arXiv subjects

K. Lalwani

Publications and source records attributed to K. Lalwani.

At least 37 records · Page 2Linked to original sources

arXiv2021

Search for the dark photon in $B^0 \to A^{\prime} A^{\prime}$, $A^{\prime} \to e^+ e^-$, $μ^+ μ^-$, and $π^+ π^-$ decays at Belle

We present a search for the dark photon $A^{\prime}$ in the $B^0 \to A^{\prime} A^{\prime}$ decays, where $A^{\prime}$ subsequently decays to $e^+ e^-$, $μ^+ μ^-$, and $π^+ π^-$. The search is performed by analyzing $772 \times 10^6$ $B\overline{B}$ events collected by the Belle detector at the KEKB $e^+ e^-$ energy-asymmetric collider at the $Υ(4S)$ resonance. No signal is found in the dark photon mass range $0.01~\mathrm{GeV}/c^2 \le m_{A^{\prime}} \le 2.62~\mathrm{GeV}/c^2$, and we set upper limits of the branching fraction of $B^0 \to A^{\prime} A^{\prime}$ at the 90\% confidence level. The products of branching fractions, $\mathcal{B}(B^0 \to A^{\prime} A^{\prime}) \times \mathcal{B}(A^{\prime} \to e^+ e^-)^2$ and $\mathcal{B}(B^0 \to A^{\prime} A^{\prime}) \times \mathcal{B}(A^{\prime} \to μ^+ μ^-)^2$, have limits of the order of $10^{-8}$ depending on the $A^{\prime}$ mass. Furthermore, considering $A^{\prime}$ decay rate to each pair of charged particles, the upper limits of $\mathcal{B}(B^0 \to A^{\prime} A^{\prime})$ are of the order of $10^{-8}$-$10^{-5}$. From the upper limits of $\mathcal{B}(B^0 \to A^{\prime} A^{\prime})$, we obtain the Higgs portal coupling for each assumed dark photon and dark Higgs mass. The Higgs portal couplings are of the order of $10^{-2}$-$10^{-1}$ at $m_{h'} \simeq m_{B^0} \pm 40~\mathrm{MeV}/c^2$ and $10^{-1}$-$1$ at $m_{h'} \simeq m_{B^0} \pm 3~\mathrm{GeV}/c^2$.

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arXiv2021

Measurement of the Branching Fraction of the Decay $\boldsymbol{B^{+}\toπ^{+}π^{-}\ell^{+}ν_\ell}$ in Fully Reconstructed Events at Belle

We present an analysis of the exclusive $B^{+}\toπ^{+}π^{-}\ell^{+}ν_{\ell}$ decay, where $\ell$ represents an electron or a muon, with the assumption of charge-conjugation symmetry and lepton universality. The analysis uses the full $Υ(4S)$ data sample collected by the Belle detector, corresponding to 711 fb$^{-1}$ of integrated luminosity. We select the events by fully reconstructing one $B$ meson in hadronic decay modes, subsequently determining the properties of the other $B$ meson. We extract the signal yields using a binned maximum-likelihood fit to the missing-mass squared distribution in bins of the invariant mass of the two pions or the momentum transfer squared. We measure a total branching fraction of ${{\cal B}(B^{+}\to π^{+}π^{-}\ell^{+}ν_{\ell})= [22.7 ^{+1.9}_{-1.6} (\mathrm{stat}) \pm 3.5(\mathrm{syst}) ]\times 10^{-5}}$, where the uncertainties are statistical and systematic, respectively. This result is the first reported measurement of this decay.

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arXiv2021

Measurement of branching fractions and $CP$ asymmetries for $D_s^{+} \rightarrow K^+ (η, π^0) $ and $D_s^{+} \rightarrow π^+ (η, π^0)$ decays at Belle

We report measurements of the branching fractions and $CP$ asymmetries for $D_s^{+} \rightarrow K^{+} η$, $D_s^{+} \rightarrow K^{+} π^0 $, and $D_s^{+} \rightarrow π^{+} η$ decays, and the branching fraction for $D_s^{+} \rightarrow π^{+} π^0$. Our results are based on a data sample corresponding to an integrated luminosity of 921 fb$^{-1}$ collected by the Belle detector at the KEKB $e^+e^-$ asymmetric-energy collider. Our measurements of $CP$ asymmetries in these decays are the most precise to-date; no evidence for $CP$ violation is found.

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arXiv2021

Measurement of Branching Fraction and Search for $CP$ Violation in $B\to ϕϕK$

We report the measurement of branching fractions and $CP$-violation asymmetries in $B\to ϕϕK$ decays based on a $711\,{\rm fb}^{-1}$ data sample containing $772\times 10^6$ $B\bar{B}$ events. The data were recorded at the $Υ(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. For $B^+ \to ϕϕK^+$, the branching fraction and $CP$-violation asymmetry measured below the $η_{c}$ threshold ($m_{ϕϕ}<2.85\,{\rm GeV}/c^2$) are $[3.43^{\,+\,0.48}_{\,-\,0.46}({\rm stat})\pm 0.22({\rm syst})] \times10^{-6}$ and $-0.02\pm0.11({\rm stat})\pm0.01({\rm syst})$, respectively. Similarly, the branching fraction obtained for $B^0 \toϕϕK^0$ below the $η_{c}$ threshold is $[3.02^{\,+\,0.75}_{\,-\,0.66} ({\rm stat})\pm \,0.20({\rm syst})]\times10^{-6}$. We also measure the $CP$-violation asymmetry for $B^+ \toϕϕK^+$ within the $η_{c}$ region ($m_{ϕϕ}\in [2.94,3.02]\,{\rm GeV}/c^2$) to be $+0.12\pm0.12({\rm stat})\pm0.01({\rm syst})$.

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arXiv2020

Search for a doubly-charged $DDK$ bound state in $Υ(1S,2S)$ inclusive decays and via direct production in $e^+e^-$ collisions at $\sqrt{s}$ = 10.520, 10.580, and 10.867 GeV

We report the results of a first search for a doubly-charged $DDK$ bound state, denoted the $R^{++}$, in $Υ(1S)$ and $Υ(2S)$ inclusive decays and via direct production in $e^+e^-$ collisions at $\sqrt{s}$ = 10.520, 10.580, and 10.867 GeV. The search uses data accumulated with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. No significant signals are observed in the $D^{+}D_{s}^{*+}$ invariant-mass spectra of all studied modes. The 90\% credibility level upper limits on their product branching fractions in $Υ(1S)$ and $Υ(2S)$ inclusive decays (${\cal B}(Υ(1S,2S) \to R^{++} + anything) \times {\cal B}(R^{++} \to D^{+} D_{s}^{*+})$), and the product values of Born cross section and branching fraction in $e^+e^-$ collisions ($σ(e^+e^- \to R^{++} + anything) \times {\cal B}(R^{++} \to D^{+} D_{s}^{*+})$) at $\sqrt{s}$ = 10.520, 10.580, and 10.867 GeV under different assumptions of $R^{++}$ masses varying from 4.13 to 4.17 GeV/$c^2$, and widths varying from 0 to 5 MeV are obtained.

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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

Search for the $η$ mesic $^3$He in the $pd\rightarrow d p π^{0}$ reaction with the WASA-at-COSY facility

The excitation function for the $pd\rightarrow$ $d p π^{0}$ reaction has been measured by WASA-at-COSY experiment with the aim of searching for $^{3}\hspace{-0.03cm}\mbox{He}$-$η$ mesic nuclei. The measurement in the vicinity of $η$ meson production was performed using a ramped proton beam. The data analysis and interpretation was carried out with the assumption that the $η$-mesic Helium decays via the formation of an intermediate N$^{*}$(1535) resonance. No direct signal of the $η$-mesic nucleus is observed in the excitation function. We determine a new improved upper limit for the total cross section for the bound state production and decay in the $pd\rightarrow$ $(^{3}\hspace{-0.03cm}\mbox{He}$-$η)_{bound} \rightarrow$ $d p π^{0}$ process. It varies between 13 nb to 24 nb for the bound state with width in the range $Γ\in (5,50)$ MeV.

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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

Isoscalar Single-Pion Production in the Region of Roper and $d^*(2380)$ Resonances

Exclusive measurements of the quasi-free $pn \to ppπ^-$ and $pp \to ppπ^0$ reactions have been performed by means of $pd$ collisions at $T_p$ = 1.2 GeV using the WASA detector setup at COSY. Total and differential cross sections have been obtained covering the energy region $T_p = 0.95 - 1.3$ GeV ($\sqrt s$ = 2.3 - 2.46 GeV), which includes the regions of $Δ(1232)$, $N^*(1440)$ and $d^*(2380)$ resonance excitations. From these measurements the isoscalar single-pion production has been extracted, for which data existed so far only below $T_p$ = 1 GeV. We observe a substantial increase of this cross section above 1 GeV, which can be related to the Roper resonance $N^*(1440)$, the strength of which shows up isolated from the $Δ$ resonance in the isoscalar $(Nπ)_{I=0}$ invariant-mass spectrum. No evidence for a decay of the dibaryon resonance $d^*(2380)$ into the isoscalar $(NNπ)_{I=0}$ channel is found. An upper limit of 90 $μ$b (90 $\%$ C.L.) corresponding to a branching ratio of 5 $\%$ has been deduced.

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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

Differential Cross Sections for Neutron-Proton Scattering in the Region of the $d^*(2380)$ Dibaryon Resonance

Differential cross sections have been extracted from exclusive and kinematically complete high-statistics measurements of quasifree polarized $\vec{n}p$ scattering performed in the energy region of the $d^*(2380)$ dibaryon resonance covering the the range of beam energies $T_n$ = 0.98 - 1.29 GeV ($\sqrt s$ = 2.32 - 2.44 GeV). The experiment was carried out with the WASA-at-COSY setup having a polarized deuteron beam impinged on the hydrogen pellet target and utilizing the quasifree process $dp \to np + p_{spectator}$. That way the $np$ differential cross section $σ(Θ)$ was measured over a large angular range. The obtained angular distributions complement the corresponding analyzing power $A_y(Θ)$ measurements published previously. A SAID partial-wave analysis incorporating the new data strengthens the finding of a resonance pole in the coupled $^3D_3 - ^3G_3$ waves.

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arXiv2020

Search for eta mesic 3He with the WASA-at-COSY facility in the pd-> 3He 2gamma and pd-> 3He 6gamma reactions

We report on the experimental search for the bound state of an $η$ meson and $^{3}\hspace{-0.03cm}\mbox{He}$ nucleus performed using the WASA-at-COSY detector setup. In order to search for the $η$-mesic nucleus decay, the $pd\rightarrow$ $^{3}\hspace{-0.03cm}\mbox{He} 2γ$ and $pd\rightarrow$ $^{3}\hspace{-0.03cm}\mbox{He} 6γ$ channels have been analysed. These reactions manifest the direct decay of $η$ meson bound in $^{3}\hspace{-0.03cm}\mbox{He}$ nucleus. This non-mesonic decay channel has been considered for the first time. When taking into account only statistical errors, the obtained excitation functions reveal a slight indication for a possible bound state signal corresponding to an $^3$He-$η$ nucleus width $Γ$ above 20 MeV and binding energy $B_s$ between 0 and 15 MeV. However, the determined cross sections are consistent with zero in the range of the systematic uncertainty. Therefore, as final result we estimate only the upper limit for the cross section of the $η$-mesic $^{3}\hspace{-0.03cm}\mbox{He}$ nucleus formation followed by the $η$ meson decay which varies between $2$ nb and $15$ nb depending on possible bound state parameters.

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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

Study of Three-Nucleon Dynamics in the dp breakup collisions using the WASA detector

Differential cross section for the 1H(d,pp)n breakup reaction at deuteron beam energy of 340 MeV has been measured with the use of WASA detector at COSY-Juelich. The set of proton-proton coincidences registered at Forward Detector has been analysed on dense grid of kinematic variables, giving in total around 5600 data points. The cross section data are compared to theoretical predictions based on the state-of-the-art nucleon-nucleon potentials, combined with three-nucleon force, Coulomb interaction or carried out in a relativistic regime.

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arXiv2019

Search for $B^+ \to μ^+\, ν_μ$ and $B^+ \to μ^+\, N$ with inclusive tagging

We report the result for a search for the leptonic decay of $B^+ \to μ^+ \, ν_μ$ using the full Belle data set of 711 fb${}^{-1}$ of integrated luminosity at the $Υ(4S)$ resonance. In the Standard Model leptonic $B$-meson decays are helicity and CKM suppressed. To maximize sensitivity an inclusive tagging approach is used to reconstruct the second $B$ meson produced in the collision. The directional information from this second $B$ meson is used to boost the observed $μ$ into the signal $B$ meson rest-frame, in which the $μ$ has a monochromatic momentum spectrum. Though its momentum is smeared by the experimental resolution, this technique improves the analysis sensitivity considerably. Analyzing the $μ$ momentum spectrum in this frame we find $\mathcal{B}(B^+ \to μ^+ \, ν_μ) = \left( 5.3 \pm 2.0 \pm 0.9 \right) \times 10^{-7}$ with a one-sided significance of 2.8 standard deviations over the background-only hypothesis. This translates to a frequentist upper limit of $\mathcal{B}(B^+ \to μ^+ \, ν_μ) < 8.6 \times 10^{-7}$ at 90% CL. The experimental spectrum is then used to search for a massive sterile neutrino, $B^+ \to μ^+ \, N$, but no evidence is observed for a sterile neutrino with a mass in a range of 0 - 1.5 GeV. The determined $B^+ \to μ^+ \, ν_μ$ branching fraction limit is further used to constrain the mass and coupling space of the type II and type III two-Higgs-doublet models.

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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.

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arXiv2019

Observation of $ τ^- \rightarrow π^- ν_τ e^+ e^-$ and search for $τ^- \rightarrow π^- ν_τ μ^+ μ^-$

We present the first measurements of branching fractions of rare tau-lepton decays, $τ^- \rightarrow π^- ν_τ \ell^+ \ell^-$ ($\ell = e$ or $μ$), using a data sample corresponding to 562 fb$^{-1}$ collected at a center-of-mass energy of 10.58 GeV with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. The $τ^- \rightarrow π^- ν_τe^+ e^-$ decay is observed for the first time with 7.0$σ$ significance. The partial branching fraction determined by the structure-dependent mechanisms mediated by either a vector or an axial-vector current for the mass region $M_{πe e}>1.05$ GeV/$c^2$ is measured to be $\mathcal{B}(τ^-\rightarrow π^- ν_τe^+ e^-)[M_{π^- e^+ e^-}>1.05~{\rm GeV}/c^2] = (5.90 \pm 0.53 \pm 0.85 \pm 0.11) \times 10^{-6}$, where the first uncertainty is statistical, the second is systematic, and the third is due to the model dependence. In the full phase space, due to the different detection efficiencies for the structure-dependent mechanisms mediated by axial-vector and vector currents, the branching fraction varies from $\mathcal{B}_{A}(τ^-\rightarrow π^- ν_τe^+ e^-) = (1.46 \pm 0.13 \pm 0.21) \times 10^{-5}$ to $\mathcal{B}_{V}(τ^-\rightarrow π^- ν_τe^+ e^-) = (3.01 \pm 0.27 \pm 0.43) \times 10^{-5}$, respectively. An upper limit is set on the branching fraction of the $τ^- \rightarrow π^- ν_τμ^+ μ^-$ decay, $\mathcal{B}(τ^-\rightarrow π^- ν_τμ^+ μ^-) < 1.14 \times 10^{-5}$, at the 90% confidence level.

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