arXiv subjects

Y. B. Li

Publications and source records attributed to Y. B. Li.

At least 55 records · Page 3Linked to original sources

arXiv2020

Study of Electromagnetic Decays of Orbitally Excited $Ξ_c$ Baryons

Using 980 $fb^-1$ of data collected with the Belle detector operating at the KEKB asymmetric-energy e^+e^- collider, we report a study of the electromagnetic decays of excited {charmed baryons} $Ξ_c(2790)$ and $Ξ_c(2815)$. A clear signal (8.6 standard deviations) is observed for $Ξ_c(2815)^0 \to Ξ_c^0γ$, and we measure: $B[Ξ_c(2815)^0 \to Ξ_c^0γ]/B[Ξ_c(2815)^0 \to Ξ_c(2645)^+π^- \to Ξ_c^0π^+π^-] = 0.41 \pm 0.05 \pm 0.03$. We also present evidence (3.8 standard deviations) for the similar decay of the $Ξ_c(2790)^0$ and measure: $B[Ξ_c(2790)^{0}\toΞ_c^{0}γ]/B[Ξ_c(2790)^0\toΞ_c^{\prime +}π^{-}\toΞ_c^{+}γπ^-] = 0.13 \pm 0.03 \pm 0.02$. The first quoted uncertainties are statistical and the second systematic. We find no hint of the analogous decays of the $Ξ_c(2815)^+$ and $Ξ_c(2790)^+$ baryons and set upper limits at the 90% confidence level of: $B[Ξ_c(2815)^{+}\toΞ_c^{+}γ]/B[Ξ_c(2815)^+\toΞ_c(2645)^0π^+\toΞ_c^+π^-π^+] < 0.09,$ and $B[Ξ_c(2790)^{+}\toΞ_c^{+}γ]/B[Ξ_c(2790)^+\toΞ_c^{\prime 0}π^{+}\toΞ_c^{0}γπ^+] < 0.06.$ Approximate values of the partial widths of the decays are extracted, which can be used to discriminate between models of the underlying quark structure of these excited states.

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arXiv2020

Measurement of the charm-mixing parameter $y_{CP}$ in $D^{0}\to K^{0}_{S}ω$ decays at Belle

We report the first measurement of the charm-mixing parameter $y_{CP}$ in $D^{0}$ decays to the $CP$-odd final state $K^{0}_{S}ω$. The study uses the full Belle $e^{+}e^-$ annihilation data sample of $976\rm~ fb^{-1}$ taken at or near the $Υ(4S)$ centre-of-mass energy. We find $y_{CP} = (0.96 \pm 0.91 \pm 0.61 {}^{+0.17}_{-0.00})\%$, where the first uncertainty is statistical, the second is systematic due to event selection and background, and the last is due to possible presence of $CP$-even decays in the data sample.

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arXiv2020

Test of lepton-flavor universality in ${B\to K^\ast\ell^+\ell^-}$ decays at Belle

We present a measurement of $R_{K^{\ast}}$, the branching fraction ratio ${{\cal B}(B\to K^\ast μ^+ μ^-)}$/ ${{\cal B}(B\to K^\ast e^+ e^-)}$, for both charged and neutral $B$ mesons. The ratio for the charged case, $R_{K{^{\ast +}}}$, is the first measurement ever performed. In addition, we report absolute branching fractions for the individual modes in bins of the squared dilepton invariant mass, $q^2$. The analysis is based on a data sample of $711~\mathrm{fb}^{-1}$, containing $772\times 10^{6}$ $B\bar B$ events, recorded at the $Υ(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. The obtained results are consistent with Standard Model expectations.

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arXiv2020

Measurement of Branching Fractions of $Λ_{c}^{+} \rightarrow ηΛπ^{+}$, $ηΣ^{0} π^{+}$, $Λ(1670) π^{+}$, and $ηΣ(1385)^{+}$

We report branching fraction measurements of four decay modes of the $Λ_{c}^{+}$ baryon, each of which includes an $η$ meson and a $Λ$ baryon in the final state, and all of which are measured relative to the $Λ_{c}^{+} \rightarrow p K^{-} pi^{+}$ decay mode. The results are based on a $980~\mathrm{fb^{-1}}$ data sample collected by the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. Two decays, $ηΣ^{0} π^{+}$ and $Λ(1670) π^{+}$, are observed for the first time, while the measurements of the other decay modes, $Λ_{c}^{+} \rightarrow ηΛπ^{+}$ and $ηΣ(1385)^{+}$, are more precise than those made previously. We obtain $\mathcal{B}(Λ_{c}^{+} \rightarrow ηΛπ^{+})/\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} π^{+})$ = $0.293 \pm 0.003 \pm 0.014$, $\mathcal{B}(Λ_{c}^{+} \rightarrow ηΣ^{0} π^{+})/\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} π^{+})$ = $0.120 \pm 0.006 \pm 0.006$, $\mathcal{B}(Λ_{c}^{+} \rightarrow Λ(1670) π^{+}) \times \mathcal{B}(Λ(1670) \rightarrow ηΛ)/\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} π^{+})$ = $(5.54 \pm 0.29 \pm 0.73 ) \times 10^{-2}$, and $\mathcal{B}(Λ_{c}^{+} \rightarrow ηΣ(1385)^{+})/\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} π^{+})$ = $0.192 \pm 0.006 \pm 0.016$. The mass and width of the $Λ(1670)$ are also precisely determined to be $1674.3 \pm 0.8 \pm 4.9~{\rm MeV}/c^{2}$ and $36.1 \pm 2.4 \pm 4.8~{\rm MeV}$, respectively, where the uncertainties are statistical and systematic, respectively.

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arXiv2020

Spectroscopic Monitoring of Blazar S5 0716+714: Brightness-Dependent Spectral Behavior

In this paper, we report the new results of spectroscopic observations of $γ$-ray blazar S5 0716+714 from 2019 September to 2020 March with the 2.4 m optical telescope at Lijiang Observatory of Yunnan Observatories. The median cadence of observations is $\sim$ 1 day. During the second observation period (Epoch2), the observational data reveal an extremely bright state and a bluer-when-brighter (BWB) chromatism. The BWB trend of Epoch2 differs significantly from that of the first observation period (Epoch1). A significantly brightness-dependent BWB chromatism emerges in the total data of Epoch1 and Epoch2. The BWB trend becomes weaker towards the brighter states, and likely becomes saturated at the highest state. Based on a log-parabolic function, a power-law of synchrotron peak flux and frequency $ν_{\rm{p}}$, and a power-law of the curvature of synchrotron spectrum and its $ν_{\rm{p}}$, simulation well reproduces the brightness-dependent BWB trend of S5 0716+714. The BWB trend is seemingly controlled by the shift of $ν_{\rm{p}}$ with respect to the observational window, and effectively may be dominated by the variations of electron average energy and magnetic field in emitting region.

astro-ph.HE↗

arXiv2020

Dalitz analysis of $D^{0}\to K^{-}π^{+}η$ decays at Belle

We present the results of the first Dalitz plot analysis of the decay $D^{0}\to K^{-}π^{+}η$. The analysis is performed on a data set corresponding to an integrated luminosity of 953 $\rm{fb}^{-1}$ collected by the Belle detector at the asymmetric-energy $e^{+}e^{-}$ KEKB collider. The Dalitz plot is well described by a combination of the six resonant decay channels $\bar{K}^{*}(892)^0η$, $K^{-}a_0(980)^+$, $K^{-}a_2(1320)^+$, $\bar{K}^{*}(1410)^0η$, $K^{*}(1680)^-π^{+}$ and $K_2^{*}(1980)^-π^{+}$, together with $Kπ$ and $Kη$ S-wave components. The decays $K^{*}(1680)^{-}\to K^{-}η$ and $K_{2}^{*}(1980)^{-}\to K^{-}η$ are observed for the first time. We measure ratio of the branching fractions, $\frac{\mathcal{B}(D^{0}\to K^{-}π^{+}η)}{\mathcal{B}(D^{0}\to K^{-}π^{+})}=0.500\pm0.002{\rm(stat)}\pm0.020{\rm(syst)}\pm0.003{\rm (\mathcal{B}_{PDG})}$. Using the Dalitz fit result, the ratio $\frac{\mathcal{B}(K^{*}(1680)\to Kη)}{\mathcal{B}(K^{*}(1680)\to Kπ)}$ is measured to be $0.11\pm0.02{\rm(stat)}^{+0.06}_{-0.04}{\rm(syst)}\pm0.04{\rm(\mathcal{B}_{\text{PDG}})}$; this is much lower than the theoretical expectations ($\approx1$) made under the assumption that $K^{*}(1680)$ is a pure $1^{3}D_1$ state. The product branching fraction $\mathcal{B}(D^0\to [K_2^{*}(1980)^-\to K^{-}η]π^{+})=(2.2^{+1.7}_{-1.9})\times10^{-4}$ is determined. In addition, the $πη^{\prime}$ contribution to the $a_0(980)^{\pm}$ resonance shape is confirmed with 10.1$σ$ statistical significance using the three-channel Flatté model. We also measure $\mathcal{B}(D^0\to\bar{K}^{*}(892)^0η)=(1.41^{+0.13}_{-0.12})\%$. This is consistent with, and more precise than, the current world average $(1.02\pm0.30)\%$, deviates with a significance of more than $3σ$ from the theoretical predictions of (0.51-0.92)%.

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arXiv2020

Search for $B^0$ Decays to Invisible Final States ($+γ$) at Belle

We report searches for $B^0\to\rm{invisible}$ and $B^0\to\rm{invisible}+γ$ decays, where the energy of the photon is required to be larger than 0.5 GeV. These results are obtained from a $711\,{\rm fb}^{-1}$ data sample that contains $772 \times 10^6 B\bar{B}$ pairs and was collected near the $Υ\,(4S)$ resonance with the Belle detector at the KEKB $e^+ e^-$ collider. We observe no significant signal for either decay and set upper limits on their branching fractions at $90\%$ confidence level of $\mathcal{B}\,(B^0\to\rm{invisible}) < 7.8\times10^{-5}$ and $\mathcal{B}\,(B^0\to\rm{invisible}+γ) < 1.6\times10^{-5}$.

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arXiv2020

First search for the $η_{c2}(1D)$ in $B$ decays at Belle

The first dedicated search for the $η_{c2}(1D)$ is carried out using the decays $B^+ \rightarrow η_{c2}(1D) K^+$, $B^0 \rightarrow η_{c2}(1D) K^0_S$, $B^0 \rightarrow η_{c2}(1D) π^- K^+$, and $B^+ \rightarrow η_{c2}(1D) π^+ K^0_S$ with $η_{c2}(1D) \to h_c γ$. No significant signal is found. For the $η_{c2}(1D)$ mass range between $3795$ and $3845\ \mathrm{MeV}/c^2$, the branching-fraction upper limits are determined to be $\mathcal{B}(B^+ \rightarrow η_{c2}(1D) K^+) \times \mathcal{B}(η_{c2}(1D) \to h_c γ) < 3.7 \times 10^{-5}$, $\mathcal{B}(B^0 \rightarrow η_{c2}(1D) K^0_S) \times \mathcal{B}(η_{c2}(1D) \to h_c γ) < 3.5 \times 10^{-5}$, $\mathcal{B}(B^0 \rightarrow η_{c2}(1D) π^- K^+) \times \mathcal{B}(η_{c2}(1D) \to h_c γ) < 1.0 \times 10^{-4}$, and $\mathcal{B}(B^+ \rightarrow η_{c2}(1D) π^+ K^0_S) \times \mathcal{B}(η_{c2}(1D) \to h_c γ) < 1.1 \times 10^{-4}$ at 90% C. L. The analysis is based on the 711 $\mathrm{fb}^{-1}$ data sample collected on the $Υ(4S)$ resonance by the Belle detector, which operated at the KEKB asymmetric-energy $e^+ e^-$ collider.

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arXiv2020

Evidence for a vector charmonium-like state in $e^+e^- \to D^+_sD^*_{s2}(2573)^-+c.c.$

We report the measurement of $e^+e^- \to D^+_sD^*_{s2}(2573)^-+c.c.$ via initial-state radiation using a data sample of an integrated luminosity of 921.9 fb$^{-1}$ collected with the Belle detector at the $Υ(4S)$ and nearby. We find evidence for an enhancement with a 3.4$σ$ significance in the invariant mass of $D^+_sD^*_{s2}(2573)^- +c.c.$ The measured mass and width are $(4619.8^{+8.9}_{-8.0}({\rm stat.})\pm2.3({\rm syst.}))~{\rm MeV}/c^{2}$ and $(47.0^{+31.3}_{-14.8}({\rm stat.})\pm4.6({\rm syst.}))~{\rm MeV}$, respectively. The mass, width, and quantum numbers of this enhancement are consistent with the charmonium-like state at 4626 MeV/$c^2$ recently reported by Belle in $e^+e^-\to D^+_sD_{s1}(2536)^-+c.c.$ The product of the $e^+e^-\to D^+_sD^*_{s2}(2573)^-+c.c.$ cross section and the branching fraction of $D^*_{s2}(2573)^-\to{\bar D}^0K^-$ is measured from $D^+_sD^*_{s2}(2573)^-$ threshold to 5.6 GeV.

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arXiv2020

Multi-wavelength observations of the BL Lac object Fermi J1544-0649: one year after its awakening

We report observations of a transient source \fermi\ from radio to \grs. \fermi\ was discovered by the {\it Fermi-LAT} in May 2017. Follow-up {\it Swift-XRT} observations revealed three flaring episodes through March 2018, and the peak X-ray flux is about $10^3$ higher than the {\it ROSAT all-sky survey (RASS)} flux upper limit. Optical spectral measurements taken by the {\it Magellan 6.5-m telescope} and the {\it Lick-Shane telescope} both show a largely featureless spectrum, strengthening the BL Lac interpretation first proposed by \citet{Bruni18}. The optical and mid-infrared (MIR) emission goes to a higher state in 2018, when the flux in high energies goes down to a lower level. Our {\it RATAN-600m} measurements at 4.8~GHz and 8.2~GHz do not indicate any significant radio flux variation over the monitoring seasons in 2017 and 2018, nor deviate from the archival {\it NVSS} flux level. During GeV flaring times, the spectrum is very hard ($Γ_γ\sim$1.7) in the GeV band and at times also very hard (($Γ_{\rm X}\lesssim2$) in the X-rays, similar to a high-synchrotron-peak (or even an extreme) BL Lac object, making \fermi\ a good target for ground-based {\it Cherenkov telescopes}.

astro-ph.HE↗

arXiv2020

Update of inclusive cross sections of single and pairs of identified light charged hadrons

We report new measurements of the production cross sections of pairs of charged pions and kaons as a function of their fractional energies using various fractional-energy definitions. Two different fractional-energy definitions were used and compared to the conventional fractional-energy definition reported previously. The new variables aim at either identifying dihadron cross sections in terms of single-hadron fragmentation functions, or to provide a means of characterizing the transverse momentum created in the fragmentation process. The results were obtained applying the updated initial-state radiation correction used in other recent Belle publications on light-hadron production cross sections. In addition, production cross sections of single charged pions, kaons, and protons were also updated using this initial-state radiation correction. The cross sections are obtained from a $558\,{\rm fb}^{-1}$ data sample collected at the $Υ(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider.

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arXiv2019

Measurements of the Branching Fractions ${\cal B}(B^{-} \to \barΛ_{c}^{-} Ξ_{c}^{'0})$, ${\cal B}(B^{-} \to \barΛ_{c}^{-} Ξ_{c}(2645)^{0})$ and ${\cal B}(B^{-} \to \barΛ_{c}^{-} Ξ_{c}(2790)^{0}) $

Using the data sample of 711 fb$^{-1}$ of $Υ(4S)$ on-resonance data taken by the Belle detector at the KEKB asymmetric-energy electron-positron collider, we present the first measurements of branching fractions of the decays $B^{-} \to \barΛ_{c}^{-} Ξ_{c}^{'0}$, $B^{-} \to \barΛ_{c}^{-} Ξ_{c}(2645)^{0}$, and $B^{-} \to \barΛ_{c}^{-} Ξ_{c}(2790)^{0} $. The signal yields for these decays are extracted from the recoil mass spectrum of the system recoiling against $\barΛ_{c}^{-}$ baryons in selected $B^-$ candidates. The branching fraction of $B^{-} \to \barΛ_{c}^{-} Ξ_{c}(2790)^{0}$ is measured to be $ (1.1 \pm 0.4 \pm 0.2)\times 10^{-3}$, where the first uncertainty is statistical and the second systematic. The 90\% credibility level upper limits on ${\cal B}(B^{-} \to \barΛ_{c}^{-} Ξ_{c}^{'0})$ and ${\cal B}(B^{-} \to \barΛ_{c}^{-} Ξ_{c}(2645)^{0})$ are determined to be $6.5\times 10^{-4}$ and $7.9\times 10^{-4}$, respectively.

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arXiv2019

Quasi-simultaneous Spectroscopic and Multi-band Photometric Observations of Blazar S5 0716+714 during 2018-2019

In order to study short timescale optical variability of $γ$-ray blazar S5 0716+714, quasi-simultaneous spectroscopic and multi-band photometric observations were performed from 2018 November to 2019 March with the 2.4 m optical telescope located at Lijiang Observatory of Yunnan Observatories. The observed spectra are well fitted with a power-law $F_λ=Aλ^{-α}$ (spectral index $α>0$). Correlations found between $\dotα$, $\dot{A}$, $\dot{A}/A$, $\dot{F_{\rmλ}}$, and $\dot{F_{\rmλ}}/F_{\rmλ}$ are consistent with the trend of bluer-when-brighter (BWB). \textbf{The same case is for colors, magnitudes, color variation rates, and magnitude variation rates of photometric observations.} The variations of $α$ lead those of $F_{\rmλ}$. Also, the color variations lead the magnitude variations. The observational data are mostly distributed in the I(+,+) and III(-,-) quadrants of coordinate system. Both of spectroscopic and photometric observations show BWB behaviors in S5 0716+714. The observed BWB may be explained by the shock-jet model, and its appearance may depend on the relative position of the observational frequency ranges with respect to the synchrotron peak frequencies, e.g., at the left of the peak frequencies. \textbf{Fractional variability amplitudes are $F_{\rm{var}}\sim 40\%$ for both of spectroscopic and photometric observations. Variations of $α$ indicate variations of relativistic electron distribution producing the optical spectra. }

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arXiv2019

Photometric and spectroscopic Studies of Superoutbursts of Three Dwarf Novae Independently Identified by The SVOM/GWAC System in 2018

We report our photometric and spectroscopic follow-up observations of the superoutbursts of three dwarf novae (GWAC\,180415A, GWAC\,181017A and GWAC\,181211A) identified independently by the Ground Wide-angle Cameras system, one of the ground-based instruments of the China-France SVOM mission. Based on a combination of our photometry and that taken from the AAVSO, our period analysis of the superhumps enables us to determine the mass ratios to be 0.0967-0.1163, 0.1879-0.1883 and 0.0981-0.1173 for GWAC\,180415A, GWAC\,181017A and GWAC\,181211A, respectively. GWAC\,180415A can be firmly identified as a WZ sge-type dwarf novae due to its long duration ($\sim2$ weeks) multiple rebrightenings with amplitudes of 3-4 magnitudes, the early superhump associated with a double-wave modulation and the low mass ratio. The inferred low mass ratio and location in the $\varepsilon-P_{\mathrm{orb}}$ diagram suggest that GWAC\,181211A is a WZ sge-type dwarf novae candidate. The measured Balmer decrements suggest the Balmer line emission is produced from an optical thick region in GWAC\,180415A and GWAC\,181017A, and from an optical thin region in GWAC\,181211A.

astro-ph.SR↗

arXiv2019

Observation of a vector charmoniumlike state in $e^+e^- \to D^+_sD_{s1}(2536)^-+c.c.$

Using a data sample of 921.9 fb$^{-1}$ collected with the Belle detector, we study the process of $e^+e^-\to D^+_sD_{s1}(2536)^-+c.c.$ via initial-state radiation. We report the first observation of a vector charmoniumlike state decaying to $D^+_sD_{s1}(2536)^-+c.c.$ with a significance of 5.9$σ$, including the systematic uncertainties. The measured mass and width are $(4625.9^{+6.2}_{-6.0}({\rm stat.})\pm0.4({\rm syst.}))~{\rm MeV}/c^{2}$ and $(49.8^{+13.9}_{-11.5}({\rm stat.})\pm4.0({\rm syst.}))~{\rm MeV}$, respectively. The product of the $e^+e^-\to D^+_sD_{s1}(2536)^-+c.c.$ cross section and the branching fraction of $D_{s1}(2536)^-\to{\bar D}^{*0}K^-$ is measured from the $D_s \bar{D}_{s1}(2536)$ threshold to 5.59~GeV.

hep-ex↗

arXiv2019

Observation of the radiative decays of $Υ(1S)$ to $χ_{c1}$

We report the first observation of the radiative decay of the $Υ(1S)$ into a charmonium state. The statistical significance of the observed signal of $Υ(1S) \to γχ_{c1}$ is 6.3 standard deviations including systematics. The branching fraction is calculated to be Br($Υ(1S) \to γχ_{c1}$) = (4.7^{+2.4}_{-1.8} (stat) ^{+0.4}_{-0.5} (sys)) * 10^{-5}. We also searched for $Υ(1S)$ radiative decays into $χ_{c0,2}$ and $η_c(1S,2S)$ and set upper limits on their branching fractions. These results are obtained from a 24.9 fb^{-1} data sample collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider at a center-of-mass energy equal to the $Υ(2S)$ mass using $Υ(1S)$ tagging by the $Υ(2S) \to Υ(1S) π^+π^-$ transitions.

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arXiv2019

Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$ with a semileptonic tagging method

The experimental results on the ratios of branching fractions $\mathcal{R}(D) = {\cal B}(\bar{B} \to D τ^- \barν_τ)/{\cal B}(\bar{B} \to D \ell^- \barν_{\ell})$ and $\mathcal{R}(D^*) = {\cal B}(\bar{B} \to D^* τ^- \barν_τ)/{\cal B}(\bar{B} \to D^* \ell^- \barν_{\ell})$, where $\ell$ denotes an electron or a muon, show a long-standing discrepancy with the Standard Model predictions, and might hint to a violation of lepton flavor universality. We report a new simultaneous measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$, based on a data sample containing $772 \times 10^6$ $B\bar{B}$ events recorded at the $Υ(4S)$ resonance with the Belle detector at the KEKB $e^+ e^-$ collider. In this analysis the tag-side $B$ meson is reconstructed in a semileptonic decay mode and the signal-side $τ$ is reconstructed in a purely leptonic decay. The measured values are $\mathcal{R}(D)= 0.307 \pm 0.037 \pm 0.016$ and $\mathcal{R}(D^*) = 0.283 \pm 0.018 \pm 0.014$, where the first uncertainties are statistical and the second are systematic. These results are in agreement with the Standard Model predictions within $0.2$, $1.1$ and $0.8$ standard deviations for $\mathcal{R}(D)$, $\mathcal{R}(D^*)$ and their combination, respectively. This work constitutes the most precise measurements of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$ performed to date as well as the first result for $\mathcal{R}(D)$ based on a semileptonic tagging method.

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arXiv2019

First measurement of the CKM angle $ϕ_3$ with $B^{\pm}\to D(K_{\rm S}^0π^+π^-π^0)K^{\pm}$ decays

We present the first model-independent measurement of the CKM unitarity triangle angle $ϕ_3$ using $B^{\pm}\to D(K_{\rm S}^0π^+π^-π^0)K^{\pm}$ decays, where $D$ indicates either a $D^{0}$ or $\overline{D}^{0}$ meson. Measurements of the strong-phase difference of the $D \to K_{\rm S}^0π^+π^-π^0$ amplitude obtained from CLEO-c data are used as input. This analysis is based on the full Belle data set of $772\times 10^{6}$ $B\overline{B}$ events collected at the $Υ(4S)$ resonance. We obtain $ϕ_3 = (5.7~^{+10.2}_{-8.8} \pm 3.5 \pm 5.7)^{\circ}$ and the suppressed amplitude ratio $r_{B} = 0.323 \pm 0.147 \pm 0.023 \pm 0.051$. Here the first uncertainty is statistical, the second is the experimental systematic, and the third is due to the precision of the strong-phase parameters measured from CLEO-c data. The 95% confidence interval on $ϕ_3$ is $(-29.7,~109.5)^{\circ}$, which is consistent with the current world average.

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