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We report a measurement of decay-time-dependent charge-parity ($CP$) asymmetries in$B^0\to K_S^0{K}_S^0{K}_S^0$decays. We use$387\times {10}^6$$B\overline{B}$pairs collected at the$\mathrm{\Upsilon }(4S)$resonance with the Belle II detector at the SuperKEKB asymmetric-energy electron-positron collider. We reconstruct 220 signal events and extract the$CP$-violating parameters$S$and$C$from a fit to the distribution of the decay-time difference between the two$B$mesons. The resulting confidence region is consistent with previous measurements in$B^0\to K_S^0{K}_S^0{K}_S^0$and$B^0\to (c\overline{c})K^0$decays and with predictions based on the standard model.

We report results from a study ofB^±→ DK^±decays followed byDdecaying to theCP-even final stateK⁺K⁻and CP-odd final state$$ {K}_S^0{\pi}^0 $$$K_S^0{\pi }^0$, whereDis an admixture ofD⁰and$$ {\overline{D}}^0 $$${\overline{D}}^0$states. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angleϕ₃. The results are based on a combined analysis of the final data set of 772×10⁶$$ B\overline{B} $$$B\overline{B}$pairs collected by the Belle experiment and a data set of 198×10⁶$$ B\overline{B} $$$B\overline{B}$pairs collected by the Belle II experiment, both in electron-positron collisions at the Υ(4S) resonance. We measure the CP asymmetries to be$$ \mathcal{A} $$$A$_CP+= (+12.5±5.8±1.4)% and$$ \mathcal{A} $$$A$_CP−= (−16.7±5.7±0.6)%, and the ratios of branching fractions to be$$ \mathcal{R} $$$R$_CP+= 1.164±0.081±0.036 and$$ \mathcal{R} $$$R$_CP−= 1.151±0.074±0.019. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries$$ \mathcal{A} $$$A$_CP+and$$ \mathcal{A} $$$A$_CP−have similar magnitudes and opposite signs; their difference corresponds to 3.5 standard deviations. From these values we calculate 68.3% confidence intervals of (8.5^°<ϕ₃< 16.5^°) or (84.5^°<ϕ₃< 95.5^°) or (163.3^°<ϕ₃< 171.5^°) and 0.321 <r_B< 0.465.

We report the first measurement of the inclusivee⁺e⁻→$$ b\overline{b} $$$b\overline{b}$→$$ {D}_s^{\pm } $$$D_s^{\pm }$Xande⁺e⁻→$$ b\overline{b} $$$b\overline{b}$→ D⁰/$$ {\overline{D}}^0 $$${\overline{D}}^0$Xcross sections in the energy range from 10.63 to 11.02 GeV. Based on these results, we determineσ(e⁺e⁻→$$ {B}_s^0{\overline{B}}_s^0 $$$B_s^0{\overline{B}}_s^0$X) andσ(e⁺e⁻→$$ B\overline{B} $$$B\overline{B}$X) in the same energy range. We measure the fraction of$$ {B}_s^0 $$$B_s^0$events at Υ(10860) to bef_s= ($$ {22.0}_{-2.1}^{+2.0} $$${22.0}_{-2.1}^{+2.0}$)%. We determine also the ratio of the$$ {B}_s^0 $$$B_s^0$inclusive branching fractions$$ \mathcal{B} $$$B$($$ {B}_s^0 $$$B_s^0$→ D⁰/$$ {\overline{D}}^0 $$${\overline{D}}^0$X)/$$ \mathcal{B} $$$B$($$ {B}_s^0 $$$B_s^0$→$$ {D}_s^{\pm } $$$D_s^{\pm }$X) = 0.416 ± 0.018 ± 0.092. The results are obtained using the data collected with the Belle detector at the KEKB asymmetric-energye⁺e⁻collider.

A comprehensive study of the local and nonlocal amplitudes contributing to the decayB⁰→K^*0(→K⁺π⁻)μ⁺μ⁻is performed by analysing the phase-space distribution of the decay products. The analysis is based onppcollision data corresponding to an integrated luminosity of 8.4 fb⁻¹collected by the LHCb experiment. This measurement employs for the first time a model of both one-particle and two-particle nonlocal amplitudes, and utilises the complete dimuon mass spectrum without any veto regions around the narrow charmonium resonances. In this way it is possible to explicitly isolate the local and nonlocal contributions and capture the interference between them. The results show that interference with nonlocal contributions, although larger than predicted, only has a minor impact on the Wilson Coefficients determined from the fit to the data. For the local contributions, the Wilson Coefficient$$ {\mathcal{C}}_9 $$$C_9$, responsible for vector dimuon currents, exhibits a 2.1σdeviation from the Standard Model expectation. The Wilson Coefficients$$ {\mathcal{C}}_{10} $$$C_{10}$,$$ {\mathcal{C}}_9^{\prime } $$$C_9^{\prime }$and$$ {\mathcal{C}}_{10}^{\prime } $$$C_{10}^{\prime }$are all in better agreement than$$ {\mathcal{C}}_9 $$$C_9$with the Standard Model and the global significance is at the level of 1.5σ. The model used also accounts for nonlocal contributions fromB⁰→ K^*0[τ⁺τ⁻→ μ⁺μ⁻] rescattering, resulting in the first direct measurement of thebsττvector effective-coupling$$ {\mathcal{C}}_{9\tau } $$$C_{9\tau }$.

A search for the fully reconstructed$$ {B}_s^0 $$$B_s^0$→ μ⁺μ⁻γdecay is performed at the LHCb experiment using proton-proton collisions at$$ \sqrt{s} $$$\sqrt{s}$= 13 TeV corresponding to an integrated luminosity of 5.4 fb⁻¹. No significant signal is found and upper limits on the branching fraction in intervals of the dimuon mass are set$$ {\displaystyle \begin{array}{cc}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[2{m}_{\mu },1.70\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<7.7\times {10}^{-8},&\ m\left({\mu}^{+}{\mu}^{-}\right)\in \left[\textrm{1.70,2.88}\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[3.92,{m}_{B_s^0}\right]\textrm{GeV}/{c}^2,\end{array}} $$$\begin{array}{cc}B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(2m_{\mu },1.70\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<7.7\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(\mathrm{1.70,\; 2.88}\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(3.92,m_{B_s^0}\right)\mathrm{GeV}/c^2,\end{array}$

at 95% confidence level. Additionally, upper limits are set on the branching fraction in the [2m_μ,1.70] GeV/c²dimuon mass region excluding the contribution from the intermediateϕ(1020) meson, and in the region combining all dimuon-mass intervals.