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EOS is an open-source software for a variety of computational tasks in flavor physics. Its use cases include theory predictions within and beyond the Standard Model of particle physics, Bayesian inference of theory parameters from experimental and theoretical likelihoods, and simulation of pseudo events for a number of signal processes. EOS ensures high-performance computations through a C++ back-end and ease of usability through a Python front-end. To achieve this flexibility, EOS enables the user to select from a variety of implementations of the relevant decay processes and hadronic matrix elements at run time. In this article, we describe the general structure of the software framework and provide basic examples. Further details and in-depth interactive examples are provided as part of the EOS online documentation.

A bstract Using data samples of 983.0 fb − 1 and 427.9 fb − 1 accumulated with the Belle and Belle II detectors operating at the KEKB and SuperKEKB asymmetric-energy e + e − colliders, singly Cabibbo-suppressed decays Ξ c + → p K S 0 , Ξ c + → Λ π + , and Ξ c + → Σ 0 π + are observed for the first time. The ratios of branching fractions of Ξ c + → p K S 0 , Ξ c + → Λ π + , and Ξ c + → Σ 0 π + relative to that of Ξ c + → Ξ − π + π + are measured to be B Ξ c + → p K S 0 B Ξ c + → Ξ − π + π + = 2.47 ± 0.16 ± 0.07 % , B Ξ c + → Λ π + B Ξ c + → Ξ − π + π + = 1.56 ± 0.14 ± 0.09 % , B Ξ c + → Σ 0 π + B Ξ c + → Ξ − π + π + = 4.13 ± 0.26 ± 0.22 % . Multiplying these values by the branching fraction of the normalization channel, B Ξ c + → Ξ − π + π + = 2.9 ± 1.3 % , the absolute branching fractions are determined to be B Ξ c + → p K S 0 = 7.16 ± 0.46 ± 0.20 ± 3.21 × 10 − 4 , B Ξ c + → Λ π + = 4.52 ± 0.41 ± 0.26 ± 2.03 × 10 − 4 , B Ξ c + → Σ 0 π + = 1.20 ± 0.08 ± 0.07 ± 0.54 × 10 − 3 . The first and second uncertainties above are statistical and systematic, respectively, while the third ones arise from the uncertainty in B Ξ c + → Ξ − π + π + .

We present measurements ofB → K^(*)(892)γdecays using365 \\rm fb⁻¹of data collected from 2019 to 2022 by the Belle II experiment at the SuperKEKB asymmetric-energye⁺e⁻collider. The data sample contains(387 ± 6) × 10⁶Υ(4S)events. We measure branching fractions ( 𝓑 ) andC\\!{P}{}{a}symmetries ( 𝓐_(C\\!P) ) for bothB⁰→ K^(*0)γandB⁺→ K^(*+)γdecays. The difference inC\\!{P}{}{a}symmetries ( Δ𝓐_(C\\!P) ) and the isospin asymmetry ( Δ₀₊ ) between these neutral and charged channels are also measured. We obtain the following branching fractions andC\\!{P}{}{a}symmetries:𝓑 (B⁰ → K^(*0)γ) = (4.14 ± 0.10 ± 0.11 ) × 10⁻⁵ ,𝓑 (B⁺ → K^(*+)γ) = (4.04 ± 0.13 ^(+0.13)_(-0.15) )× 10⁻⁵ ,𝓐_(C\\!P) (B⁰ → K^(*0)γ) = (-3.3 ± 2.3 ± 0.4 )% , and𝓐_(C\\!P) (B⁺ → K^(*+)γ) = (-0.7 ± 2.9 ± 0.5 )% . The measured difference inC\\!{P}{}{a}symmetries isΔ𝓐_(C\\!P) = (+2.6 ± 3.8 ± 0.6 )% , and the measured isospin asymmetry isΔ₀₊ = (+4.8 ± 2.0 ± 1.8 )% . The first uncertainties listed are statistical and the second are systematic. These results are consistent with world-average values and theory predictions.

We perform the first search for CP violation in$$ {D}_{(s)}^{+}\\to {K}_S^0{K}^{-}{\\pi}^{+}{\\pi}^{+} $$D s + → K S 0 K − π + π + decays. We use a combined data set from the Belle and Belle II experiments, which study e + e − collisions at center-of-mass energies at or near the Υ(4 S ) resonance. We use 980 fb − 1 of data from Belle and 428 fb − 1 of data from Belle II. We measure six CP -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 + → K S 0 K − π + π + decays, and better than 0.3% for$$ {D}_s^{+}\\to {K}_S^0{K}^{-}{\\pi}^{+}{\\pi}^{+} $$D s + → K S 0 K − π + π + decays. No evidence of CP violation is found. Our results for the triple-product asymmetries are the most precise to date for singly-Cabibbo-suppressed D + decays. Our results for the other asymmetries are the first such measurements performed for charm decays.

A bstract We perform the first search for CP violation in D s + → K S 0 K − π + π + decays. We use a combined data set from the Belle and Belle II experiments, which study e + e − collisions at center-of-mass energies at or near the Υ(4 S ) resonance. We use 980 fb − 1 of data from Belle and 428 fb − 1 of data from Belle II. We measure six CP -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 + → K S 0 K − π + π + decays, and better than 0.3% for D s + → K S 0 K − π + π + decays. No evidence of CP violation is found. Our results for the triple-product asymmetries are the most precise to date for singly-Cabibbo-suppressed D + decays. Our results for the other asymmetries are the first such measurements performed for charm decays.

We report measurements of the absolute branching fractions𝓑(B_(s)⁰ → D_(s)^(±) X) ,𝓑(B_(s)⁰ → D⁰/D̄⁰ X) , and𝓑(B_(s)⁰ → D^(±) X) , where the latter is measured for the first time. The results are based on a 121.4 fb ⁻¹data sample collected at theΥ(10860)resonance by the Belle detector at the KEKB asymmetric-energye⁺ e⁻collider. We reconstruct oneB_(s)⁰meson ine⁺e⁻ → Υ(10860) → B_(s)^(*) B̄_(s)^(*)events and measure yields ofD_(s)⁺ ,D⁰ , andD⁺mesons in the rest of the event. We obtain𝓑(B_(s)⁰ → D_(s)^(±) X) = (68.6 ± 7.2 ± 4.0)% ,𝓑(B_(s)⁰ → D⁰/D̄⁰ X) = (21.5 ± 6.1 ± 1.8)% , and𝓑(B_(s)⁰ → D^(±) X) = (12.6 ± 4.6 ± 1.3)% , where the first uncertainty is statistical and the second is systematic. Averaging with previous Belle measurements gives𝓑(B_(s)⁰ → D_(s)^(±) X) = (63.4 ± 4.5 ± 2.2)%and𝓑(B_(s)⁰ → D⁰/D̄⁰ X) = (23.9 ± 4.1 ± 1.8)% . For theB_(s)⁰production fraction at theΥ(10860) , we findf_(s) = (21.4^(+1.5)_(-1.7))% .

Using data samples of 983.0 fb − 1 and 427.9 fb − 1 accumulated with the Belle and Belle II detectors operating at the KEKB and SuperKEKB asymmetric-energy e + e − colliders, singly Cabibbo-suppressed decays$$ {\\Xi}_c^{+}\\to p{K}_S^0 $$Ξ c + → p K S 0 ,$$ {\\Xi}_c^{+}\\to \\Lambda {\\pi}^{+} $$Ξ c + → Λ π + , and$$ {\\Xi}_c^{+}\\to {\\Sigma}^0{\\pi}^{+} $$Ξ c + → Σ 0 π + are observed for the first time. The ratios of branching fractions of$$ {\\Xi}_c^{+}\\to p{K}_S^0 $$Ξ c + → p K S 0 ,$$ {\\Xi}_c^{+}\\to \\Lambda {\\pi}^{+} $$Ξ c + → Λ π + , and$$ {\\Xi}_c^{+}\\to {\\Sigma}^0{\\pi}^{+} $$Ξ c + → Σ 0 π + relative to that of$$ {\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+} $$Ξ c + → Ξ − π + π + are measured to be$$ {\\displaystyle \\begin{array}{c}\\frac{\\mathcal{B}\\left({\\Xi}_c^{+}\\to p{K}_S^0\\right)}{\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+}\\right)}=\\left(2.47\\pm 0.16\\pm 0.07\\right)\\%,\\\ {}\\frac{\\mathcal{B}\\left({\\Xi}_c^{+}\\to \\Lambda {\\pi}^{+}\\right)}{\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+}\\right)}=\\left(1.56\\pm 0.14\\pm 0.09\\right)\\%,\\\ {}\\frac{\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Sigma}^0{\\pi}^{+}\\right)}{\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Xi}^{-}{\\pi}^{+}{\\pi}^{+}\\right)}=\\left(4.13\\pm 0.26\\pm 0.22\\right)\\%.\\end{array}} $$B Ξ c + → p K S 0 B Ξ c + → Ξ − π + π + = 2.47 ± 0.16 ± 0.07 % , B Ξ c + → Λ π + B Ξ c + → Ξ − π + π + = 1.56 ± 0.14 ± 0.09 % , B Ξ c + → Σ 0 π + B Ξ c + → Ξ − π + π + = 4.13 ± 0.26 ± 0.22 % . 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 Ξ c + → Ξ − π + π + = 2.9 ± 1.3 % , the absolute branching fractions are determined to be$$ {\\displaystyle \\begin{array}{c}\\mathcal{B}\\left({\\Xi}_c^{+}\\to p{K}_S^0\\right)=\\left(7.16\\pm 0.46\\pm 0.20\\pm 3.21\\right)\\times {10}^{-4},\\\ {}\\mathcal{B}\\left({\\Xi}_c^{+}\\to \\Lambda {\\pi}^{+}\\right)=\\left(4.52\\pm 0.41\\pm 0.26\\pm 2.03\\right)\\times {10}^{-4},\\\ {}\\mathcal{B}\\left({\\Xi}_c^{+}\\to {\\Sigma}^0{\\pi}^{+}\\right)=\\left(1.20\\pm 0.08\\pm 0.07\\pm 0.54\\right)\\times {10}^{-3}.\\end{array}} $$B Ξ c + → p K S 0 = 7.16 ± 0.46 ± 0.20 ± 3.21 × 10 − 4 , B Ξ c + → Λ π + = 4.52 ± 0.41 ± 0.26 ± 2.03 × 10 − 4 , B Ξ c + → Σ 0 π + = 1.20 ± 0.08 ± 0.07 ± 0.54 × 10 − 3 . 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 Ξ c + → Ξ − π + π + .

We perform the first search for$C\\!P$violation in${D_{(s)}^{+}\\to{}K_{S}^{0}K^{-}\\pi^{+}\\pi^{+}}$decays. We use a combined data set from the Belle and Belle II experiments, which study$e^+e^-$collisions at center-of-mass energies at or near the$\\Upsilon(4S)$resonance. We use 980 fb $^{-1}$of data from Belle and 428 fb $^{-1}$of data from Belle~II. We measure six$C\\!P$ -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$D^+\\to{}K_{S}^{0}K^{-}\\pi^{+}\\pi^{+}$decays, and better than 0.3% for$D^+_{s}\\to{}K_{S}^{0}K^{-}\\pi^{+}\\pi^{+}$decays. No evidence of$C\\!P$violation is found. Our results for the triple-product asymmetries are the most precise to date for singly-Cabibbo-suppressed$D^+$decays. Our results for the other asymmetries are the first such measurements performed for charm decays. 21 pages, 10 figures

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

We report measurements of thee⁺e⁻ → BB̄ ,BB̄^(*) , andB^(*)B̄^(*)cross sections at four energies, 10653, 10701, 10746 and 10805 MeV, using data collected by the Belle II experiment. We reconstruct oneBmeson in a large number of hadronic final states and use its momentum to identify the production process. In the first2-5MeV aboveB^(*)B̄^(*)threshold, thee⁺e⁻ → B^(*)B̄^(*)cross section increases rapidly. This may indicate the presence of a pole close to the threshold.