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Aims. An analysis of the methylidyne (CH) radical in non-local thermodynamic equilibrium (NLTE) is performed for the physical conditions of cool stellar atmospheres typical of red giants (log ɡ = 2.0, T eff = 4500 K) and the Sun. The aim of the present work is to explore whether the G band of the CH molecule, which is commonly used in abundance diagnostics of carbon-enhanced metal-poor stars, is sensitive to NLTE effects. Methods. LTE and NLTE theoretical spectra were computed with the MULTI code. We used one-dimensional (1D) LTE hydrostatic MARCS model atmospheres with parameters representing eleven red giant stars with metallicities ranging from [Fe/H] = −4.0 to [Fe/H] = 0.0 and carbon-to-iron ratios of [C/Fe] = 0.0, +0.7, +1.5, and +3.0. The CH molecule model was represented by 1981 energy levels, 18 377 radiative bound-bound transitions, and 932 photo-dissociation reactions. The rates due to transitions caused by collisions with free electrons and hydrogen atoms were computed using classical recipes. Results. Our calculations suggest that NLTE effects in the statistical equilibrium of the CH molecule are significant and cannot be neglected for precision spectroscopic analysis of C abundances. The NLTE effects are mostly driven by radiative over-dissociation, owing to the very low dissociation threshold of the molecule and significant resonances in the photo-dissociation cross-sections. The NLTE effects in the G band increase with decreasing metallicity. When comparing the C abundances determined from the CH G band in LTE and in NLTE, we show that the C abundances are always under-estimated if LTE is assumed. The NLTE corrections to C abundance inferred from the CH feature range from +0.04 dex for the Sun to +0.21 dex for a red giant with metallicity [Fe/H] = −4.0. Conclusions. Departures from the LTE assumption in the CH molecule are non-negligible, and NLTE effects have to be taken into account in the diagnostic spectroscopy based on the CH lines. We show here that the NLTE effects in the optical CH lines are non-negligible for the Sun and red giant stars, but further calculations are warranted to investigate the effects in other regimes of stellar parameters. 

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 

Abstract A series of data samples was collected with the Belle II detector at the SuperKEKB collider from March 2019 to June 2022. We determine the integrated luminosities of these data samples using three distinct methodologies involving Bhabha (), digamma (), and dimuon () events. The total integrated luminosity obtained with Bhabha, digamma, and dimuon events is (426.88 ± 0.03 ± 2.61) fb⁻¹, (429.28 ± 0.03 ± 2.62) fb⁻¹, and (423.99 ± 0.04 ± 3.83) fb⁻¹, where the first uncertainties are statistical and the second are systematic. The resulting total integrated luminosity obtained from the combination of the three methods is (427.87 ± 2.01) fb⁻¹. 

We present a measurement of the branching fraction and time-dependent charge-parity ( $CP$) decay-rate asymmetries in $B^0\to J/\psi {\pi }^0$decays. The data sample was collected with the Belle II detector at the SuperKEKB asymmetric $e^{+}{e}^{-}$collider in 2019–2022 and contains $(387\pm 6)\times {10}^{6}B\overline{B}$meson pairs from $\mathrm{\Upsilon }\left(4S\right)$decays. We reconstruct $392\pm 24$signal decays and fit the $CP$parameters from the distribution of the proper-decay-time difference of the two $B$mesons. We measure the branching fraction to be $\left({\mathcal{B}}^0\to J/\psi {\pi }^0\right)=(2.00\pm 0.12\pm 0.09)\times {10}^{-5}$and the direct and mixing-induced $CP$asymmetries to be $C_{CP}=0.13\pm 0.12\pm 0.03$and $S_{CP}=-0.88\pm 0.17\pm 0.03$, respectively, where the first uncertainties are statistical and the second are systematic. We observe mixing-induced $CP$violation with a significance of 5.0 standard deviations for the first time in this mode. Published by the American Physical Society2025