs.

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arXiv2026

Measurement of the branching fraction of $η\to μ^+ μ^-$ and search for $η\to e^+ e^-$

We analyze the decay of $η\rightarrow \ell^+\ell^-(\ell=e, μ)$ via $J/ψ\rightarrowγη'$ and $η'\rightarrowπ^+π^-η$, based on (10087 $\pm$ 44) $\times$ 10$^{6}$ $J/ψ$ events collected with the BESIII detector at the BEPCII storage rings. The branching fraction of $η\rightarrowμ^+ μ^-$ is measured to be $(5.8 \pm 1.0_{\rm stat} \pm 0.2_{\rm syst}) \times 10^{-6}$, which is consistent with the previous measurements and theoretical expectations. In addition, no significant $η\to e^+e^-$ signal is observed in the $e^+ e^-$ invariant mass spectrum, and an improved upper limit of ${\cal B}(η\to e^+ e^-) < 2.2 \times 10^{-7}$ is set at 90\% confidence level.

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arXiv2026

Multi-channel joint analysis of the exotic charmonium-like state $T_{c\bar{c}}(4020)$

This paper reports the first multi-channel joint analysis to identify the properties of the exotic charmonium-like state $T_{c\bar{c}}(4020)$ via the electron-positron annihilation process $e^{+}e^{-}\toπ^{+}T_{c\bar{c}}(4020)^{-}+c.c$. A partial wave analysis is performed simultaneously in three decay channels $T_{c\bar{c}}(4020)^{-}\to {D}^{*0}D^{*-}$, $π^{-}J/ψ$, and $π^{-}h_{c}$, based on data samples taken at $\sqrt{s}=4.395$ and $4.416\,\mathrm{GeV}$ with an integrated luminosity of $1598.9\,\mathrm{pb}^{-1}$ collected with the BESIII detector operating on the BEPCII collider. For the first time, the spin-parity of the $T_{c\bar{c}}(4020)^{-}$ is determined to be $J^{P}=1^{+}$ with a significance $11.7σ$. Pole positions are extracted on the Riemann sheets with three branch points in the complex energy plane. Furthermore, the relative branching fractions are obtained as $\mathcal{B}[T_{c\bar{c}}(4020)^{-}\toπ^{-}J/ψ]/\mathcal{B}[T_{c\bar{c}}(4020)^{-}\to{D}^{*0}D^{*-}]=(3.6\pm0.6\pm1.6)\times10^{-3}$ and $\mathcal{B}[T_{c\bar{c}}(4020)^{-}\toπ^{-}h_{c}]/\mathcal{B}[T_{c\bar{c}}(4020)^{-}\to{D}^{*0}D^{*-}]=(8.9\pm1.3\pm2.3)\times10^{-2}$, where the first uncertainties are statistical, and the second are systematic.

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arXiv2026

Precise measurement of the form factors in $D^0\rightarrow K^(892)^-\ell^+ν_{\ell}$ and observation of $D^0\rightarrow K_2^(1430)^-\ell^+ν_{\ell}$

We report a study of the semileptonic decays $D^0 \rightarrow \bar{K}^0π^-\ell^+ν_{\ell}$ (where $\ell=e,~μ$) based on a sample of $20.3~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector at the BEPCII collider. Based on an investigation of the decay dynamics in $D^0 \rightarrow \bar{K}^0π^-\ell^+ν_{\ell}$ decays, a $\mathcal{D}-$wave component of $D^0\rightarrow K_2^*(1430)^-\ell^+ν_{\ell}$ is observed for the first time with a statistical significance of $8.0σ$, in addition to the dominant $K^*(892)^-$ and $\mathcal{S}-$wave components. The $\mathcal{D}-$wave component is determined to account for $(0.092 \pm 0.028_{\rm stat} \pm 0.018_{\rm syst})\%$ of the total decay rate. The branching fractions of the dominant $K^*(892)^-$ components are measured as $\mathcal{B}(D^0\rightarrow K^{*}(892)^-e^+ν_{e}) = (2.043 \pm 0.018_{\rm stat} \pm 0.012_{\rm syst})\%$ and $\mathcal{B}(D^0\rightarrow K^{*}(892)^-μ^+ν_μ) = (1.964 \pm 0.018_{\rm stat} \pm 0.012_{\rm syst})\%$, which are the most precise measurements to date and represent significant improvements over the previous world averages. The hadronic form-factor parameters are measured to be $r_{V} = V(0)/A_1(0) = 1.444 \pm 0.026_{\rm stat} \pm 0.010_{\rm syst}$, $r_{2} = A_2(0)/A_1(0) = 0.752 \pm 0.020_{\rm stat} \pm 0.004_{\rm syst}$, and $A_1(0)=0.618\pm0.002_{\rm stat} \pm0.004_{\rm syst}$, where $V(0)$ is the vector form factor and $A_{1,2}(0)$ are the axial-vector form factors evaluated at $q^2=0$. This is the most precise determination of the form-factor parameters to date measured in a $D\rightarrow K^*(892)$ transition. In addition, we report the first model-independent measurement of the $\mathcal{S}-$wave phase shift in the hadronic $\bar{K}^0π^-$ system.

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arXiv2026

First Amplitude Analysis of $D^0\rightarrow K^-π^0e^+ν_e$ and Observation of $D^0\rightarrow K^*_2(1430)^-e^+ν_e$

We present the first amplitude analysis of the semileptonic decay $D^0\to K^-π^0 e^{+}ν_{e}$ by analyzing $e^+e^-$ annihilation data corresponding to an integrated luminosity of 20.3 fb$^{-1}$ collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. A tiny $\mathcal{D}$-wave component of the $K^*_2(1430)^-$ accounting for $(0.16 \pm 0.05_{\rm stat} \pm 0.02_{\rm syst})\%$ of the $K^-π^0$ is observed for the first time with a significance of $7.9σ$ in addition to the dominant $\mathcal{P}$-wave component of $K^*(892)^-$ and the sub-dominant $K^-π^0$ $\mathcal{S}$-wave. The hadronic form factors of the $D^0 \to K^*(892)^-$ transition are measured precisely as $r_V=V(0)/A_1(0)=1.41 \pm 0.05_{\rm stat} \pm 0.01_{\rm syst}$ and $r_2=A_2(0)/A_1(0)=0.77 \pm 0.04_{\rm stat} \pm 0.02_{\rm syst}$. The branching fraction of $D^0\to K^*(892)^-e^+ν_e$ with $K^*(892)^-\to K^-π^0$ is measured to be $(7.403\pm0.061_{\rm stat.} \pm 0.048_{\rm syst.})\times10^{-3}$. Combining the measurements of the $D^0\to K^*(892)^-(K^*(892)^-\to K^-π^0)\ell^+ ν_\ell$, lepton flavor universality is tested by the ratio $\mathcal{R}_{\rm LFU}=\mathcal{B}(D^0\to K^*(892)^-μ^+ ν_μ)/\mathcal{B}(D^0\to K^*(892)^-e^+ν_e)=0.928\pm0.020_{\rm stat}\pm0.012_{\rm syst}$ with unprecedented precision; no violation is found. Furthermore, isospin symmetry in the decay $K^*(892) \to Kπ$ is tested by $\mathcal R_{K^{*-}} =\mathcal{B}(K^*(892)^-\to K^- π^0)/\mathcal{B}(K^*(892)^-\to K_S^0 π^-)= 1.09\pm0.02_{\rm stat}\pm0.02_{\rm syst}$ for the first time using the previous measurement of $D^0\to K^*(892)^-e^+ν_e$ with $K^*(892)^-\to K^0_Sπ^-$. Finally, the phase shift of the $Kπ$ \wv{S} is extracted in a model-independent way, which sheds light on the nature of the lightest strange scalar meson, the $K^*_0(700)$.

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arXiv2026

Study of the $f_{0}(980)$ and $f_{0}(500)$ Scalar Mesons through the Decay $D_{s}^{+} \to π^{+} π^{-} e^{+} ν_{e}$

Using $e^+e^-$ collision data corresponding to an integrated luminosity of 7.33~${\rm fb^{-1}}$ recorded by the BESIII detector at center-of-mass energies between 4.128 and 4.226~${\rm GeV}$, we present an analysis of the decay $D_{s}^{+} \to π^{+}π^{-} e^{+}ν_{e}$, where the $D_s^+$ is produced via the process $e^+e^- \to D_{s}^{*\pm}D_{s}^{\mp}$. We observe the $f_{0}(980)$ in the $π^+π^-$ system and the branching fraction of the decay $D_{s}^{+} \to f_{0}(980)e^{+}ν_{e}$ with $f_0(980)\toπ^+π^-$ measured to be $(1.72 \pm 0.13_{\rm stat} \pm 0.10_{\rm syst}) \times10^{-3}$, where the uncertainties are statistical and systematic, respectively. The dynamics of the $D_{s}^{+} \to f_{0}(980)e^{+}ν_{e}$ decay are studied with the simple pole parametrization of the hadronic form factor and the Flatté formula describing the $f_0(980)$ in the differential decay rate, and the product of the form factor $f^{f_0}_{+}(0)$ and the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is determined for the first time to be $f^{f_0}_+(0)|V_{cs}|=0.504\pm0.017_{\rm stat}\pm0.035_{\rm syst}$. Furthermore, the decay $D^+_s\to f_0(500) e^+ν_e$ is searched for the first time but no signal is found. The upper limit on the branching fraction of $D^+_s\to f_0(500) e^+ν_e,~f_0(500)\toπ^+π^-$ decay is set to be $3.3 \times 10^{-4}$ at 90\% confidence level.

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arXiv2026

Measurement of Born Cross Sections for $e^+e^-\toΣ^-\barΣ^+$ at $\sqrt{s}=3.51-4.95$ GeV and Observation of $ψ(3770)\toΣ^-\barΣ^+$

Using $e^+e^-$ collision data corresponding to an integrated luminosity of 44 fb$^{-1}$ collected with the BESIII detector at the BEPCII collider, we report the first measurement of Born cross sections and effective form factors for $e^+e^-\toΣ^-\barΣ^+$ at centre-of-mass energies between 3.51 and 4.95 GeV. With a fit to the $\sqrt{s}$-dependent dressed cross sections, the decay $ψ(3770)\toΣ^-\barΣ^+$ is observed for the first time with a significance of 5.5$σ$, including systematic uncertainties. Upper limits at the 90\% confidence level on the product of the branching fraction and the electronic partial width are provided for other possible charmonium(-like) states. The ratios of Born cross sections for the $Σ$ isospin-triplet states are determined and can be used to test the vector-meson-dominance model.

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arXiv2026

Experimental study of the reaction $Ξ^{0}n\rightarrowΛΛX$ using $Ξ^{0}$-nucleus scattering

Using $(10087\pm44)\times10^{6}$$J/ψ$ events collected with the BESIII detector operating at the BEPCII storage ring in $2009$, $2012$, $2018$, and $2019$, we perform a search for the reaction $Ξ^0n\rightarrowΛΛX$, where $X$ denotes any additional final particles. Given the highly suppressed phase space for producing extra pions, the $X$ consists of either nothing or a photon, corresponding to the processes $Ξ^0 n \rightarrow ΛΛ$ and $Ξ^{0}n\rightarrowΛΣ^0\rightarrowΛΛγ$. The $Ξ^0$ comes from the decay of $J/ψ\rightarrowΞ^0\barΞ^0$, while the neutron originates from material of the beam pipe. A signal is observed for the first time with a statistical significance of 6.4$σ$. The cross section for the reaction $Ξ^0+{^9\rm{Be}}\rightarrowΛ+Λ+X$ is measured to be $(43.6\pm10.5_{\text{stat}}\pm11.1_{\text{syst}})$ mb at $P_{Ξ^0}\approx0.818$ GeV/$c$, where the first uncertainty is statistical and the second systematic. No significant $H$-dibaryon signal is observed in the $ΛΛ$ final state.

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arXiv2026

Dark Energy Survey Year 6 Results: Clustering-redshifts and importance sampling of Self-Organised-Maps $n(z)$ realizations for $3\times2$pt samples

This work is part of a series establishing the redshift framework for the $3\times2$pt analysis of the Dark Energy Survey Year 6 (DES Y6). For DES Y6, photometric redshift distributions are estimated using self-organizing maps (SOMs), calibrated with spectroscopic and many-band photometric data. To overcome limitations from color-redshift degeneracies and incomplete spectroscopic coverage, we enhance this approach by incorporating clustering-based redshift constraints (clustering-z, or WZ) from angular cross-correlations with BOSS and eBOSS galaxies, and eBOSS quasar samples. We define a WZ likelihood and apply importance sampling to a large ensemble of SOM-derived $n(z)$ realizations, selecting those consistent with the clustering measurements to produce a posterior sample for each lens and source bin. The analysis uses angular scales of 1.5-5 Mpc to optimize signal-to-noise while mitigating modeling uncertainties, and marginalizes over redshift-dependent galaxy bias and other systematics informed by the N-body simulation Cardinal. While a sparser spectroscopic reference sample limits WZ constraining power at $z>1.1$, particularly for source bins, we demonstrate that combining SOMPZ with WZ improves redshift accuracy and enhances the overall cosmological constraining power of DES Y6. We estimate an improvement in $S_8$ of approximately 10\% for cosmic shear and $3\times2$pt analysis, primarily due to the WZ calibration of the source samples.

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arXiv2026

LHAASO observation of Mrk 421 during 2021 March - 2024 March: a comprehensive VHE catalog of multi-timescale outbursts and its time average behavior

The Large High Altitude Air Shower Observatory (LHAASO) monitors sources within its field of view for up to 7 hours daily, achieving a duty cycle exceeding 98% and an annual point-source sensitivity of 1.5% Crab Units (CU) in the very high energy (VHE) band. This unbiased sky-survey mode facilitates systematic monitoring and investigation of outburst phenomena. In this paper, we present results from an unprecedented three-year monitoring campaign (March 2021--March 2024) of Mrk421 using LHAASO, spanning energies from 0.4 TeV to 20 TeV. We find that the blazar stayed in a quiescent state in 2021 and became active starting in 2022 with a total of 23 VHE outburst events identified, where the highest observed daily significance reaches $20\,σ$ with a flux equivalent to approximately 3.3~CU. LHAASO's continuous monitoring suggests the flaring occupancy of Mrk~421 to be around 14%. During long-term monitoring, multiwavelength (MWL) variability and correlation analyses are conducted using complementary data from Fermi-LAT, MAXI-GSC, Swift-XRT, and ZTF. A significant correlation ($>3\,σ$) is observed between X-ray and VHE bands with no detectable time lag, while the correlation between GeV and TeV bands is weaker. The flux distribution of the TeV emission during the quiescent state is different from that in the active state, implying the existence of two modes of energy dissipation in the blazar jet. Using simultaneous MWL data, we also analyzed both the long-term and outburst-period SEDs, and discussed the possible origin of the outburst events.

astro-ph.HE↗

arXiv2026

Improved measurements of the coherence factors and strong-phase differences in $D\to K^-π^+π^+π^-$ and $D\to K^-π^+π^0$ with quantum-correlated $D\bar{D}$ decays

Improved measurements of the coherence factors and strong-phase differences in $D\to K^-π^+π^+π^-$ and $D\to K^-π^+π^0$ decays are reported, using quantum-correlated $D\bar{D}$ pairs produced in $e^+e^-$ annihilation at a center-of-mass energy of $3.773\,\mathrm{GeV}$, where $D$ denotes a quantum superposition of the flavour-specific $D^{0}$ and $\bar{D}^{0}$ mesons. The analysis employs a dataset collected by the BESIII experiment, corresponding to an integrated luminosity of $7.93~\rm fb^{-1}$. The observables sensitive to the coherence factors and strong-phase differences are measured by reconstructing one $D$ meson in the signal mode and the other in a tag mode. These parameters provide essential inputs to the measurement of the angle $γ$ of the Cabibbo-Kobayashi-Maskawa Unitarity Triangle in the LHCb and Belle II experiments. The coherence factors are determined to be $R_{K3π}=0.51\pm0.04$ and $R_{Kππ^0}=0.75\pm0.03$, and the strong-phase differences are $δ_D^{K3π}=\left(182^{+14}_{-13}\right)^\circ$ and $δ_D^{Kππ^0}=\left(209^{+7}_{-8}\right)^\circ$, where the uncertainties include both statistical and systematic contributions. For $D\to K^-π^+π^+π^-$, the parameters have been further determined in four phase-space bins with improved precision compared to the previous BESIII results. The uncertainty on future $γ$ measurements from the knowledge of $D\to K^-π^+π^+π^-$ parameters is expected to be reduced to approximately 3.5$^\circ$.

hep-ex↗

arXiv2026

Observation of $ψ(3686)\to γη(1405)$ via $η(1405)\to f_0(980)π^0$

The decay $ψ(3686)\toγπ^+π^-π^0$ is studied using a sample of $(2712.4\pm14.3)\times10^6$ $ψ(3686)$ events collected with the BESIII detector. The decay $η(1405)\toπ^+π^-π^0$ is observed for the first time in $ψ(3686)$ decays via the intermediate state $f_0(980)$ and the product branching fraction $\mathcal{B}(ψ(3686)\toγη(1405))\times\mathcal{B}(η(1405)\to f_0(980)π^0)\times \mathcal{B}(f_0(980)\toπ^+π^-)$ is determined to be $(3.77\pm0.43\pm0.29)\times10^{-7}$, where the first uncertainty is statistical and the second is systematic. The isospin-violating decay of $ψ(3686)\toγf_1(1285)\toγf_0(980)π^0\toγπ^+π^-π^0$ has been observed with signal significance of $2.9σ$. And the branching fraction $\mathcal{B}(ψ(3686)\toγf_1(1285)\toγf_0(980)π^0\toγπ^+π^-π^0)$ is determined to be $ (7.36\pm2.25\pm2.26)\times 10^{-8}$. Since no $η_c$ signal is evident in either the $π^+π^-π^0$ or $f_0(980)π^0$ mass spectrum, upper limits are set to be $\mathcal{B}(ψ(3686)\toγη_c)\times\mathcal{B}(η_c\toπ^+π^-π^0)<3.09\times10^{-7}$ and $\mathcal{B}(ψ(3686)\toγη_c)\times\mathcal{B}(η_c\to f_0(980)π^0)\times\mathcal{B}(f_0(980)\toπ^+π^-)<7.97\times10^{-8}$ at 90\% confidence level, respectively.

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