arXiv subjects

F. Feldbauer

Publications and source records attributed to F. Feldbauer.

At least 415 records · Page 23Linked to original sources

arXiv2022

Measurement of the $e^+e^-\toπ^+π^-J/ψ$ cross section in the vicinity of 3.872 GeV

We report a measurement of the cross section for the process $e^+e^-\toπ^+π^-J/ψ$ around the $X(3872)$ mass in search for the direct formation of $e^+e^-\to X(3872)$ 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 $X(3872)\toπ^+π^-J/ψ$ is determined to be $Γ_{ee}\times\mathcal{B}(X(3872)\toπ^+π^-J/ψ)<7.5\times10^{-3}\,\text{eV}$ at $90\,\%$ confidence level under an assumption of total width of $1.19\pm0.21$ MeV. This is an improvement of a factor of about $17$ compared to the previous limit. Furthermore, using the latest result of $\mathcal{B}(X(3872)\toπ^+π^-J/ψ)$, an upper limit on the electronic width $Γ_{ee}$ of $X(3872)$ is obtained to be $<0.32\,\text{eV}$ at the $90\,\%$ confidence level.

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arXiv2022

Precise Measurements of Decay Parameters and $CP$ Asymmetry with Entangled $Λ-\barΛ$ Pairs

Based on 10 billion $J/ψ$ events collected at the BESIII experiment, a search for $CP$ violation in $Λ$ decay is performed in the difference between $CP$-odd decay parameters $α_{-}$ for $Λ\rightarrow pπ^-$ and $α_{+}$ for $\barΛ\rightarrow \bar{p}π^+$ by using the process $e^+e^- \to J/ψ\rightarrow Λ\barΛ$. With a five-dimensional fit to the full angular distributions of the daughter baryon, the most precise values for the decay parameters are determined to be $α_{-} = 0.7519 \pm 0.0036 \pm 0.0024$ and $α_{+} = -0.7559 \pm 0.0036 \pm 0.0030$, respectively. The $Λ$ and $\barΛ$ averaged value of the decay parameter is extracted to be $α_{\rm{avg}} = 0.7542 \pm 0.0010 \pm 0.0024$ with unprecedented accuracy. The $CP$ asymmetry $A_{CP}=(α_{-}+α_{+})/(α_{-}-α_{+})$ is determined to be $-0.0025 \pm 0.0046 \pm 0.0012$, which is one of the most precise measurements in the baryon sector. The reported results for the decay parameter will play an important role in the studies of the polarizations and $CP$ violations for the strange, charmed and beauty baryons.

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arXiv2022

Improved measurement of the strong-phase difference $δ_D^{Kπ}$ in quantum-correlated $D\bar{D}$ decays

The decay $D\to K^-π^+$ is studied in a sample of quantum-correlated $D\bar{D}$ pairs, based on a data set corresponding to an integrated luminosity of 2.93\,fb$^{-1}$ collected at the $ψ(3770)$ resonance by the BESIII experiment. The asymmetry between $C\!P$-odd and $C\!P$-even eigenstate decays into $K^-π^+$ is determined to be ${\cal A}_{Kπ} = 0.132 \pm 0.011 \pm 0.007$, where the first uncertainty is statistical and the second is systematic. This measurement is an update of an earlier study exploiting additional tagging modes, including several decay modes involving a $K^0_L$ meson. The branching fractions of the $K^0_L$ modes are determined as input to the analysis in a manner that is independent of any strong phase uncertainty. Using the predominantly $C\!P$-even tag $D\to π^+π^-π^0$ and the ensemble of $C\!P$-odd eigenstate tags, the observable ${\cal A}_{Kπ}^{πππ^0}$ is measured to be $0.130 \pm 0.012 \pm 0.008$. The two asymmetries are sensitive to $r_D^{Kπ} \cos δ_D^{Kπ}$, where $r_D^{Kπ}$ and $δ_D^{Kπ}$ are the ratio of amplitudes and phase difference, respectively, between the doubly Cabibbo-suppressed and Cabibbo-favoured decays. In addition, events containing $D \to K^-π^+$ tagged by $D \to K^0_{S,L} π^+π^-$ are studied in bins of phase space of the three-body decays. This analysis has sensitivity to both $r_D^{Kπ} \cos δ_D^{Kπ}$ and $r_D^{Kπ} \sin δ_D^{Kπ}$. A fit to ${\cal A}_{Kπ}$, ${\cal A}_{Kπ}^{πππ^0}$ and the phase-space distribution of the $D \to K^0_{S,L} π^+π^-$ tags yields $δ_D^{Kπ}= \left( 187.6 {^{+8.9}_{-9.7}}{^{+5.4}_{-6.4}} \right)$ degrees, where external constraints are applied for $r_D^{Kπ}$ and other relevant parameters. This is the most precise measurement of $δ_D^{Kπ}$ in quantum-correlated $D\bar{D}$ decays.

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arXiv2022

Observation of resonance structures in $e^+e^-\to π^+π^-ψ_2(3823)$ and mass measurement of $ψ_2(3823)$

Using a data sample corresponding to an integrated luminosity of 11.3 $\rm fb^{-1}$ collected at center-of-mass energies from $4.23$ to $4.70$ GeV with the BESIII detector, we measure the product of the $e^+e^-\to π^+π^-ψ_2(3823)$ cross section and the branching fraction $\mathcal{B}[ψ_2(3823)\to γχ_{c1}]$. For the first time, resonance structure is observed in the cross section line shape of $e^+e^-\to π^+π^-ψ_2(3823)$ with significances exceeding $5σ$. A fit to data with two coherent Breit-Wigner resonances modeling the $\sqrt{s}$-dependent cross section yields $M(R_1)=4406.9\pm 17.2\pm 4.5$ MeV/$c^2$, $Γ(R_1)=128.1\pm 37.2\pm 2.3$ MeV, and $M(R_2)=4647.9\pm 8.6\pm 0.8$ MeV/$c^2$, $Γ(R_2)=33.1\pm 18.6\pm 4.1$ MeV. Though weakly disfavored by the data, a single resonance with $M(R)=4417.5\pm26.2\pm3.5$ MeV/$c^2$, $Γ(R)=245\pm48\pm13$ MeV is also possible to interpret data. This observation deepens our understanding of the nature of the vector charmoniumlike states. The mass of the $ψ_2(3823)$ state is measured as $(3823.12\pm 0.43\pm 0.13)$ MeV/$c^2$, which is the most precise measurement to date.

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arXiv2022

Observation of the doubly Cabibbo-Suppressed decays $D^+\to K^+π^0π^0$ and $D^+\to K^+π^0η$

By analyzing $e^+e^-$ annihilation data corresponding to an integrated luminosity of $2.93\,\rm fb^{-1}$ collected at the center-of-mass energy of 3.773\,GeV with the BESIII detector, we report the first observations of the doubly Cabibbo-suppressed decays $D^+\to K^+π^0π^0$ and $D^+\to K^+π^0η$. The branching fractions of $D^+\to K^+π^0π^0$ and $D^+\to K^+π^0η$ are measured to be $(2.1 \pm 0.4_{\rm stat} \pm 0.1_{\rm syst})\times 10^{-4}$ and $(2.1 \pm 0.5_{\rm stat} \pm 0.1_{\rm syst})\times 10^{-4}$ with statistical significances of 8.8$σ$ and 5.5$σ$, respectively. In addition, we search for the subprocesses $D^+\to K^{*}(892)^{+}π^0$ and $D^+\to K^{*}(892)^{+}η$ with $K^{*}(892)^+\to K^+π^0$. The branching fraction of $D^+\to K^{*}(892)^{+}η$ is determined to be $({4.4^{+1.8}_{-1.5}}_{\rm stat}\pm0.2_{\rm syst})\times10^{-4}$, with a statistical significance of 3.2$σ$. No significant signal for $D^+\to K^{*}(892)^{+}π^0$ is found and we set an upper limit on the branching fraction of this decay at the 90\% confidence level to be $5.4\times10^{-4}$.

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arXiv2022

Observation of $η_c(2S) \to 3(π^+π^-)$ and measurements of $χ_{cJ} \to 3(π^+π^-)$ in $ψ(3686)$ radiative transitions

The hadronic decay $η_c(2S) \to 3(π^+π^-)$ is observed with a statistical significance of 9.3 standard deviations using $(448.1\pm2.9)\times10^6$ $ψ(3686)$ events collected by the BESIII detector at the BEPCII collider. The measured mass and width of $η_c(2S)$ are $(3643.4 \pm 2.3 (\rm stat.) \pm 4.4 (\rm syst.))$ MeV/$c^2$ and $(19.8 \pm 3.9 (\rm stat.) \pm 3.1 (\rm syst.))$ MeV, respectively, which are consistent with the world average values within two standard deviations. The product branching fraction $\mathcal{B}[ψ(3686)\to γη_c(2S)]\times\mathcal{B}[η_c(2S)\to3(π^+π^-)]$ is measured to be $(9.2 \pm 1.0 (\rm stat.) \pm 0.9 (\rm syst.))\times10^{-6}$. Using $\mathcal{B}[ψ(3686)\to γη_c(2S)]=(7.0^{+3.4}_{-2.5})\times10^{-4}$, we obtain $\mathcal{B}[η_c(2S) \to 3(π^+π^-)] = (1.31 \pm 0.15 (\rm stat.) \pm 0.13 (\rm syst.)(^{+0.64}_{-0.47}) (\rm extr))\times10^{-2}$, where the third uncertainty is from $\mathcal{B}[ψ(3686) \to γη_c(2S)]$. We also measure the $χ_{cJ} \to 3(π^+π^-)$ ($J=0, 1, 2$) decays via $ψ(3686) \to γχ_{cJ}$ transitions. The branching fractions are $\mathcal{B}[χ_{c0} \to 3(π^+π^-)] = (2.080\pm0.006 (\rm stat.)\pm0.068 (\rm syst.))\times10^{-2}$, $\mathcal{B}[χ_{c1} \to 3(π^+π^-)] = (1.092\pm0.004 (\rm stat.)\pm0.035 (\rm syst.))\times10^{-2}$, and $\mathcal{B}[χ_{c2} \to 3(π^+π^-)] = (1.565\pm0.005 (\rm stat.)\pm0.048 (\rm syst.))\times10^{-2}$.

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arXiv2022

Measurement of the $C\!P$-even fraction of $D^{0}\toπ^{+}π^{-}π^{+}π^{-}$

A measurement of the $C\!P$-even fraction of the decay $D^{0}\toπ^{+}π^{-}π^{+}π^{-}$ is performed with a quantum-correlated $ψ(3770)\to D\bar{D}$ data sample collected by the BESIII experiment, corresponding to an integrated luminosity of 2.93 $\textrm{fb}^{-1}$. Using a combination of $C\!P$ eigenstates, $D \to π^+π^-π^0$ and $D \to K_{S,L}^0π^{+}π^{-}$ as tagging modes, the $C\!P$-even fraction is measured to be $F_{+}^{4π} = 0.735 \pm 0.015 \pm 0.005$, 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 $B^\pm\to D K^\pm$ decays, and for time-dependent studies of $C\!P$ violation and mixing in the $D^{0}$-$\bar{D}^{0}$ system.

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arXiv2022

Amplitude analysis and branching fraction measurement of the decay $D_{s}^{+} \to K^+π^+π^-$

Using $6.32$ fb$^{-1}$ of $e^{+}e^{-}$ collision data collected at the center-of-mass energies between 4.178 and 4.226 GeV with the BESIII detector, we perform an amplitude analysis of the decay $D^+_s \to K^+π^+π^-$ and determine the amplitudes of the various intermediate states. The absolute branching fraction of $D^+_s\to K^+π^+π^-$ is measured to be ($6.11\pm0.18_{\rm stat.}\pm0.11_{\rm syst.})\times 10^{-3}$. The branching fractions of the dominant intermediate processes $D_{s}^{+} \to K^+ρ^0, ρ^0 \to π^+π^-$ and $D_{s}^{+} \to K^*(892)^0π^+, K^*(892)^0 \to K^+π^-$ are determined to be $(1.96\pm0.19_{\rm stat.}\pm0.23_{\rm syst.})\times 10^{-3}$ and $(1.85\pm0.12_{\rm stat.}\pm0.13_{\rm syst.})\times 10^{-3}$, respectively. The intermediate resonances $f_0(500)$, $f_0(980)$, and $f_0(1370)$ are observed for the first time in this channel.

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arXiv2022

Study of the resonance structures in $e^{+}e^{-} \rightarrow π^{+}π^{-}J/ψ$ process

Using about 23 $\mathrm{fb^{-1}}$ of data collected with the BESIII detector operating at the BEPCII storage ring, a precise measurement of the $e^{+}e^{-} \rightarrow π^{+}π^{-}J/ψ$ 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 ($M, Γ$) = ($4221.4\pm1.5\pm2.0$ MeV/$c^{2}$, $41.8\pm2.9\pm2.7$ MeV) and ($M, Γ$) = ($4298\pm12\pm26$ MeV/$c^{2}$, $127\pm17\pm10$ 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.

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arXiv2022

Measurement of the branching fraction for $ψ(3686)\to ωK^0_SK^0_S$

Analyzing $(448.1\pm2.9)\times10^6$ $ψ(3686)$ events collected with the BESIII detector at the BEPCII collider, the $ψ(3686)\to ωK_{S}^{0}K_{S}^{0}$ decay is observed for the first time. The branching fraction for this decay is determined to be $\mathcal{B}_{ψ(3686)\to ωK_{S}^{0}K^{0}_{S}}$=$(7.04\pm0.39\pm0.36)$$\times10^{-5}$, where the first uncertainty is statistical and the second is systematic.

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arXiv2022

Search for baryon and lepton number violating decays $D^{0}\to \bar{p}e^{+}$ and $D^{0}\to pe^{-}$

Using an electron-positron collision data sample corresponding to an integrated luminosity of 2.93~fb$^{-1}$ collected with the BESIII detector at a center-of-mass energy of 3.773 GeV, we search for the baryon and lepton number violating decays $D^{0}\to \bar{p}e^{+}$ and $D^{0}\to pe^{-}$. No obvious signals are found with the current statistics. The upper limits on the branching fractions for $D^{0}\to \bar{p}e^{+}$ and $D^{0}\to pe^{-}$ are set to be $1.2\times 10^{-6}$ and $2.2\times 10^{-6}$ at 90\% confidence level, respectively.

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arXiv2022

Measurements of Absolute Branching Fractions of $D^0\to K_L^0ϕ$, $K_L^0η$, $K_L^0ω$, and $K_L^0η^{\prime}$

We report the first measurements of the absolute branching fractions of $D^0\to K_L^0ϕ$, $D^0\to K_L^0η$, $D^0\to K_L^0ω$, and $D^0\to K_L^0η^{\prime}$, obtained by analyzing $2.93\,\rm fb^{-1}$ of $e^+e^-$ collision data taken at a center-of-mass energy of 3.773 GeV with the BESIII detector. Taking the world averages of the branching fractions of $D^0\to K_S^0ϕ$, $D^0\to K_S^0η$, $D^0\to K_S^0ω$, and $D^0\to K_S^0η^{\prime}$, the $K_S^0$-$K_L^0$ asymmetry $\mathcal{R}(D^0)$ in these decay modes are obtained. The CP asymmetries in these decays are also determined. No significant $CP$ violation is observed.

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arXiv2022

Measurements of the absolute branching fractions of hadronic $D$-meson decays involving kaons and pions

By analyzing an electron-positron collision data sample corresponding to an integrated luminosity of $2.93\,\rm fb^{-1}$ taken at the center-of-mass energy of 3.773 GeV with the BESIII detector, we obtain for the first time the absolute branching fractions for seven $D^0$ and $D^+$ hadronic decay modes and search for the hadronic decay $D^0\to K^0_S K^0_Sπ^0$ with much improved sensitivity. The results are ${\mathcal B}(D^0\to K^0_Sπ^0π^0π^0 )=( 7.64\pm 0.30\pm 0.29)\times 10^{-3}$, ${\mathcal B}(D^0\to K^-π^+π^0π^0π^0 )=( 9.54\pm 0.30\pm 0.31)\times 10^{-3}$, ${\mathcal B}(D^0\to K^0_Sπ^+π^-π^0π^0)=(12.66\pm 0.45\pm 0.43)\times 10^{-3}$, ${\mathcal B}(D^+\to K^0_Sπ^+π^0π^0 )=(29.04\pm 0.62\pm 0.87)\times 10^{-3}$, ${\mathcal B}(D^+\to K^0_Sπ^+π^+π^-π^0)=(15.28\pm 0.57\pm 0.60)\times 10^{-3}$, ${\mathcal B}(D^+\to K^0_Sπ^+π^0π^0π^0)=( 5.54\pm 0.44\pm 0.32)\times 10^{-3}$, ${\mathcal B}(D^+\to K^-π^+π^+π^0π^0 )=( 4.95\pm 0.26\pm 0.19)\times 10^{-3}$, ${\mathcal B}({D^0\to K^0_S K^0_Sπ^0}) < 1.57 \times 10^{-4}$ at the 90\% confidence level. Here the first uncertainties are statistical and the second ones systematic. The newly studied decays greatly enrich the knowledge of the $D\to \bar Kπππ$ and $D\to \bar Kππππ$ hadronic decays, and open a bridge to access more two-body hadronic $D$ decays containing scalar, vector, axial and tensor mesons in the charm sector.

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arXiv2022

Measurement of $e^{+}e^{-}\rightarrowπ^{+}π^{-}D^{+}D^{-}$ cross sections at center-of-mass energies from 4.190 to 4.946 GeV

Using data samples collected with the BESIII detector operating at the BEPCII storage ring, we measure the cross sections of the $e^{+}e^{-}\rightarrowπ^{+}π^{-}D^{+}D^{-}$ process at center-of-mass energies from 4.190 to 4.946 GeV with a partial reconstruction method. Two resonance structures are seen and the resonance parameters are determined from a fit to the cross section line shape. The first resonance we observe has a mass of (4373.1 $\pm$ 4.0 $\pm$ 2.2) MeV/$c^2$ and a width of (146.5 $\pm$ 7.4 $\pm$ 1.3) MeV, in agreement with those of the $Y(4390)$ state; the other resonance has a mass of (4706 $\pm$ 11 $\pm$ 4) MeV/$c^2$, a width of (45 $\pm$ 28 $\pm$ 9) MeV, and a statistical significance of $4.1$ standard deviations ($σ$). This is the first evidence for a vector state at this mass value. The spin-$3$ $D$-wave charmonium state $X(3842)$ is searched for through the $e^{+}e^{-}\rightarrowπ^{+}π^{-}X(3842)\rightarrowπ^{+}π^{-}D^{+}D^{-}$ process, and evidence with a significance of $4.2σ$ is found in the data samples with center-of-mass energies from 4.600 to 4.700 GeV.

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arXiv2022

Evidence for a neutral near-threshold structure in the $K^{0}_{\rm S}$ recoil-mass spectra in $e^+e^-\rightarrow K^{0}_{\rm S}D_s^+D^{-}$ and $e^+e^-\rightarrow K^{0}_{\rm S}D_s^{+}D^{-}$

We study the processes $e^+e^-\rightarrow K^{0}_{\rm S}D_s^+D^{*-}$ and $e^+e^-\rightarrow K^{0}_{\rm S}D_s^{*+}D^{-}$, as well as their charge conjugated processes, at five center-of-mass energies between 4.628~GeV and 4.699~GeV, using data samples corresponding to an integrated luminosity of $3.8~\rm{fb^{-1}}$ collected by the BESIII detector at the BEPCII storage ring. Based on a partial reconstruction technique, we find evidence of a structure near the thresholds for $D_s^+D^{*-}$ and $D_s^{*+}D^{-}$ production in the $K^{0}_{\rm S}$ recoil-mass spectrum, which we refer to as the $ Z_{cs}(3985)^0$. Fitting with a Breit-Wigner line shape, we find the mass of the structure to be $(3992.2\pm{1.7}\pm{1.6})~\rm{MeV}/c^2$ and the width to be $(7.7_{-3.8}^{+4.1}\pm{4.3})~\rm{MeV}$, where the first uncertainties are statistical and the second are systematic. The significance of the $ Z_{cs}(3985)^0$ signal is found to be $4.6σ$ including both the statistical and systematic uncertainty. We report the Born cross section multiplied by the branching fraction at different energy points. The mass of the $Z_{cs}(3985)^0$ is close to that of the $Z_{cs}(3985)^+$. Assuming SU(3) symmetry, the cross section of the neutral channel is consistent with that of the charged one. Hence, we conclude that the $Z_{cs}(3985)^0$ is the isospin partner of the $Z_{cs}(3985)^+$.

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arXiv2022

Cross section measurements of the processes $e^+e^- \rightarrow ωπ^{0}$ and $ωη$ at center-of-mass energies between 3.773 and 4.701 GeV

The Born cross sections of the processes $e^+e^- \rightarrow ωπ^{0}$ and $e^+e^- \rightarrow ωη$ are measured at center-of-mass energies between 3.773 and 4.701 GeV using a total integrated luminosity of 22.7 fb$^{-1}$ collected with the BESIII detector operating at the BEPCII collider. A simple $s^{-n}$ dependence for the continuum process can describe the measured Born cross sections. No significant contributions from the $ψ(4160)$, $Y(4230)$, $Y(4360)$, $ψ(4415)$, $Y(4660)$ resonances are found, which indicates relative small branching fractions for these resonances into the $ωπ^{0}$ and $ωη$ final states.

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arXiv2022

Measurement of the total and leptonic decay widths of the $J/ψ$ resonance with an energy scan method at BESIII

Using $e^+e^-$ annihilation data sets collected with the BESIII detector, we measure the cross sections of the processes $e^+e^- \to e^+e^-$ and $e^+e^- \to μ^+μ^-$ at fifteen center-of-mass energy points in the vicinity of the $J/ψ$ resonance. By a simultaneous fit to the measured, center-of-mass energy dependent cross sections of the two processes, the combined quantities $Γ_{ee} Γ_{ee} / Γ_{\rm tot}$ and $Γ_{ee} Γ_{μμ} / Γ_{\rm tot}$ are determined to be ($0.346 \pm 0.009$) and ($0.335 \pm 0.006$) keV, respectively, where $Γ_{ee}$, $Γ_{μμ}$, and $Γ_{\rm tot}$ are the electronic, muonic, and total decay widths of the $J/ψ$ resonance, respectively. Using the resultant $Γ_{ee} Γ_{μμ} / Γ_{\rm tot}$ and $Γ_{ee} Γ_{ee} / Γ_{\rm tot}$, the ratio $Γ_{ee} / Γ_{μμ}$ is calculated to be $1.031 \pm 0.015$, which is consistent with the expectation of lepton universality within about two standard deviations. Assuming lepton universality and using the branching fraction of the $J/ψ$ leptonic decay measured by BESIII in 2013, $Γ_{\rm tot}$ and $Γ_{ll}$ are determined to be ($93.0 \pm 2.1$) and ($5.56 \pm 0.11$) keV, respectively, where $Γ_{ll}$ is the average leptonic decay width of the $J/ψ$ resonance.

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arXiv2022

Absolute Measurements of Branching Fractions of Cabibbo-Suppressed Hadronic $D^{0(+)}$ Decays Involving Multiple Pions

By analyzing $e^+e^-$ annihilation data with an integrated luminosity of $2.93~\rm fb^{-1}$ collected at the center-of-mass energy $\sqrt s=$ 3.773 GeV with the BESIII detector, we present the first absolute measurements of the branching fractions of twenty Cabibbo-suppressed hadronic $D^{0(+)}$ decays involving multiple pions. The largest four branching fractions obtained are $\mathcal{B}(D^0\toπ^+π^-π^0)= (1.343\pm0.013_{\rm stat}\pm0.016_{\rm syst})\%$, $\mathcal{B}(D^0\toπ^+π^-2π^0)= (0.998\pm0.019_{\rm stat}\pm0.024_{\rm syst})\%$, $\mathcal{B}(D^+\to 2π^+π^-π^0)= (1.174\pm0.021_{\rm stat}\pm0.021_{\rm syst})\%$, and $\mathcal{B}(D^+\to 2π^+π^-2π^0)=(1.074\pm0.040_{\rm stat}\pm0.030_{\rm syst})\%$. The $CP$ asymmetries for the six decays with highest event yields are also determined.

hep-ex↗