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SUMMARY In previous publications, we presented a general framework, which we called ‘box tomography’, that allows the coupling of any two different numerical seismic wave propagation solvers, respectively outside and inside a target region, or ‘box’. The goal of such hybrid wavefield computations is to reduce the cost of computations in the context of full-waveform inversion for structure within the target region, when sources and/or receivers are located at large distances from the box. Previously, we had demonstrated this approach with sources and receivers outside the target region in a 2-D acoustic spherical earth model, and demonstrated and applied this methodology in the 3-D spherical elastic Earth in a continental scale inversion in which all stations were inside the target region. Here we extend the implementation of the approach to the case of a 3-D global elastic earth model in the case where both sources and stations are outside the box. We couple a global 3-D solver, SPECFEM3D_GLOBE, for the computation of the wavefield and Green’s functions in a reference 3-D model, with a regional 3-D solver, RegSEM, for the computation of the wavefield within the box, by means of time-reversal mirrors. We briefly review key theoretical aspects, showing in particular how only the displacement is needed to be stored at the boundary of the box. We provide details of the practical implementation, including the geometrical design of the mirrors, how we deal with different sizes of meshes in the two solvers, and how we address memory-saving through the use of B-spline compression of the recorded wavefield on the mirror. The proposed approach is numerically efficient but also versatile, since adapting it to other solvers is straightforward and does not require any changes in the solver codes themselves, as long as the displacement can be recovered at any point in time and space. We present benchmarks of the hybrid computations against direct computations of the wavefield between a source and an array of stations in a realistic geometry centred in the Yellowstone region, with and without a hypothetical plume within the ‘box’, and with a 1-D or a 3-D background model, down to a period of 20 s. The ultimate goal of this development is for applications in the context of imaging of remote target regions in the deep mantle, such as, for example, Ultra Low Velocity Zones. 

We present a measurement of the branching fraction and fraction of longitudinal polarization of $B^0\to {\rho }^{+}{\rho }^{-}$decays, which have two ${\pi }^0$’s in the final state. We also measure time-dependent $CP$violation parameters for decays into longitudinally polarized ${\rho }^{+}{\rho }^{-}$pairs. This analysis is based on a data sample containing $(387\pm 6)\times {10}^6$ $\mathrm{\Upsilon }\left(4S\right)$mesons collected with the Belle II detector at the SuperKEKB asymmetric-energy $e^{+}{e}^{-}$collider in 2019–2022. We obtain $\mathcal{B}(B^0\to {\rho }^{+}{\rho }^{-})=\left(2.89_{-0.22}^{+0.23}{}_{-0.27}^{+0.29}\right)\times {10}^{-5}$, $f_L=0.921_{-0.025}^{+0.024}{}_{-0.015}^{+0.017}$, $S=-0.26\pm 0.19\pm 0.08$, and $C=-0.02\pm 0.12_{-0.05}^{+0.06}$, where the first uncertainties are statistical and the second are systematic. We use these results to perform an isospin analysis to constrain the Cabibbo-Kobayashi-Maskawa angle ${\varphi }_2$and obtain two solutions; the result consistent with other Standard Model constraints is ${\varphi }_2=\left({92.6}_{-4.7}^{+4.5}\right)°$. Published by the American Physical Society2025 

A<sc>bstract</sc> We perform the first search forCPviolation in$$ {D}_{(s)}^{+}\to {K}_S^0{K}^{-}{\pi}^{+}{\pi}^{+} $$ $D_{\left(s\right)}^{+}\to K_S^0{K}^{-}{\pi }^{+}{\pi }^{+}$decays. We use a combined data set from the Belle and Belle II experiments, which studye⁺e⁻collisions at center-of-mass energies at or near the Υ(4S) resonance. We use 980 fb⁻¹of data from Belle and 428 fb⁻¹of data from Belle II. We measure sixCP-violating asymmetries that are based on triple products and quadruple products of the momenta of final-state particles, and also the particles’ helicity angles. We obtain a precision at the level of 0.5% for$$ {D}^{+}\to {K}_S^0{K}^{-}{\pi}^{+}{\pi}^{+} $$ $D^{+}\to K_S^0{K}^{-}{\pi }^{+}{\pi }^{+}$decays, and better than 0.3% for$$ {D}_s^{+}\to {K}_S^0{K}^{-}{\pi}^{+}{\pi}^{+} $$ $D_s^{+}\to K_S^0{K}^{-}{\pi }^{+}{\pi }^{+}$decays. No evidence ofCPviolation is found. Our results for the triple-product asymmetries are the most precise to date for singly-Cabibbo-suppressedD⁺decays. Our results for the other asymmetries are the first such measurements performed for charm decays. 

A<sc>bstract</sc> Using data samples of 983.0 fb⁻¹and 427.9 fb⁻¹accumulated with the Belle and Belle II detectors operating at the KEKB and SuperKEKB asymmetric-energye⁺e⁻colliders, singly Cabibbo-suppressed decays$$ {\Xi}_c^{+}\to p{K}_S^0 $$ ${\Xi }_c^{+}\to p{K}_S^0$,$$ {\Xi}_c^{+}\to \Lambda {\pi}^{+} $$ ${\Xi }_c^{+}\to \Lambda {\pi }^{+}$, and$$ {\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+} $$ ${\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}$are observed for the first time. The ratios of branching fractions of$$ {\Xi}_c^{+}\to p{K}_S^0 $$ ${\Xi }_c^{+}\to p{K}_S^0$,$$ {\Xi}_c^{+}\to \Lambda {\pi}^{+} $$ ${\Xi }_c^{+}\to \Lambda {\pi }^{+}$, and$$ {\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+} $$ ${\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}$relative to that of$$ {\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+} $$ ${\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}$are measured to be$$ {\displaystyle \begin{array}{c}\frac{\mathcal{B}\left({\Xi}_c^{+}\to p{K}_S^0\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(2.47\pm 0.16\pm 0.07\right)\%,\\ {}\frac{\mathcal{B}\left({\Xi}_c^{+}\to \Lambda {\pi}^{+}\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(1.56\pm 0.14\pm 0.09\right)\%,\\ {}\frac{\mathcal{B}\left({\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+}\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(4.13\pm 0.26\pm 0.22\right)\%.\end{array}} $$ $\begin{array}{c}\frac{B\left({\Xi }_c^{+}\to p{K}_S^0\right)}{B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=\left(2.47\pm 0.16\pm 0.07\right)\%,\\ \frac{B\left({\Xi }_c^{+}\to \Lambda {\pi }^{+}\right)}{B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=\left(1.56\pm 0.14\pm 0.09\right)\%,\\ \frac{B\left({\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}\right)}{B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=\left(4.13\pm 0.26\pm 0.22\right)\%.\end{array}$ Multiplying these values by the branching fraction of the normalization channel,$$ \mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)=\left(2.9\pm 1.3\right)\% $$ $B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)=\left(2.9\pm 1.3\right)\%$, the absolute branching fractions are determined to be$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^{+}\to p{K}_S^0\right)=\left(7.16\pm 0.46\pm 0.20\pm 3.21\right)\times {10}^{-4},\\ {}\mathcal{B}\left({\Xi}_c^{+}\to \Lambda {\pi}^{+}\right)=\left(4.52\pm 0.41\pm 0.26\pm 2.03\right)\times {10}^{-4},\\ {}\mathcal{B}\left({\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+}\right)=\left(1.20\pm 0.08\pm 0.07\pm 0.54\right)\times {10}^{-3}.\end{array}} $$ $\begin{array}{c}B\left({\Xi }_c^{+}\to p{K}_S^0\right)=\left(7.16\pm 0.46\pm 0.20\pm 3.21\right)\times {10}^{-4},\\ B\left({\Xi }_c^{+}\to \Lambda {\pi }^{+}\right)=\left(4.52\pm 0.41\pm 0.26\pm 2.03\right)\times {10}^{-4},\\ B\left({\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}\right)=\left(1.20\pm 0.08\pm 0.07\pm 0.54\right)\times {10}^{-3}.\end{array}$ The first and second uncertainties above are statistical and systematic, respectively, while the third ones arise from the uncertainty in$$ \mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right) $$ $B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)$. 

We measure the branching fraction and $CP$-violating flavor-dependent rate asymmetry of $B^0\to {\pi }^0{\pi }^0$decays reconstructed using the Belle II detector in an electron-positron collision sample containing $387\times {10}^6\mathrm{\Upsilon }\left(4S\right)$mesons. Using an optimized event selection, we find $125\pm 20$signal decays in a fit to background-discriminating and flavor-sensitive distributions. The resulting branching fraction is $(1.25\pm 0.23)\times {10}^{-6}$and the $CP$-violating asymmetry is $0.03\pm 0.30$. Published by the American Physical Society2025 

A<sc>bstract</sc> We report measurements of the absolute branching fractions$$\mathcal{B}\left({B}_{s}^{0}\to {D}_{s}^{\pm }X\right)$$,$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{0}/{\overline{D} }^{0}X\right)$$, and$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{\pm }X\right)$$, where the latter is measured for the first time. The results are based on a 121.4 fb⁻¹data sample collected at the Υ(10860) resonance by the Belle detector at the KEKB asymmetric-energye⁺e⁻collider. We reconstruct one$${B}_{s}^{0}$$meson in$${e}^{+}{e}^{-}\to \Upsilon\left(10860\right)\to {B}_{s}^{*}{\overline{B} }_{s}^{*}$$events and measure yields of$${D}_{s}^{+}$$,D⁰, andD⁺mesons in the rest of the event. We obtain$$\mathcal{B}\left({B}_{s}^{0}\to {D}_{s}^{\pm }X\right)=\left(68.6\pm 7.2\pm 4.0\right)\%$$,$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{0}/{\overline{D} }^{0}X\right)=\left(21.5\pm 6.1\pm 1.8\right)\%$$, and$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{\pm }X\right)=\left(12.6\pm 4.6\pm 1.3\right)\%$$, where the first uncertainty is statistical and the second is systematic. Averaging with previous Belle measurements gives$$\mathcal{B}\left({B}_{s}^{0}\to {D}_{s}^{\pm }X\right)=\left(63.4\pm 4.5\pm 2.2\right)\%$$and$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{0}/{\overline{D} }^{0}X\right)=\left(23.9\pm 4.1\pm 1.8\right)\%$$. For the$${B}_{s}^{0}$$production fraction at the Υ(10860), we find$${f}_{s}=\left({21.4}_{-1.7}^{+1.5}\right)\%$$. 

We measure the branching fraction of the decay $B^0\to J/\psi \omega$using data collected with the Belle II detector at the SuperKEKB collider. The data contain $(387\pm 6)\times {10}^{6}B\overline{B}$meson pairs produced in energy-asymmetric $e^{+}{e}^{-}$collisions at the $\mathrm{\Upsilon }\left(4S\right)$resonance. The measured branching fraction $\mathcal{B}(B^0\to J/\psi \omega )=(2.16\pm 0.30\pm 0.14)\times {10}^{-5}$, where the first uncertainty is statistical and the second is systematic, is more precise than previous results and constitutes the first observation of the decay with a significance of 6.5 standard deviations. Published by the American Physical Society2025 

We measure the time-integrated $CP$asymmetry in $D^0\to K_S^0{K}_S^0$decays reconstructed in $e^{+}{e}^{-}\to c\overline{c}$events collected by the Belle and Belle II experiments. The corresponding data samples have integrated luminosities of 980 and $428{\mathrm{fb}}^{-1}$, respectively. The $D^0$decays are required to originate from the $D^{*+}\to D^0{\pi }^{+}$decay, which determines the charm flavor at production time. A control sample of $D^0\to K^{+}{K}^{-}$decays is used to correct for production and detection asymmetries. The result, $(-1.4\pm 1.3\left(\mathrm{stat}\right)\pm 0.1\left(\mathrm{syst}\right))\%$, is consistent with previous determinations and with $CP$symmetry. Published by the American Physical Society2025 

We report a measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$cross section in the energy range from 0.62 to 3.50 GeV using an initial-state radiation technique. We use an $e^{+}{e}^{-}$data sample corresponding to $191{\mathrm{fb}}^{-1}$of integrated luminosity, collected at a center-of-mass energy at or near the $\mathrm{\Upsilon }\left(4S\right)$resonance with the Belle II detector at the SuperKEKB collider. Signal yields are extracted by fitting the two-photon mass distribution in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$events, which involve a ${\pi }^0\to \gamma \gamma$decay and an energetic photon radiated from the initial state. Signal efficiency corrections with an accuracy of 1.6% are obtained from several control data samples. The uncertainty on the cross section at the $\omega$and $\varphi$resonances is dominated by the systematic uncertainty of 2.2%. The resulting cross sections in the 0.62–1.80 GeV energy range yield $a_{\mu }^{3\pi }=[48.91\pm 0.23(\mathrm{stat})\pm 1.07(\mathrm{syst}\left)\right]\times {10}^{-10}$for the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. This result differs by 2.5 standard deviations from the most precise current determination. Published by the American Physical Society2024