arXiv subjects

G. De Pietro

Publications and source records attributed to G. De Pietro.

At least 181 records · Page 10Linked to original sources

arXiv2022

Measurements of the branching fractions $\mathcal{B} (\bar{B}{}^0 \to D^{+} π^-)$ and $\mathcal{B} (\bar{B}{}^0 \to D^{+} K^-)$ and tests of QCD factorization

Using $(771.6 \pm 10.6) \times 10^6$ $B\bar{B}$ meson pairs recorded by the Belle experiment at the KEKB $e^+ e^-$ collider, we report the branching fractions $\mathcal{B}(\bar{B}^0 \to D^{*+} π^-) = (2.62 \pm 0.02 \pm 0.09)\times 10^{-3}$ and $\mathcal{B}(\bar{B}^0 \to D^{*+} K^-) = (2.22 \pm 0.06 \pm 0.08)\times 10^{-4}$; the quoted uncertainties are statistical and systematic, respectively. A measurement of the ratio of these branching fractions is also presented, $\mathcal{R}_{K/π}=\mathcal{B}(\bar{B} \to D^{*+}K^-) /\mathcal{B}( \bar{B} \to D^{*+}π^-) = (8.41 \pm 0.24 \pm 0.13)\times 10^{-2}$, where systematic uncertainties due to the $D^{*+}$ meson reconstruction cancel out. Furthermore, we report a new QCD factorization test based on the measured ratios for $\bar{B} \to D^{*+}h^-$ and $\bar{B} \to D^{*+}\ell^-ν$ decays at squared momentum transfer values equivalent to the mass of the $h = π$ or $K$ hadron. The parameters $|a_1(h)|$ are measured to be $|a_1(π)|= 0.884 \pm 0.004 \pm 0.003 \pm 0.016$ and $|a_1(K)|=0.913 \pm 0.019 \pm 0.008 \pm 0.013$, where the last uncertainties account for all external inputs. These values are approximately $15\%$ lower than those expected from theoretical predictions. Subsequently, flavor $SU(3)$ symmetry is tested by measuring the ratios for pions and kaons, $|a_1(K)|^2/ |a_1(π)|^2=1.066 \pm 0.042 \pm 0.018 \pm 0.023$, as well as for different particle species. The ratio is consistent with unity and therefore no evidence for $SU(3)$ symmetry breaking effects is found at the $5\%$ precision level.

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arXiv2022

First search for the weak radiative decays $Λ_c^+ \to Σ^+ γ$ and $Ξ_c^0 \to Ξ^0 γ$

We present the first search for the weak radiative decays $Λ_c^+ \to Σ^+ γ$ and $Ξ_c^0 \to Ξ^0 γ$ using a data sample of 980~fb$^{-1}$ collected by the Belle detector operating at the KEKB asymmetric-energy $e^+e^-$ collider. There are no evident $Λ_c^+ \to Σ^+ γ$ or $Ξ_c^0 \to Ξ^0 γ$ signals. Taking the decays $Λ_c^+ \to p K^- π^+$ and $Ξ_c^0 \to Ξ^- π^+$ as normalization channels, the upper limits at 90\% credibility level on the ratios of branching fractions ${\cal B}(Λ_c^+ \to Σ^+ γ)/{\cal B}(Λ_c^+ \to p K^{-} π^+) < 4.0 \times 10^{-3}$ and ${\cal B}(Ξ_c^0 \to Ξ^0 γ)/{\cal B}(Ξ_c^0 \to Ξ^- π^+) < 1.2 \times 10^{-2}$ are determined. We obtain the upper limits at 90\% credibility level on the absolute branching fractions ${\cal B}(Λ_c^+ \to Σ^+ γ) < 2.6 \times 10^{-4}$ and ${\cal B}(Ξ_c^0 \to Ξ^0 γ) < 1.8 \times 10^{-4}$.

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arXiv2022

Evidence of a new excited charmed baryon decaying to $Σ_{c}(2455)^{0,++} π^{\pm}$

We present the study of $\bar{B}^{0} \to Σ_{c}(2455)^{0,++} π^{\pm} \bar{p}$ decays based on $772\times 10^{6}$ $B\bar{B}$ events collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. The $Σ_{c}(2455)^{0,++} $ candidates are reconstructed via their decay to $Λ_{c}^{+} π^{\mp}$ and $Λ_{c}^{+}$ decays to $pK^{-}π^{+},~pK_{S}^{0},$ and $Λπ^{+}$ final states. The corresponding branching fractions are measured to be ${\cal B}(\bar{B}^{0} \to Σ_{c}(2455)^{0} π^{+} \bar{p}) = (1.09 \pm 0.06 \pm 0.07)\times10^{-4}$ and ${\cal B}(\bar{B}^{0} \to Σ_{c}(2455)^{++} π^{-} \bar{p}) = (1.84\pm 0.11 \pm 0.12)\times 10^{-4}$, which are consistent with the world average values with improved precision. A new structure is found in the $M_{Σ_{c}(2455)^{0,++}π^{\pm}}$ spectrum with a significance of $4.2σ$ including systematic uncertainty. The structure is possibly an excited $Λ_{c}^{+}$ and is tentatively named $Λ_{c}(2910)^{+}$. Its mass and width are measured to be $(2913.8 \pm 5.6 \pm 3.8)$ MeV/$c^{2}$ and $(51.8\pm20.0 \pm 18.8)$ MeV, respectively. The products of branching fractions for the $Λ_{c}(2910)^{+}$ are measured to be ${\cal B}(\bar{B}^{0} \to Λ_{c}(2910)^{+}\bar{p})\times{\cal B}(Λ_{c}(2910)^{+} \to Σ_{c}(2455)^{0}π^{+}) = (9.5 \pm 3.6 \pm 1.6)\times 10^{-6}$ and ${\cal B}(\bar{B}^{0} \to Λ_{c} (2910)^{+}\bar{p})\times {\cal B}(Λ_{c}(2910)^{+} \to Σ_{c}(2455)^{++}π^{-}) = (1.24 \pm 0.35 \pm 0.10)\times 10^{-5}$. Here, the first and second uncertainties are statistical and systematic, respectively.

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arXiv2022

Measurement of the branching fraction of $Ξ_{c}^{0}\to Λ_{c}^{+}π^{-}$ at Belle

Based on a data sample of 983 fb$^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider, we present the study of the heavy-flavor-conserving decay $Ξ_{c}^{0}\to Λ_{c}^{+}π^{-}$ with $Λ_{c}^{+}$ reconstructed via its $pK^{-} π^{+}$ decay mode. The branching fraction ratio $\mathcal{B}(Ξ_{c}^{0}\to Λ_{c}^{+}π^{-})/\mathcal{B}(Ξ_{c}^{0}\to Ξ^{-}π^{+})$ is measured to be $0.38 \pm 0.04 \pm 0.04$. Combing with the world average value of $\mathcal{B}(Ξ_{c}^{0}\to Ξ^{-}π^{+})$, the branching fraction $\mathcal{B}(Ξ_{c}^{0}\to Λ_{c}^{+}π^{-})$ is deduced to be $(0.54 \pm 0.05 \pm 0.05 \pm 0.12)\%$. Here, the uncertainties above are statistical, systematic, and from $\mathcal{B}(Ξ_c^{0} \to Ξ^{-}π^{+})$, respectively.

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arXiv2022

Determination of $|V_{ub}|$ from untagged $B^0\toπ^- \ell^+ ν_{\ell}$ decays using 2019-2021 Belle II data

We present an analysis of the charmless semileptonic decay $B^0\toπ^- \ell^+ ν_{\ell}$, where $\ell = e, μ$, from 198.0 million pairs of $B\bar{B}$ mesons recorded by the Belle II detector at the SuperKEKB electron-positron collider. The decay is reconstructed without identifying the partner $B$ meson. The partial branching fractions are measured independently for $B^0\toπ^- e^+ ν_{e}$ and $B^0\toπ^- μ^+ ν_μ$ as functions of $q^{2}$ (momentum transfer squared), using 3896 $B^0\toπ^- e^+ ν_{e}$ and 5466 $B^0\toπ^- μ^+ ν_μ$ decays. The total branching fraction is found to be $(1.426 \pm 0.056 \pm 0.125) \times 10^{-4}$ for $B^0\toπ^- \ell^+ ν_{\ell}$ decays, where the uncertainties are statistical and systematic, respectively. By fitting the measured partial branching fractions as functions of $q^{2}$, together with constraints on the nonperturbative hadronic contribution from lattice QCD calculations, the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$, $(3.55 \pm 0.12 \pm 0.13 \pm 0.17) \times 10^{-3}$, is extracted. Here, the first uncertainty is statistical, the second is systematic and the third is theoretical.

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arXiv2022

Measurement of the branching fractions and $CP$ asymmetries of $B^+ \rightarrow π^+ π^0$ and $B^+ \rightarrow K^+ π^0$ decays in 2019-2021 Belle II data

We determine the branching fractions ${\mathcal{B}}$ and $CP$ asymmetries ${\mathcal{A}_{\it CP}}$ of the decays $B^+ \rightarrow π^+ π^0$ and $B^+ \rightarrow K^+ π^0$. The results are based on a data set containing 198 million bottom-antibottom meson pairs corresponding to an integrated luminosity of $190\;\text{fb}^{-1}$ recorded by the Belle II detector in energy-asymmetric electron-positron collisions at the $Υ(4S)$ resonance. We measure ${\mathcal{B}(B^+ \rightarrow π^+ π^0) = (6.12 \pm 0.53 \pm 0.53)\times 10^{-6}}$, ${\mathcal{B}(B^+ \rightarrow K^+ π^0) = (14.30 \pm 0.69 \pm 0.79)\times 10^{-6}}$, ${\mathcal{A}_{\it CP}(B^+ \rightarrow π^+ π^0) = -0.085 \pm 0.085 \pm 0.019}$, and ${\mathcal{A}_{\it CP}(B^+ \rightarrow K^+ π^0) = 0.014 \pm 0.047 \pm 0.010}$, where the first uncertainties are statistical and the second are systematic. These results improve a previous Belle II measurement and agree with the world averages.

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arXiv2022

Measurement of Branching Fraction and Longitudinal Polarization in $B^0 \to ρ^+ ρ^-$ Decays at Belle II

We present a measurement of the branching fraction and longitudinal polarization of $B^0 \to ρ^+ ρ^-$ decays. SuperKEKB electron-positron collision data corresponding to 189~fb$^{-1}$ of integrated luminosity and containing $198 \times 10^6 B\bar{B}$ pairs collected with the Belle II detector are used. We obtain \begin{eqnarray*} \mathcal{B}(B^0\toρ^+ρ^-) &=& [2.67\pm0.28\,(\mathrm{stat})\,\pm0.28\,(\mathrm{syst})] \times 10^{-5}, \end{eqnarray*} \begin{eqnarray*} f_L &=& 0.956\pm0.035\,(\mathrm{stat})\,\pm 0.033\,(\mathrm{syst}), \end{eqnarray*} These results are consistent with previous measurements and can be used to constrain penguin pollution and to extract the quark-mixing angle $ϕ_2$.

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arXiv2022

First test of Lepton Flavor Universality in the charmed baryon decays $Ω^{0}_{c} \to Ω^{-} \ell^{+} ν_{\ell}$ using data of the Belle experiment

We present the first observation of the $Ω_{c}^{0} \to Ω^{-} μ^{+} ν_μ$ decay and present measurements of the branching fraction ratios of the $Ω_{c}^{0} \to Ω^{-} \ell^{+} ν_{\ell}$ decays compared to the reference mode $Ω_{c}^{0} \to Ω^{-} π^+$, ($\ell = e$ or $μ$). This analysis is based on 89.5 fb$^{-1}$, 711 fb$^{-1}$, and 121.1 fb$^{-1}$ data samples collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider at the center-of-mass energies of 10.52 GeV, 10.58 GeV, and 10.86 GeV, respectively. The $Ω_{c}^{0}$ signal yields are extracted by fitting $M_{Ω^{-} \ell^{+}}$ and $M_{Ω^{-}π^+}$ spectra. The branching fraction ratios ${\cal B}(Ω_{c}^{0} \to Ω^{-} e^{+} ν_{e})/{\cal B}(Ω_{c}^{0} \to Ω^{-} π^+)$ and ${\cal B}(Ω_{c}^{0} \to Ω^{-} μ^{+} ν_μ)/{\cal B}(Ω_{c}^{0} \to Ω^{-} π^+)$ are measured to be $1.98 \pm0.13~({\rm stat.}) \pm 0.08~({\rm syst.})$ and $ 1.94 \pm 0.18~({\rm stat.}) \pm 0.10~({\rm syst.})$, respectively. The ratio of ${\cal B}(Ω_{c}^{0} \to Ω^{-} e^{+} ν_{e})/{\cal B}(Ω_{c}^{0} \to Ω^{-} μ^{+} ν_μ)$ is measured to be $1.02 \pm 0.10~({\rm stat.}) \pm 0.02~({\rm syst.})$, which is consistent with the expectation of lepton flavor universality.

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arXiv2022

Search for charged lepton flavor violating decays of $Υ(1S)$

We present a search for the charged lepton-flavor-violating decays $Υ(1S)\rightarrow\ell\ell^\prime$ and radiative charged lepton-flavour-violating decays $Υ(1S)\rightarrowγ\ell\ell^\prime$ [$\ell,\ell^\prime = e, μ, τ$] using the 158 million $Υ(2S)$ sample collected by the Belle detector at the KEKB collider. This search uses $Υ(1S)$ mesons produced in $π^+π^-Υ(1S)$ transitions. We do not find any significant signal, so we provide upper limits on the branching fractions at the 90% confidence level.

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arXiv2022

$B$-flavor tagging at Belle II

We report on new flavor tagging algorithms developed to determine the quark-flavor content of bottom ($B$) mesons at Belle II. The algorithms provide essential inputs for measurements of quark-flavor mixing and charge-parity violation. We validate and evaluate the performance of the algorithms using hadronic $B$ decays with flavor-specific final states reconstructed in a data set corresponding to an integrated luminosity of $62.8$ fb$^{-1}$, collected at the $Υ$(4$S$) resonance with the Belle II detector at the SuperKEKB collider. We measure the total effective tagging efficiency to be $\varepsilon_{\rm eff} = \big(30.0 \pm 1.2(\text{stat}) \pm 0.4(\text{syst})\big)\%$ for a category-based algorithm and $\varepsilon_{\rm eff} = \big(28.8 \pm 1.2(\text{stat}) \pm 0.4(\text{syst})\big)\%$ for a deep-learning-based algorithm.

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arXiv2022

Search for $B^{0} \to K_S^{0}K_S^{0}γ$ decays at Belle

We report the first search for the penguin-dominated process $B^0 \rightarrow K_S^0 K_S^0 γ$ using the full data sample of $772\times 10^6$ $B\bar{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We do not observe any statistically significant signal yield in the $K_S^0$-pair invariant mass range 1 GeV/$c^2 < M_{K_S^0 K_S^0} < $ 3 GeV/$c^2$, and set the following upper limits at 90% confidence level: $\mathcal{B}(B^0 \to K_S^0 K_S^0 γ) < 5.8\times10^{-7}$, $\mathcal{B}(B^0 \to f_2 γ)\times \mathcal{B}(f_2 (1270) \to K_S^0 K_S^0 ) < 3.1\times10^{-7}$, and $\mathcal{B}(B^0 \to f_2^{\prime} γ)\times \mathcal{B}(f_2^{\prime} (1525) \to K_S^0 K_S^0 ) < 2.1\times10^{-7}$. Further, 90% confidence upper limits have also been set in the range of [0.7-2.9]$\times10^{-7}$ on the $B^0 \rightarrow K_S^0 K_S^0 γ$ branching fraction in bins of $M_{K_S^0 K_S^0}$.

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arXiv2022

First Measurement of the $Λ_c^+ \to p η'$ decay

We present the first measurement of the branching fraction of the singly Cabibbo-suppressed (SCS) decay $Λ_c^+ \to p η'$ with $η' \to ηπ^+π^-$, using a data sample corresponding to an integrated luminosity of 981 $\rm fb^{-1}$, collected by the Belle detector at the KEKB $e^{+}$$e^{-}$ asymmetric-energy collider. A significant $Λ_c^+$ signal is observed for the first time with a signal significance of 5.4$σ$. The relative branching fraction with respect to the normalization mode $Λ_c^+ \to pK^-π^+$ is measured to be \begin{equation*} \frac{{\cal B}(Λ_c^+ \to p η')}{{\cal B}(Λ_c^+ \to p K^-π^+)} = (7.54 \pm 1.32 \pm 0.75) \times 10^{-3}, \end{equation*} where the uncertainties are statistical and systematic, respectively. Using the world-average value of ${\cal B}(Λ_c^+ \to p K^-π^+) = (6.28\pm0.32)\times10^{-2}$, we obtain \begin{equation*} {\cal B}(Λ_c^+ \to p η') = (4.73 \pm 0.82 \pm 0.47 \pm 0.24)\times 10^{-4}, \end{equation*} where the uncertainties are statistical, systematic, and from ${\cal B}(Λ_c^+ \to pK^-π^+)$, respectively.

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arXiv2022

Search for a light Higgs boson in single-photon decays of $Υ(1S)$ using $Υ(2S) \to π^+ π^- Υ(1S)$ tagging method

We search for a light Higgs boson ($A^0$) decaying into a $τ^+τ^-$ or $μ^+μ^-$ pair in the radiative decays of $Υ(1S)$. The production of $Υ(1S)$ mesons is tagged by $Υ(2S)\to π^+ π^- Υ(1S)$ transitions, using 158 million $Υ(2S)$ events accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. No significant $A^0$ signals in the mass range from the $τ^+τ^-$ or $μ^+μ^-$ threshold to 9.2 GeV/$c^2$ are observed. We set the upper limits at 90\% credibility level (C.L.) on the product branching fractions for $Υ(1S)\to γA^0$ and $A^0\to τ^+τ^-$ varying from $3.8\times10^{-6}$ to $1.5\times10^{-4}$. Our results represent an approximately twofold improvement on the current world best upper limits for the $Υ(1S)\to γA^0(\to τ^+τ^-)$ production. For $A^0\to μ^+μ^-$, the upper limits on the product branching fractions for $Υ(1S)\to γA^0$ and $A^0\to μ^+μ^-$ are at the same level as the world average limits, and vary from $3.1\times10^{-7}$ to $1.6\times10^{-5}$. The upper limits at 90\% C.L. on the Yukawa coupling $f_{Υ(1S)}$ and mixing angle ${\rm sin}θ_{A^0}$ are also given.

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arXiv2022

Search for tetraquark states $X_{cc\bar{s}\bar{s}}$ in $D_{s}^{+}D_{s}^{+}~(D_{s}^{+}D_{s}^{+})$ final states at Belle

A search for double-heavy tetraquark state candidates $X_{cc\bar{s}\bar{s}}$ decaying to $D_{s}^{+}D_{s}^{+}$ and $D_{s}^{*+} D_{s}^{*+}$ is presented for the first time using the data samples of 102 million $Υ(1S)$ and 158 million $Υ(2S)$ events, and the data samples at $\sqrt{s}$ = 10.52~GeV, 10.58~GeV, and 10.867~GeV corresponding to integrated luminosities of 89.5~fb$^{-1}$, 711.0~fb$^{-1}$, and 121.4~fb$^{-1}$, respectively, accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. The invariant-mass spectra of the $D_{s}^{+}D_{s}^{+}$ and $D_{s}^{*+} D_{s}^{*+}$ are studied to search for possible resonances. No significant signals are observed, and the 90\% confidence level upper limits on the product branching fractions [${\cal B}(Υ(1S,2S) \to X_{cc\bar{s}\bar{s}} + anything) \times {\cal B}(X_{cc\bar{s}\bar{s}} \to D_{s}^{+}D_{s}^{+}(D_{s}^{*+} D_{s}^{*+}))$] in $Υ(1S,2S)$ inclusive decays and the product values of Born cross section and branching fraction [$σ(e^+e^- \to X_{cc\bar{s}\bar{s}} + anything ) \times {\cal B}(X_{cc\bar{s}\bar{s}} \to D_{s}^{+}D_{s}^{+}(D_{s}^{*+} D_{s}^{*+}))$] in $e^+e^-$ collisions at $\sqrt{s}$ = 10.52~GeV, 10.58~GeV, and 10.867~GeV under different assumptions of $X_{cc\bar{s}\bar{s}}$ masses and widths are obtained.

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arXiv2022

Study of $\overline{B}{}^0\rightarrow D^{+}h^{-} (h=K/π)$ decays at Belle

We present a measurement of the branching fractions of the Cabibbo favored $\overline{B}{}^0\rightarrow D^{+}π^{-}$ and the Cabibbo suppressed $\overline{B}{}^0\rightarrow D^{+}K^{-}$ decays. We find $\mathcal{B}(\overline{B}{}^0\rightarrow D^{+}π^{-}) = (2.48 \pm 0.01 \pm 0.09 \pm 0.04) \times 10^{-3}$ and $\mathcal{B}(\overline{B}{}^0\rightarrow D^{+}K^{-})= (2.03 \pm 0.05 \pm 0.07 \pm 0.03) \times 10^{-4}$ decays, where the first uncertainty is statistical, the second is systematic, and the third uncertainty is due to the $D^{+} \rightarrow K^{-}π^{+}π^{+}$ branching fraction. The ratio of branching fractions of $\overline{B}{}^0\rightarrow D^{+}K^{-}$ and $\overline{B}{}^0\rightarrow D^{+}π^{-}$ is measured to be $R^{D} = [8.19 \pm 0.20(\rm stat) \pm 0.23(\rm syst)] \times 10^{-2} $. These measurements are performed using the full Belle data set, which corresponds to $772 \times 10^{6} B\overline{B} $ pairs.

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arXiv2022

Search for the decay $B_s^0 \to η^\prime K_S^0$

We report the results of the first search for the decay $B_s^0 \to η^\prime K_S^0$ using $121.4\,{\rm fb}^{-1}$ of data collected at the $Υ(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We observe no signal and set a 90\% confidence-level upper limit of $8.16 \times 10^{-6}$ on the $B_s^0 \to η^\prime K_S^0$ branching fraction.

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arXiv2022

Measurement of Two-Particle Correlations of Hadrons in $e^{+}e^{-}$ Collisions at Belle

The measurement of two-particle angular correlation functions in high-multiplicity $e^+e^-$ collisions at $\sqrt{s}=10.52$ GeV is reported. In this study, the $89.5~{\text{fb}}^{-1}$ of hadronic $e^+e^-$ annihilation data collected by the Belle detector at KEKB are used. Two-particle angular correlation functions are measured in the full relative azimuthal angle ($Δϕ$) and three units of pseudorapidity ($Δη$), defined by either the electron beam axis or the event-shape thrust axis, and are studied as a function of charged-particle multiplicity. The measurement in the thrust axis analysis, with mostly outgoing quark pairs determining the reference axis, is sensitive to the region of additional soft gluon emissions. No significant anisotropic collective behavior is observed with either coordinate analyses. Near-side jet correlations appear to be absent in the thrust axis analysis. The measurements are compared to predictions from various event generators and are expected to provide new constraints to the phenomenological models in the low-energy regime.

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arXiv2021

Combined analysis of Belle and Belle II data to determine the CKM angle $ ϕ_{3} $ using $B^+ \to D(K_{S}^0 h^- h^+) h^+$ decays

We present a measurement of the Cabibbo-Kobayashi-Maskawa unitarity triangle angle $ ϕ_{3} $ (also known as~$γ$) using a model-independent Dalitz plot analysis of \linebreak $B^+\to D\left(K_{S}^{0}h^{+}h^{-}\right)h^+$, where $D$ is either a $D^0$ or $\bar{D}{}^0$ meson and $h$ is either a $π$ or $K$. This is the first measurement that simultaneously uses Belle and Belle~II data, combining samples corresponding to integrated luminosities of \SI{711}{fb^{-1}} and \SI{128}{fb^{-1}}, respectively. All data were accumulated from energy-asymmetric $e^+e^-$ collisions at a centre-of-mass energy corresponding to the mass of the $Υ(4S)$ resonance. We measure $ϕ_3 = \left(78.4 \pm 11.4 \pm 0.5 \pm 1.0 \right)^{\circ}$, where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is from the uncertainties on external measurements of the $D$-decay strong-phase parameters.

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