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K. Lieret

Publications and source records attributed to K. Lieret.

At least 19 recordsLinked to original sources

Search for a heavy neutral lepton that mixes predominantly with the tau neutrino

We report a search for a heavy neutral lepton (HNL) that mixes predominantly with $\nu_\tau$. The search utilizes data collected with the Belle detector at the KEKB asymmetric energy $e^+ e^-$ collider. The data sample was collected at and just below the center-of-mass energies of the $\Upsilon(4S)$ and $\Upsilon(5S)$ resonances and has an integrated luminosity of $915~\textrm{fb}^{-1}$, corresponding to $(836\pm 12)\times 10^6$ $e^+e^\to\tau^+\tau^-$ events. We search for production of the HNL (denoted $N$) in the decay $\tau^-\to \pi^- N$ followed by its decay via $N \to \mu^+\mu^- \nu_\tau$. The search focuses on the parameter-space region in which the HNL is long lived, so that the $\mu^+\mu^-$ originate from a common vertex that is significantly displaced from the collision point of the KEKB beams. Consistent with the expected background yield, one event is observed in the data sample after application of all the event-selection criteria. We report limits on the mixing parameter of the HNL with the $\tau$ neutrino as a function of the HNL mass.

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Training and Onboarding initiatives in High Energy Physics experiments

In this paper we document the current analysis software training and onboarding activities in several High Energy Physics (HEP) experiments: ATLAS, CMS, LHCb, Belle II and DUNE. Fast and efficient onboarding of new collaboration members is increasingly important for HEP experiments as analyses and the related software become ever more complex with growing datasets. A meeting series was held by the HEP Software Foundation (HSF) in 2022 for experiments to showcase their initiatives. Here we document and analyse these in an attempt to determine a set of key considerations for future experiments.

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Search for baryon and lepton number violating decays $\boldsymbol{D \rightarrow p\ell}$

We search for the baryon and lepton number violating charm decays, $D \rightarrow p\ell$, where $D$ is either a $D^0$ or a $\overline{D}^0$ and $\ell$ is a muon or an electron, using a data sample of $921\,\mathrm{fb}^{-1}$ collected by the Belle detector at the KEKB asymmetric energy $e^{+}e^{-}$ collider. In the absence of significant signals, we set upper limits on the branching fractions in the range $(5 - 8) \times 10^{-7}$ at a 90\% confidence level, depending on the decay mode.

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Observation of charmed strange meson pair production in $\Upsilon(2S)$ decays and in $e^{+}e^{-}$ annihilation at $\sqrt{s} = 10.52~ \rm{GeV}$

We observe the process $\Upsilon(2S)\to D_s^{(*)+} D_{sJ}^{-}$ and continuum production $e^+e^- \to D_s^{(*)+} D_{sJ}^- $ at $\sqrt{s} = 10.52$ GeV (and their charge conjugates) using the data samples collected by the Belle detector at KEKB, where $D_{sJ}^-$ is $D_{s1}(2536)^-$ or $D^{*}_{s2}(2573)^-$. Both $D_{sJ}^-$ states are identified through their decay into $\bar{K}\bar{D}^{(*)}$. We measure the products of branching fractions ${\cal B}(\Upsilon(2S) \to D_{s}^{(*)+} D_{sJ}^-) {\cal B}(D_{sJ}^-\to \bar{K} \bar{D}^{(*)})$ and the Born cross sections $\sigma^{\rm Born}(e^+e^- \to D_{s}^{(*)+} D_{sJ}^-) {\cal B}(D_{sJ}^-\to \bar{K} \bar{D}^{(*)})$, and then compare the ratios $R_1 \equiv {\cal B}(\Upsilon(2S)\to D_{s}^{(*)+} D_{sJ}^-)/{\cal B}(\Upsilon(2S)\to\mu^{+}\mu^-)$ for $\Upsilon(2S)$ decays and $R_2 \equiv \sigma^{\rm Born}(e^+e^-\to D_{s}^{(*)+}D_{sJ}^-)/\sigma^{\rm Born}(e^+e^-\to \mu^{+}\mu^-)$ for continuum production. We obtain $R_1/R_2 = 9.7\pm 2.3 \pm 1.1$, $6.8 \pm 2.1 \pm 0.8$, $10.2 \pm 3.3 \pm 2.5$, and $3.4 \pm 2.1 \pm 0.5$ for the $D_s^+ D_{s1}(2536)^-$, $D_s^{*+} D_{s1}(2536)^-$, $D_s^+ D_{s2}^{*}(2573)^{-}$, and $D_s^{*+} D_{s2}^{*}(2573)^{-}$ final states in the $D_{sJ}^-\to K^{-} \bar{D}^{(*)0}$ modes, respectively. Therefore, the strong decay is expected to dominate in the $\Upsilon(2S)\to D_{s}^{(*)+}D_{sJ}^-$ processes. We also measure the ratios of branching fractions ${\cal B}(D_{s1}(2536)^-\to K_S^0 D^{*}(2010)^{-})/{\cal B}(D_{s1}(2536)^-\to K^{-} D^{*}(2007)^0) = 0.48 \pm 0.07 \pm 0.02$ and ${\cal B}(D_{s2}^{*}(2573)^- \to K_S^0 D^-)/{\cal B}(D_{s2}^{*}(2573)^- \to K^{-}D^0) = 0.49 \pm 0.10 \pm 0.02$, which are consistent with isospin symmetry. The second ratio is the first measurement of this quantity. Here, the first uncertainties are statistical and the second are systematic.

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Search for $C\!P$ violation using $T$-odd correlations in $D_{(s)}^{+}\to K^{+} K^{-}\pi^{+}\pi^{0}$, $D_{(s)}^{+}\to K^{+} \pi^{-}\pi^{+}\pi^{0}$, and $D^{+}\to K^{-}\pi^{+}\pi^{+}\pi^{0}$ decays

We search for $C\!P$ violation using $T$-odd correlations in five $D_{(s)}^{+}$ and $D_{(s)}^{-}$ four-body decays. Our analysis is based on 980 $\rm fb^{-1}$ of data collected by the Belle detector at the KEKB energy-asymmetric $e^+e^-$ collider. Our results for the $T$-odd $C\!P$-violating parameter $a^{T\text{-odd}}_{C\!P}$ are: $a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{-}K^{+}\pi^{+}\pi^{0}}) = (+2.6\pm 6.6\pm 1.3 )\times10^{-3}$, $a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{+}\pi^{-}\pi^{+}\pi^{0}}) = (-1.3\pm 4.2\pm 0.1 )\times10^{-2}$, $a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{-}\pi^{+}\pi^{+}\pi^{0}}) = (+0.2\pm 1.5\pm 0.8 )\times10^{-3}$, $a^{T\text{-odd}}_{C\!P}({D_s^{+}\to K^{+}\pi^{-}\pi^{+}\pi^{0}}) = (-1.1\pm 2.2\pm 0.1 )\times10^{-2}$, and $a^{T\text{-odd}}_{C\!P}({D_s^{+}\to K^{-}K^{+}\pi^{+}\pi^{0}}) = (+2.2\pm 3.3\pm 4.3 )\times10^{-3}$, where the uncertainties are statistical and systematic, respectively. These results are the first such measurements and are all consistent with zero. They include the first measurement for a $D^+_s$ singly Cabibbo-suppressed decay, and the first measurement for a $D$ meson doubly Cabibbo-suppressed decay. We also measure $a^{T\text{-odd}}_{C\!P}$ in different subregions of phase space, where the decays are dominated by different intermediate resonance states such as $D^+\to\phi\rho^+$, $\bar{K}^{*0}K^{*+}$, and $\bar{K}^{*0}\rho^+$; and $D_s^+\to K^{*+}\rho^{0}$, $K^{*0}\rho^{+}$, $\phi\rho^+$, and $\bar{K}^{*0}K^{*+}$. No evidence for $C\!P$ violation is found.

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Measurement of Differential Distributions of $B \to D^* \ell \bar \nu_\ell$ and Implications on $|V_{cb}|$

We present a measurement of the differential shapes of exclusive $B\to D^* \ell \bar{\nu}_\ell$ ($B = B^-, \bar{B}^0 $ and $\ell = e, \mu$) decays with hadronic tag-side reconstruction for the full Belle data set of $711\,\mathrm{fb}^{-1}$ integrated luminosity. We extract the Caprini-Lellouch-Neubert (CLN) and Boyd-Grinstein-Lebed (BGL) form factor parameters and use an external input for the absolute branching fractions to determine the Cabibbo-Kobayashi-Maskawa matrix element and find $|V_{cb}|_\mathrm{CLN} = (40.1\pm0.9)\times 10^{-3}$ and $|V_{cb}|_\mathrm{BGL} = (40.6\pm 0.9)\times 10^{-3}$ with the zero-recoil lattice QCD point $\mathcal{F}(1) = 0.906 \pm 0.013$. We also perform a study of the impact of preliminary beyond zero-recoil lattice QCD calculations on the $|V_{cb}|$ determinations. Additionally, we present the lepton flavor universality ratio $R_{e\mu} = \mathcal{B}(B \to D^* e \bar{\nu}_e) / \mathcal{B}(B \to D^* \mu \bar{\nu}_\mu) = 0.990 \pm 0.021 \pm 0.023$, the electron and muon forward-backward asymmetry and their difference $\Delta A_{FB}=0.022\pm0.026\pm 0.007$, and the electron and muon $D^*$ longitudinal polarization fraction and their difference $\Delta F_L^{D^*} = 0.034 \pm 0.024 \pm 0.007$. The uncertainties quoted correspond to the statistical and systematic uncertainties, respectively.

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Search for lepton-flavor-violating $\tau$ decays into a lepton and a vector meson using the full Belle data sample

Charged-lepton-flavor-violation is predicted in several new physics scenarios. We update the analysis of $\tau$ lepton decays into a light charged lepton ($\ell$ = $e^{\pm}$ or $\mu^{\pm}$) and a vector meson ($V^0$ = $\rho^0$, $\phi$, $\omega$, $K^{\ast0}$, or $\overline{K}{}^{\ast0}$) using 980 fb$^{-1}$ of data collected with the Belle detector at the KEKB collider. No significant excess of such signal events is observed, and thus 90% credibility level upper limits are set on the $\tau \rightarrow \ell V^0$ branching fractions in the range of (1.7--$4.3) \times 10^{-8}$. These limits are improved by 30% on average from the previous results.

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Measurement of the mass and width of the $\Lambda_c(2625)^+$ and the branching ratios of $\Lambda_c(2625)^+ \to \Sigma_c^{0}\pi^{+}$ and $\Lambda_c(2625)^+ \to \Sigma_c^{++}\pi^{-}$

Using the entire data sample of $980\,\textrm{fb}^{-1}$ collected with the Belle detector operating at the KEKB asymmetric-energy collider, we report the measurement of the mass, width, and the relative branching ratios of the $\Lambda_c(2625)^+$ charmed baryon. The mass difference between $\Lambda_c(2625)^+$ and $\Lambda_c^+$ is measured to be $M(\Lambda_c(2625)^{+}) - M(\Lambda_c^{+}) = 341.518 \pm 0.006 \pm 0.049\ \mathrm{MeV}/\mathit{c}^2$. The upper limit on the width is measured to be $\Gamma(\Lambda_c(2625)^+) < 0.52\,\mathrm{MeV}/\textit{c}^2$ at 90\% credibility level. Based on a full Dalitz plot fit, branching ratios with respect to the mode $\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^+ \pi^-$ are measured to be $\frac{\mathcal{B}(\Lambda_c(2625)^+ \to \Sigma_c^{0} \pi^{+})} {\mathcal{B}(\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-})} = (5.19 \pm 0.23 \pm 0.40) \%$ and $\frac{\mathcal{B}(\Lambda_c(2625)^+ \to \Sigma_c^{++} \pi^{-})} {\mathcal{B}(\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-})} = (5.13 \pm 0.26 \pm 0.32) \%$. These measurements can be used to further constrain the parameters of the underlying theoretical models.

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Measurements of branching fractions of $\Lambda_c^+ \to \Sigma^+ \eta$ and $\Lambda_c^+ \to \Sigma^+ \eta'$ and asymmetry parameters of $\Lambda_c^+ \to \Sigma^+ \pi^0$, $\Lambda_c^+ \to \Sigma^+ \eta$, and $\Lambda_c^+ \to \Sigma^+ \eta'$

We report a study of $\Lambda_c^+ \to \Sigma^+ \pi^0$, $\Lambda_c^+ \to \Sigma^+ \eta$, and $\Lambda_c^+ \to \Sigma^+ \eta'$ using the data sample corresponding to an integrated luminosity of 980 $\rm fb^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. The branching fractions relative to $\Lambda_c^+ \to \Sigma^+ \pi^0$ are measured as: $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta}/\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \pi^0}=0.25 \pm 0.03 \pm 0.01$ and $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta'}/\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \pi^0}=0.33 \pm 0.06 \pm 0.02$. Using $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \pi^0}=(1.25 \pm 0.10)\%$, we obtain $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta}=(3.14 \pm 0.35 \pm 0.11 \pm 0.25)\times10^{-3}$ and $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta'}=(4.16 \pm 0.75 \pm 0.21 \pm 0.33)\times10^{-3}$. Here the uncertainties are statistical, systematic, and from $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \pi^0}$, respectively. The ratio of the branching fraction of $\Lambda_c^+ \to \Sigma^+ \eta'$ with respect to that of $\Lambda_c^+ \to \Sigma^+ \eta$ is measured to be $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta'}/\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta}=1.34 \pm 0.28 \pm 0.06$. We update the asymmetry parameter of $\Lambda_c^+ \to \Sigma^+ \pi^0$, $\alpha_{\Sigma^+ \pi^0} = -0.48 \pm 0.02 \pm 0.02$, with a considerably improved precision. The asymmetry parameters of $\Lambda_c^+ \to \Sigma^+ \eta$ and $\Lambda_c^+ \to \Sigma^+ \eta'$ are measured to be $\alpha_{\Sigma^+ \eta} = -0.99 \pm 0.03 \pm 0.05$ and $\alpha_{\Sigma^+ \eta'} = -0.46 \pm 0.06 \pm 0.03$ for the first time.

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Search for $C\!P$ violation and measurement of branching fractions and decay asymmetry parameters for $\Lambda_c^+\to\Lambda h^+$ and $\Lambda_c^+\to\Sigma^{0} h^+$ ($h\!=\!K,\,\pi$)

We report a study of $\Lambda_c^+\to\Lambda h^+$ and $\Lambda_c^+\to\Sigma^{0} h^+$ ($h\!=\!K,\,\pi$) decays based on a data sample of 980~${\rm fb}^{-1}$ collected with the Belle detector at the KEKB energy-asymmetric $e^+e^-$ collider. The first results of direct $C\!P$ asymmetry in two-body singly Cabibbo-suppressed (SCS) decays of charmed baryons are measured, $A_{C\!P}^{\rm{dir}}(\Lambda_c^+\to\Lambda K^+)\!=\!+0.021\pm0.026\pm0.001$ and $A_{C\!P}^{\rm{dir}}(\Lambda_c^+\to\Sigma^0K^+)\!=\!+0.025\pm0.054\pm0.004$. We also make the most precise measurement of the decay asymmetry parameters ($\alpha$) for the four modes of interest and search for $C\!P$ violation via the $\alpha$-induced $C\!P$ asymmetry ($A_{C\!P}^{\alpha}$). We measure $A_{C\!P}^{\alpha}(\Lambda_c^+\to\Lambda K^+)\!=\!{-0.023\pm0.086\pm0.071}$ and $A_{C\!P}^{\alpha}(\Lambda_c^+\to\Sigma^0K^+)\!=\!{+0.08\pm 0.35\pm 0.14}$, which are the first $A_{C\!P}^{\alpha}$ results for SCS decays of charmed baryons. We search for $\Lambda$-hyperon $C\!P$ violation in $\Lambda_c^+\to(\Lambda,\,\Sigma^0)\pi^+$ and find $A_{C\!P}^{\alpha}(\Lambda\to p\pi^{-})\!=\!{+0.013\pm0.007\pm0.011}$. This is the first time that hyperon $C\!P$ violation has been measured via Cabibbo-favored charm decays. No evidence of baryon $C\!P$ violation is found. We also obtain the most precise branching fractions for two SCS $\Lambda_c^+$ decays, $\mathcal{B}(\Lambda_c^+\to\Lambda K^+)\!=\!(6.57\pm0.17\pm0.11\pm0.35)\times10^{-4}$ and $\mathcal{B}(\Lambda_c^+\to\Sigma^0K^+)\!=\!(3.58\pm0.19\pm0.06\pm0.19)\times10^{-4}$. The first uncertainties are statistical and the second systematic, while the third uncertainties come from the uncertainties on the world average branching fractions of $\Lambda_c^+\to(\Lambda,\,\Sigma^0)\pi^+$.

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Search for a dark leptophilic scalar produced in association with $\tau^+\tau^-$ pair in $e^+e^-$ annihilation at center-of-mass energies near 10.58 GeV

A dark leptophilic scalar $(\phi_L)$ is a hypothetical particle that couples only to leptons rather than quarks. We report on a search for $\phi_L$ in the $e^+e^- \to \tau^+ \tau^- \phi_L, ~\phi_L \to \ell^+ \ell^- ~(\ell = e, \mu)$ process using 626~\invfb of data collected by the Belle experiment near the \Y4S resonance. We validate the backgrounds with multiple control regions in data, using a novel multiclass multivariate event classifier. In absence of a signal, we quote upper limits at the 90\% confidence level on the coupling between $\phi_L$ and leptons. Our bounds, obtained in a blinded approach, are 19\% more constraining than the previous limits, averaged over the mass range $0.04 \leq m_{\phi_L} \leq 6.5~\gev$. We exclude the parameter space below 4~\gev favored by measurement of the anomalous magnetic moment of the muon.

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Measurement of the branching fraction of $\Xi_{c}^{0}\to \Lambda_{c}^{+}\pi^{-}$ at Belle

Based on a data sample of 983 fb$^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider, we present the study of the heavy-flavor-conserving decay $\Xi_{c}^{0}\to \Lambda_{c}^{+}\pi^{-}$ with $\Lambda_{c}^{+}$ reconstructed via its $pK^{-} \pi^{+}$ decay mode. The branching fraction ratio $\mathcal{B}(\Xi_{c}^{0}\to \Lambda_{c}^{+}\pi^{-})/\mathcal{B}(\Xi_{c}^{0}\to \Xi^{-}\pi^{+})$ is measured to be $0.38 \pm 0.04 \pm 0.04$. Combing with the world average value of $\mathcal{B}(\Xi_{c}^{0}\to \Xi^{-}\pi^{+})$, the branching fraction $\mathcal{B}(\Xi_{c}^{0}\to \Lambda_{c}^{+}\pi^{-})$ is deduced to be $(0.54 \pm 0.05 \pm 0.05 \pm 0.12)\%$. Here, the uncertainties above are statistical, systematic, and from $\mathcal{B}(\Xi_c^{0} \to \Xi^{-}\pi^{+})$, respectively.

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Measurement of Two-Particle Correlations of Hadrons in $e^{+}e^{-}$ Collisions at Belle

The measurement of two-particle angular correlation functions in high-multiplicity $e^+e^-$ collisions at $\sqrt{s}=10.52$ GeV is reported. In this study, the $89.5~{\text{fb}}^{-1}$ of hadronic $e^+e^-$ annihilation data collected by the Belle detector at KEKB are used. Two-particle angular correlation functions are measured in the full relative azimuthal angle ($\Delta \phi$) and three units of pseudorapidity ($\Delta \eta$), defined by either the electron beam axis or the event-shape thrust axis, and are studied as a function of charged-particle multiplicity. The measurement in the thrust axis analysis, with mostly outgoing quark pairs determining the reference axis, is sensitive to the region of additional soft gluon emissions. No significant anisotropic collective behavior is observed with either coordinate analyses. Near-side jet correlations appear to be absent in the thrust axis analysis. The measurements are compared to predictions from various event generators and are expected to provide new constraints to the phenomenological models in the low-energy regime.

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Search for the decay $B_s^0\rightarrow\eta\eta$

We report results from a search for the decay $B_s^0\rightarrow\eta\eta$ using 121.4 fb$^{-1}$ of data collected at the $\Upsilon(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. We do not observe any signal and set an upper limit on the branching fraction of $14.3\times 10^{-5}$ at $90\%$ confidence level. This result represents a significant improvement over the previous most stringent limit.

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Search for $B^0$ meson decays into $\Lambda$ and missing energy with a hadronic tagging method at Belle

We present a search for the decays of $B^0$ mesons into a final state containing a $\Lambda$ baryon and missing energy. These results are obtained from a $711\text{fb}^{-1}$ data sample that contains $772 \times 10^6$ $B{\kern 0.18em}\overline{\kern -0.18em B}$ pairs and was collected near the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. We use events in which one $B$ meson is fully reconstructed in a hadronic decay mode and require the remainder of the event to consist of only a single $\Lambda$. No evidence for these decays is found and we set $90\%$ confidence level upper limits on the branching fractions in the range $2.1$-$3.8\times 10^{-5}$. This measurement provides the world's most restrictive limits, with implications for baryogenesis and dark matter production.

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Punzi-loss: A non-differentiable metric approximation for sensitivity optimisation in the search for new particles

We present the novel implementation of a non-differentiable metric approximation and a corresponding loss-scheduling aimed at the search for new particles of unknown mass in high energy physics experiments. We call the loss-scheduling, based on the minimisation of a figure-of-merit related function typical of particle physics, a Punzi-loss function, and the neural network that utilises this loss function a Punzi-net. We show that the Punzi-net outperforms standard multivariate analysis techniques and generalises well to mass hypotheses for which it was not trained. This is achieved by training a single classifier that provides a coherent and optimal classification of all signal hypotheses over the whole search space. Our result constitutes a complementary approach to fully differentiable analyses in particle physics. We implemented this work using PyTorch and provide users full access to a public repository containing all the codes and a training example.

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$B$-flavor tagging at Belle II

We report on new flavor tagging algorithms developed to determine the quark-flavor content of bottom ($B$) mesons at Belle II. The algorithms provide essential inputs for measurements of quark-flavor mixing and charge-parity violation. We validate and evaluate the performance of the algorithms using hadronic $B$ decays with flavor-specific final states reconstructed in a data set corresponding to an integrated luminosity of $62.8$ fb$^{-1}$, collected at the $\Upsilon$(4$S$) resonance with the Belle II detector at the SuperKEKB collider. We measure the total effective tagging efficiency to be $\varepsilon_{\rm eff} = \big(30.0 \pm 1.2(\text{stat}) \pm 0.4(\text{syst})\big)\%$ for a category-based algorithm and $\varepsilon_{\rm eff} = \big(28.8 \pm 1.2(\text{stat}) \pm 0.4(\text{syst})\big)\%$ for a deep-learning-based algorithm.

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Study of $e^+e^-\to \Upsilon(\rm1S,2S)\eta$ and $e^+e^-\to \Upsilon(\rm 1S)\eta^{\prime}$ at $\sqrt{s}=10.866$ GeV with the Belle detector

We report the first observation of the processes $e^+e^-\to\Upsilon(\rm 1S,2S)\eta$ at $\sqrt{s}=10.866$~GeV with a $10.2\sigma$ and $16.5\sigma$ significance respectively. The measured Born cross sections are $\sigma(e^+e^- \to \Upsilon(2S)\eta)=2.07 \pm 0.21 \pm 0.19$~pb, and $\sigma(e^+e^- \to \Upsilon(\rm 1S)\eta)=0.42 \pm 0.08 \pm 0.04$~pb. We also set the upper limit on the cross section of the process $e^+e^- \to \Upsilon(\rm 1S)\eta^{\prime}$ to be $\sigma(e^+e^- \to \Upsilon(\rm 1S)\eta^{\prime})<0.035$~pb at $90\%$ CL. The results are obtained with the data sample collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider in the energy range from $10.63$~GeV to $11.02$~GeV.

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