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We present an up-to-date profile of the Cabibbo-Kobayashi-Maskawa matrix with emphasis on the interpretation of recent CP-violation results from the B factories. For this purpose, we review all relevant experimental and theoretical inputs from the contributing domains of electroweak interaction. We give the “standard” determination of the apex of the Unitarity Triangle, namely the Wolfenstein parameters \\(\\overline\\rho\\) and \\(\\overline\\eta\\), by means of a global CKM fit. The fit is dominated by the precision measurement of \\(\\sin 2 \\beta\\) by the B factories. A detailed numerical and graphical study of the impact of the results is presented. We propose to include \\(\\sin 2\\alpha\\) from the recent measurement of the time-dependent CP-violating asymmetries in \\(B^0\\to\\rho^ + \\rho^-\\), using isospin relations to discriminate the penguin contribution. The constraint from \\(\\varepsilon^\\prime/\\varepsilon\\) is discussed. We study the impact from the branching fraction measurement of the rare kaon decay \\(K^ + \\to\\pi^ + \\nu\\overline\\nu\\), and give an outlook into the reach of a future measurement of \\(K^0_L\\to\\pi^0\\nu\\overline\\nu\\). The B system is investigated in detail. We display the constraint on \\(2\\beta + \\gamma\\) and \\(\\gamma\\) from \\(B^0\\to D^{(*)\\pm}\\pi^\\mp\\) and \\(B^ + \\to D^{(*)0}K^ + \\) decays, respectively. A significant part of this paper is dedicated to the understanding of the dynamics of B decays into \\(\\pi\\pi\\), \\(K\\pi\\), \\(\\rho\\pi\\), \\(\\rho\\rho\\) and modes related to these by flavor symmetry. Various phenomenological approaches and theoretical frameworks are discussed. We find a remarkable agreement of the \\(\\pi\\pi\\) and \\(K\\pi\\) data with the other constraints in the unitarity plane when the hadronic matrix elements are calculated within QCD Factorization, where we apply a conservative treatment of the theoretical uncertainties. A global fit of QCD Factorization to all \\(\\pi\\pi\\) and \\(K\\pi\\) data leads to precise predictions of the related observables. However sizable phenomenological power corrections are preferred. Using an isospin-based phenomenological parameterization, we analyze separately the \\(B\\to K\\pi\\) decays, and the impact of electroweak penguins in response to recent discussions. We find that the present data are not sufficiently precise to constrain either electroweak parameters or hadronic amplitude ratios. We do not observe any unambiguous sign of New Physics, whereas there is some evidence for potentially large non-perturbative rescattering effects. Finally we use a model-independent description of a large class of New Physics effects in both \\(B^0\\overline B^0\\) mixing and B decays, namely in the \\(b\\to d\\) and \\(b\\to s\\) gluonic penguin amplitudes, to perform a new numerical analysis. Significant non-standard corrections cannot be excluded yet, however Standard Model solutions are favored in most cases. In the appendix to this paper we propose a frequentist method to extract a confidence level on \\(\\Delta m_s\\) from the experimental information on \\(B^0_s \\overline B_s^0\\) oscillation. In addition we describe a novel approach to combine potentially inconsistent measurements. All results reported in this paper have been obtained with the numerical analysis package CKMfitter, featuring the frequentist statistical approach Rfit.

The Belle II experiment’s ability to identify particles critically affects the sensitivity of its measurements. We describe Belle II’s algorithms for identifying charged particles and evaluate their performance in separating pions, kaons, and protons using 426 fb - 1 of data collected at the energy-asymmetric e + e - collider SuperKEKB in 2019–2022 at center-of-mass energies at and near the mass of the Υ (4S).

A bstract We present the result of a search for the charged-lepton-flavor violating decay τ − → μ − μ + μ − using a 424 fb − 1 sample of data recorded by the Belle II experiment at the SuperKEKB e + e − collider. The selection of e + e − → τ + τ − events is based on an inclusive reconstruction of the non-signal tau decay, and on a boosted decision tree to suppress background. We observe one signal candidate, which is compatible with the expectation from background processes. We set a 90% confidence level upper limit of 1 . 9 × 10 − 8 on the branching fraction of the τ − → μ − μ + μ − decay, which is the most stringent bound to date.

A bstract We report measurements of the absolute branching fractions , , and , where the latter is measured for the first time. The results are based on a 121.4 fb − 1 data sample collected at the Υ(10860) resonance by the Belle detector at the KEKB asymmetric-energy e + e − collider. We reconstruct one meson in events and measure yields of , D 0 , and D + mesons in the rest of the event. We obtain , , and , where the first uncertainty is statistical and the second is systematic. Averaging with previous Belle measurements gives and . For the production fraction at the Υ(10860), we find .

A bstract We present the results of a search for charged-lepton-flavor violating decays , where ℓ − is either an electron or a muon. We combine e + e − data samples recorded by the Belle II experiment at the SuperKEKB collider (428 fb − 1 ) with samples recorded by the Belle experiment at the KEKB collider (980 fb − 1 ) to obtain a sample of 1.3 billion e + e − → τ + τ − events. We observe 0 and 1 events and set 90% confidence level upper limits of 0 . 8 × 10 − 8 and 1 . 2 × 10 − 8 on the branching fractions of the decay modes and , respectively. These are the most stringent upper limits to date.

A bstract We present the results of a search for the charged-lepton-flavor violating decays B 0 → K *0 τ ± ℓ ∓ , where ℓ ∓ is either an electron or a muon. The results are based on 365 fb − 1 and 711 fb − 1 datasets collected with the Belle II and Belle detectors, respectively. We use an exclusive hadronic B -tagging technique, and search for a signal decay in the system recoiling against a fully reconstructed B meson. We find no evidence for B 0 → K *0 τ ± ℓ ∓ decays and set upper limits on the branching fractions in the range of (2.9–6.4)×10 − 5 at 90% confidence level.

We present measurements of the branching fractions of eight$$ {\\overline{B}}^0 $$B ¯ 0 → D (*)+ K −$$ {K}_{(S)}^{\\left(\\ast \\right)0} $$K S ∗ 0 , B − → D (*)0 K −$$ {K}_{(S)}^{\\left(\\ast \\right)0} $$K S ∗ 0 decay channels. The results are based on data from SuperKEKB electron-positron collisions at the Υ(4 S ) resonance collected with the Belle II detector, corresponding to an integrated luminosity of 362 fb − 1 . The event yields are extracted from fits to the distributions of the difference between expected and observed B meson energy, and are efficiency-corrected as a function of m ( K −$$ {K}_{(S)}^{\\left(\\ast \\right)0} $$K S ∗ 0 ) and m ( D (*)$$ {K}_{(S)}^{\\left(\\ast \\right)0} $$K S ∗ 0 ) in order to avoid dependence on the decay model. These results include the first observation of$$ {\\overline{B}}^0 $$B ¯ 0 → D + K −$$ {K}_S^0 $$K S 0 , B − → D* 0 K −$$ {K}_S^0 $$K S 0 , and$$ {\\overline{B}}^0 $$B ¯ 0 → D* + K −$$ {K}_S^0 $$K S 0 decays and a significant improvement in the precision of the other channels compared to previous measurements. The helicity-angle distributions and the invariant mass distributions of the K −$$ {K}_{(S)}^{\\left(\\ast \\right)0} $$K S ∗ 0 systems are compatible with quasi-two-body decays via a resonant transition with spin-parity J P = 1 − for the K −$$ {K}_S^0 $$K S 0 systems and J P = 1 + for the K − K* 0 systems. We also present measurements of the branching fractions of four$$ {\\overline{B}}^0 $$B ¯ 0 → D (*)+$$ {D}_s^{-} $$D s − , B − → D (*)0$$ {D}_s^{-} $$D s − decay channels with a precision compatible to the current world averages.

We report measurements of the e + e − →$$ B\\overline{B} $$B B ¯ ,$$ B{\\overline{B}}^{\\ast } $$B B ¯ ∗ , and$$ {B}^{\\ast }{\\overline{B}}^{\\ast } $$B ∗ B ¯ ∗ cross sections at four energies, 10653, 10701, 10746 and 10805 MeV, using data collected by the Belle II experiment. We reconstruct one B meson in a large number of hadronic final states and use its momentum to identify the production process. In the first 2 – 5 MeV above$$ {B}^{\\ast }{\\overline{B}}^{\\ast } $$B ∗ B ¯ ∗ threshold, the e + e − →$$ {B}^{\\ast }{\\overline{B}}^{\\ast } $$B ∗ B ¯ ∗ cross section increases rapidly. This may indicate the presence of a pole close to the threshold.

We measure CP asymmetries and branching-fraction ratios for B ± → DK ± and Dπ ± decays with D →$$ {K}_{\\textrm{S}}^0 $$K S 0 K ± π ∓ , where D is a superposition of D 0 and$$ \\overline{D} $$D ¯ 0 . We use the full data set of the Belle experiment, containing 772 × 10 6$$ B\\overline{B} $$B B ¯ pairs, and data from the Belle II experiment, containing 387 × 10 6$$ B\\overline{B} $$B B ¯ pairs, both collected in electron-positron collisions at the Υ(4 S ) resonance. Our results provide model-independent information on the unitarity triangle angle ϕ 3 .