arXiv subjects

T. V. Dong

Publications and source records attributed to T. V. Dong.

At least 19 recordsLinked to original sources

arXiv2026

Study of $e^+e^- \to π^+π^-Υ(1D)$ at Belle II

The bottomonium spectrum, consisting of bound states of a $ b $ quark and an anti-$ b $ quark, provides an excellent laboratory for probing quantum chromodynamics in the non-perturbative regime. While S and P-wave bottomonium states are well studied experimentally, information on D-wave states remains scarce. We search for the D-wave bottomonium states $ Υ_2(1D) $ and $ Υ_3(1D) $ via the decay of a vector bottomonium-like state $Υ(10753)$ in the reaction $e^+e^- \to π^+π^- Υ(1D)$, using $19.6~\mathrm{fb}^{-1}$ of data collected with the Belle II detector at center-of-mass energies $\sqrt{s} = 10.653$, 10.701, 10.745, and 10.805~GeV, in the vicinity of the $ Υ(10753) $ resonance. No significant signals are observed. We set upper limits at the 90\% credibility level on the products of the cross sections and branching fractions, $σ[e^+e^- \to π^+π^- Υ_2(1D)] \times \mathcal{B}[Υ_2(1D) \to γχ_{b1}]$ and $σ[e^+e^- \to π^+π^- Υ_3(1D)] \times \mathcal{B}[Υ_3(1D) \to γχ_{b2}]$, at each center-of-mass energy.

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arXiv2026

Search for the decay $B^+ \rightarrow K^+τ^+τ^-$ using data from the Belle and Belle II experiments

We report a search for the rare decay $B^{+} \rightarrow K^{+} τ^{+} τ^{-}$ using $1.2 \times 10^9$ $Υ(4S)$ mesons produced near threshold in electron-positron collisions and collected by the Belle and Belle~II experiments. We fully reconstruct the hadronic decay of one $B$ meson produced in the $Υ(4S)\rightarrow B^{+} B^{-}$ decay, and search for $B^{\pm}\rightarrow K^{\pm} τ^{+}τ^{-}$ candidates among the remaining collision products, reconstructing a charged kaon and leptonic decays of the $τ$ leptons. We optimize the selection for best sensitivity and look for an excess over background at low values of the residual energy detected in the calorimeter after full event reconstruction. We observe no significant excess and set the limit $\mathcal{B}(B^{+}\rightarrow K^{+}τ^{+}τ^{-})< 0.56\times 10^{-3}$ at the 90% confidence level, improving on the only previous result by a factor of four.

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arXiv2026

Searches for charged-lepton-flavor violation in $χ_{bJ}(1P)$ decays

We report the first searches for charged-lepton-flavor violation in decays of $χ_{bJ}(1P)$ ($J=0, 1,$ and $2$) to a pair of charged leptons using 158 million $Υ(2S)$ decays collected with the Belle detector in $e^+e^-$ collisions at the KEKB collider. No significant signal is observed, and we set upper limits on the branching fractions for $χ_{bJ}(1P)$ decays to $e^\pmμ^\mp$ at the level of $10^{-6}$ and to $e^\pmτ^\mp$ or $μ^\pmτ^\mp$ at the level of $10^{-5}$. Limits on $χ_{b0}(1P)$ decays are translated into bounds on the corresponding Wilson coefficients of scalar operators that mediate charged-lepton-flavor violation.

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arXiv2026

Study of $B^+ \to μ^+ ν_μ$ decays at Belle and Belle II

We report a measurement of the branching fraction for the leptonic decay $B^+\toμ^+ν_μ$. This work presents the first $B^+\toμ^+ν_μ$ result using Belle~II data, an updated Belle measurement that supersedes the previous result, and their combination, which yields the most precise search to date. The analysis is based on $1076\,\mathrm{fb}^{-1}$ of $e^+e^-$ collision data collected at a center-of-mass energy of $10.58\,\mathrm{GeV}$ with the Belle and Belle~II detectors at the KEKB and SuperKEKB colliders, respectively. We measure $\mathcal{B}(B^+\toμ^+ν_μ)=(4.4\pm1.9\pm 1.0)\times10^{-7}$, where the first uncertainty is statistical and the second systematic. The observed significance relative to the background-only hypothesis is 2.4 standard deviations. We set a 90\% confidence level upper limit of $\mathcal{B}(B^+\toμ^+ν_μ)<6.7\times10^{-7}$ using a frequentist approach and a 90\% credibility level upper limit of $\mathcal{B}(B^+\toμ^+ν_μ)<7.2\times 10^{-7}$ using a Bayesian approach. These are the most stringent limits to date. The result is interpreted as an exclusion region in the parameter space of type~II and type~III two-Higgs-doublet models. We search for stable sterile neutrinos with masses $m_N\in[0,1.5]\,\mathrm{GeV}$. No signal is observed, and the resulting exclusion on the squared mixing parameter $|U_{μN}|^2$ provides improvement over previous limits. We report a measurement of the partial branching fraction of semileptonic $B\to X_u\ellν_\ell$ decays with $p_μ^B>2.2\,\mathrm{GeV}$, obtaining $Δ\mathcal{B}(B\to X_u\ellν_\ell)=(2.72\pm0.05\pm0.29)\times10^{-4}$. We present a model-dependent study of weak annihilation decays using the muon momentum spectrum. We observe a signal of 2.4 standard deviations above the background-only hypothesis in regions where the distribution resembles that of $B\to X_u\ellν_\ell$ decays.

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arXiv2026

Study of $e^{+}e^{-}\to h^{+}h^{-}J/ψ~(h=π,~K,~p)$ via initial-state radiation at Belle~II

Using a data sample of 427.9 fb$^{-1}$ collected by the Belle~II detector at or near the $Υ(4S)$ and $Υ(10753)$ resonances, the cross sections for $e^+e^-\to h^+h^-J/ψ$ $(h=π/K/p)$ at center-of-mass energies ranging from 3.8 GeV or the production threshold to 5.5/6.0/7.0 GeV have been measured via initial-state radiation. The cross sections for the processes $e^+e^-\to π^+π^-J/ψ$ and $e^+e^-\to K^+K^-J/ψ$ are consistent with previously published results. The cross sections for these channels obtained by combining with previous Belle results are also given. The process $e^+e^-\to p\bar p J/ψ$ is investigated for the first time. The yields are small and no significant structure is observed in the cross section versus energy. Searches for vector charmonium-like states in the $h^+h^-J/ψ$ systems, and for associated intermediate states in the $h^{\pm} J/ψ$ systems, are also presented.

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arXiv2026

Observation of the radiative decay $D_s (2317)^+ \to D_s^* γ$

We observe the radiative decay $D^{*}_{s0}(2317)^{+} \to D_{s}^{*+} γ$ for the first time, with a significance exceeding $10$ standard deviations. The signal is found in the continuum $e^+ e^- \to c\bar{c}$ process with the combined data samples of 980.4~$\rm fb^{-1}$ and 427.9~$\rm fb^{-1}$ collected by the Belle and Belle~II detectors operating at the KEKB and SuperKEKB asymmetric-energy $e^+e^-$ colliders, respectively. The branching fraction ratio ${\cal B}(D^{*}_{s0}(2317)^{+} \to D_{s}^{*+} γ)/{\cal B}(D^{*}_{s0}(2317)^{+} \to D_{s}^{+} π^{0})$ is measured to be $[7.13 \pm 0.70({\rm stat.}) \pm 0.23({\rm syst.})]\%$. This result provides significant new experimental input for the determination of the quark structure of the $D^{*}_{s0}(2317)^{+}$, which remains unknown.

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arXiv2026

First search for $B \rightarrow X_{s} ν\barν$ decays

We report the first search for the flavor-changing neutral-current decays $B \rightarrow X_{s} ν\barν$, where $X_{s}$ is a hadronic system with strangeness equal to 1, in data collected with the Belle~II detector at the SuperKEKB asymmetric-energy $e^+e^-$ collider. The data sample corresponds to an integrated luminosity of $365~\textrm{fb}^{-1}$ collected at the $Υ(4S)$ resonance and $43~\textrm{fb}^{-1}$ collected at a center-of-mass energy $60~\textrm{MeV}$ below resonance for estimation of $e^+e^-\to q\bar{q}$ continuum background. One of the $B$ mesons from the $Υ(4S) \to B\bar{B}$ decay is fully reconstructed in a hadronic decay mode. The $B \to X_s ν\barν$ decay is reconstructed with a sum-of-exclusives approach that uses 30 $X_s$ decay modes. This approach provides high sensitivity to the inclusive decay, despite the presence of two undetected neutrinos. The search is performed in three regions of the $X_{s}$ mass, chosen to separate contributions from prominent resonances. We do not observe a significant signal and set upper limits at 90\% confidence level on the partial branching fractions for the regions $0.0 < M_{X_{s}} < 0.6~\textrm{GeV}/c^{2}$, $0.6 < M_{X_{s}} < 1.0~\textrm{GeV}/c^{2}$, and $1.0~\textrm{GeV}/c^{2} < M_{X_{s}}$ of $2.2 \times 10^{-5}$, $9.3 \times 10^{-5}$, and $30.9 \times 10^{-5}$, respectively. Combining the three mass regions, we obtain the upper limit on the branching fraction, $B(B \to X_s ν\barν) < 3.3 \times 10^{-4}$.

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arXiv2026

Search for the lepton-flavor-violating $τ^{-} \rightarrow e^{\mp} \ell^{\pm} \ell^{\mp}$ decays at Belle II

We present the result of a search for the charged-lepton-flavor violating decays $τ^- \rightarrow e^\mp \ell^\pm \ell^-$, where $\ell$ is a muon or an electron, using a data sample with an integrated luminosity of 428 fb$^{-1}$ recorded by the Belle II experiment at the SuperKEKB $e^+e^-$ collider. The selection of $e^+e^- \toτ^+τ^-$ events containing a signal candidate is based on an inclusive-tagging reconstruction and on a boosted decision tree to suppress background. Upper limits on the branching fractions between 1.3 and 2.5 $\times 10^{-8}$ are set at the 90% confidence level. These results are the most stringent bounds to date for four of the modes.

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arXiv2026

Improved measurement of Born cross sections for $χ_{bJ}\,ω$ and $χ_{bJ}\,(π^+π^-π^0)_{\rm non-ω}$ ($J$ = 0, 1, 2) at Belle and Belle II

We study the processes $χ_{bJ}\,ω$ and $χ_{bJ}\,(π^+π^-π^0)_{\rm non-ω}$ ($J$ = 0, 1, 2) at center-of-mass energies $\sqrt{s}$ from 10.73 to 11.02 GeV using a $142.5\,\mathrm{fb}^{-1}$ data sample collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider; and at $\sqrt{s}\sim10.75$ GeV using a $19.8\,\mathrm{fb}^{-1}$ sample collected with Belle II at SuperKEKB. We find that the $Υ(10753)$ state decays into $χ_{bJ}\,ω$ but not into $χ_{bJ}\,(π^+π^-π^0)_{\rm non-ω}$, while the $Υ(10860)$ state, in contrast, decays into $χ_{bJ}\,(π^+π^-π^0)_{\rm non-ω}$ but not into $χ_{bJ}\,ω$. The mass and width of the $Υ(10753)$ state are measured to be $(10756.1\pm3.4({\rm stat.})\pm2.7({\rm syst.}))$ MeV/$c^2$ and $(32.2\pm11.3({\rm stat.})\pm14.9({\rm syst.}))$ MeV. The products of the partial width to $e^+e^-$ and branching fractions for $Υ(10753)\toχ_{b1}\,ω$ and $Υ(10753)\toχ_{b2}\,ω$ are ($1.57\pm0.27({\rm stat.})\pm 0.22({\rm syst.})$) eV and ($1.39\pm0.41({\rm stat.})\pm 0.33({\rm syst.})$) eV.

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arXiv2026

Search for $e^+ e^- \to γχ_{bJ}$ ($J$ = 0, 1, 2) near $\sqrt{s} = 10.746$ GeV at Belle II

We search for the $e^+ e^- \to γχ_{bJ}$ ($J$ = 0, 1, 2) processes at center-of-mass energies $\sqrt{s}$ = 10.653, 10.701, 10.746, and 10.804 GeV. These data were collected with the Belle II detector at the SuperKEKB collider and correspond to 3.5, 1.6, 9.8, and 4.7 fb$^{-1}$ of integrated luminosity, respectively. We set upper limits at the 90\% confidence level on the Born cross sections for $e^+ e^- \to γχ_{bJ}$ at each center-of-mass energy $\sqrt{s}$ near 10.746 GeV. The upper limits at 90\% confidence level on the Born cross sections for $e^+ e^- \to γχ_{b1}$ are significantly smaller than the corresponding measured values for $e^+e^-\toωχ_{b1}$ and $e^+e^-\toπ^+π^-Υ(2S)$ at $\sqrt{s}$ = 10.746 GeV.

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arXiv2026

Measurement of inclusive $B \to X_u \ell ν$ partial branching fractions and $|V_{ub}|$ at Belle II

A sample of 365 fb$^{-1}$ of $e^+e^- \to Υ(4S) \to B\bar{B}$ data collected by the Belle II experiment is used to measure the partial branching fractions of charmless semileptonic $B$ meson decays and determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$. Events containing a signal electron or muon $\ell$ and a fully reconstructed hadronic $B$ decay that constrains the signal kinematics are selected, while the rest of the event defines the hadronic system $X_u$ associated with the signal. To discriminate the signal from the 50-times larger background originating from CKM-favored semileptonic $B$ decays, a template fit is performed in both signal and control regions after applying an optimized selection. The partial branching fraction measured for lepton energies greater than 1 GeV in the signal $B$ meson rest frame is $Δ\mathcal{B}(B \to X_u \ell ν) = (1.54 \pm 0.08 \, {\rm (stat.)} \pm 0.12 \, {\rm (syst.)}) \times 10^{-3}$. From this measurement, using the Gambino, Giordano, Ossola, Uraltsev theoretical framework, $|V_{ub}| = (4.01 \pm 0.19 ^{+0.07} _{-0.08}) \times 10^{-3}$ is determined, where the uncertainties are experimental and theoretical, respectively. This value is consistent with the world average obtained from previous inclusive measurements. Different theoretical predictions and partial branching fractions measured in other phase-space regions, defined by additional selections on the $X_u$ and leptonic system masses, are also used to determine $|V_{ub}|$.

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arXiv2026

Test of lepton flavor universality with measurements of $R(D^{+})$ and $R(D^{*+})$ using semileptonic $B$ tagging at the Belle II experiment

We report measurements of the ratios of branching fractions ${\cal R}(D^{(*)+}) = \frac{{\cal B}(\overline{B}{}^0 \to D^{(*)+} \,τ^- \, \overlineν_τ)}{{\cal B}(\overline{B}{}^0 \to D^{(*)+} \, \ell^- \, \overlineν_\ell)}$, where $\ell$ denotes either an electron or a muon. These ratios test the universality of the charged-current weak interaction. The results are based on a $365\, \mathrm{fb}^{-1}$ data sample collected with the Belle II detector at the SuperKEKB $e^+e^-$ collider, which operates at a center-of-mass energy corresponding to the $Υ(4S)$ resonance, just above the threshold for $B\overline{B}{}$ production. Signal candidates are reconstructed by selecting events in which the companion $B$ meson from the $Υ(4S) \to B\overline{B}{}$ decay is identified in semileptonic modes. The $τ$ lepton is reconstructed via its leptonic decays. We obtain ${\cal R}(D^+) = 0.418 \pm 0.074 ~({\mathrm{stat}}) \pm 0.051 ~({\mathrm{syst}})$ and ${\cal R}(D^{*+}) = 0.306 \pm 0.034 ~({\mathrm{stat}}) \pm 0.018 ~({\mathrm{syst}})$, which are consistent with world average values. Accounting for the correlation between them, these values differ from the Standard Model expectation by a collective significance of $1.7$ standard deviations.

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arXiv2026

Measurement of the $CP$ asymmetry in $D^0\toπ^+π^-π^0$ decays at Belle II

We measure the time- and phase-space-integrated $CP$ asymmetry $A_{CP}$ in $D^0\toπ^+π^-π^0$ decays reconstructed in $e^+e^-\to c\bar c$ events collected by the Belle II experiment from 2019 to 2022. This sample corresponds to an integrated luminosity of 428 fb$^{-1}$. We require $D^0$ mesons to be produced in $D^{*+}\to D^0π^+$ decays to determine their flavor at production. Control samples of $D^0\to K^-π^+$ decays are used to correct for reconstruction-induced asymmetries. The result, $A_{CP}(D^0\toπ^+π^-π^0)=(0.29\pm0.27\pm0.13)\%$, where the first uncertainty is statistical and the second systematic, is the most precise result to date and is consistent with $CP$ conservation.

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arXiv2026

First measurements of the branching fractions for the decay modes $Ξ_c^{0} \to Λη$ and $Ξ_c^0 \to Λη'$ and search for the decay $Ξ_c^{0} \to Λπ^0$ using Belle and Belle II data

Using data samples of 988.4 fb$^{-1}$ and 427.9 fb$^{-1}$ collected with the Belle and Belle II detectors, we present a study of the singly Cabibbo-suppressed decays $Ξ_c^{0} \to Λη$, $Λη'$, and $Λπ^0$. We observe the decay $Ξ_c^0 \to Λη$ and find evidence for the decay $Ξ_c^0 \to Λη'$, with corresponding branching ratios determined to be ${\mathcal{B}(Ξ_c^0 \to Λη)}/{\mathcal{B}(Ξ_c^0 \to Ξ^- π^+)}= (4.16 \pm 0.91 \pm {0.23})\%$ and ${\mathcal{B}(Ξ_c^0 \to Λη')}/{\mathcal{B}(Ξ_c^0 \to Ξ^- π^+)}= (2.48 \pm 0.82 \pm {0.12})\%$, respectively. We find no significant signal in the $Ξ_c^0 \to Λπ^0$ decay mode and set an upper limit at the 90% credibility level of ${\mathcal{B}(Ξ_c^0 \to Λπ^0)}/{\mathcal{B}(Ξ_c^0 \to Ξ^- π^+)}< {3.5\%}$. Multiplying these ratios by the world-average branching fraction of the normalization channel, $\mathcal{B}(Ξ_c^0 \to Ξ^- π^+)=(1.43 \pm 0.27)\%$, we obtain the absolute branching fractions of $\mathcal{B}(Ξ_c^0 \to Λη)= (5.95 \pm 1.30 \pm {0.32} \pm 1.13) \times 10^{-4}$, $\mathcal{B}(Ξ_c^0 \to Λη')= (3.55 \pm 1.17 \pm {0.17} \pm 0.68) \times 10^{-4}$, and an upper limit at the 90% credibility level on the absolute branching fraction of $\mathcal{B}(Ξ_c^0 \to Λπ^0)< {5.2} \times 10^{-4}$. The quoted first and second uncertainties are statistical and systematic, respectively, while the third uncertainties arise from the branching fraction of the normalization mode. These results are consistent with most theoretical predictions and further the understanding of the underlying decay mechanisms.

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arXiv2026

Measurement of time-dependent $CP$ asymmetries in $B^0 \to K_{\rm S}^0 \: π^{+} π^{-} γ$ decays at Belle and Belle II

We present a measurement of the time-dependent $CP$ asymmetry in $B^0 \to K_{\rm S}^0 \: π^{+} π^{-} γ$ decays using a data set of 365 fb$^{-1}$ recorded by the Belle II experiment and the final data set of 711 fb$^{-1}$ recorded by the Belle experiment at the ${\rm Υ(4S)}$ resonance. The direct and mixing-induced time-dependent $CP$ violation parameters $C$ and $S$ are determined along with two additional quantities, $S^{+}$ and $S^{-}$, defined in the two halves of the $m^2(K_{\rm S}^0 π^{+})-m^2(K_{\rm S}^0 π^{-})$ plane. The measured values are $C = -0.17 \pm 0.09 \pm 0.04$, $S = -0.29 \pm 0.11 \pm 0.05$, $S^{+} = -0.57 \pm 0.23 \pm 0.10$ and $S^{-} = 0.31 \pm 0.24 \pm 0.05$, where the first uncertainty is statistical and the second systematic.

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arXiv2026

A search for feebly-interacting particles in $B$ decays with missing energy at Belle

We present a search for an invisible hidden-sector particle $ X_{\rm{inv}}$, produced in $B^0 \to \bar{D}^0 X_{\rm{inv}}$ and $B^\pm\to h X_{\rm{inv}}$ decays, where $h = π^\pm$, $K^\pm$, $D_{s}^\pm$, $p^\pm$. The search is performed using $e^+ e^-$ collision data recorded with the Belle detector, corresponding to 711~fb$^{-1}$. No significant signal is observed. We set 90\% confidence level upper limits ranging between $10^{-4}$ and $10^{-6}$ on the branching fraction $\mathcal{B}(B \to h X_{\rm{inv}})$ as a function of $m_{ X_{\rm{inv}}}$. Corresponding limits are set on $\mathcal{B}(B \to hX)\times\mathcal{B}(X\toγγ)$ for lifetimes $cτ_X$ between $10~μ$m and 10 m. Many of these limits are the first direct constraints on their respective decays. Our results provide the most stringent exclusion limits to date on the branching fractions for all search channels, and exclude previously unexplored regions of parameter space relevant to several new physics models.

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arXiv2025

Search for a Dark Higgs Boson Produced in Association with Inelastic Dark Matter at the Belle II Experiment

Inelastic dark matter models that have two dark matter particles and a massive dark photon can reproduce the observed relic dark matter density without violating cosmological limits. The mass splitting between the two dark matter particles $χ_{1}$ and $χ_{2}$, with $m(χ_{2}) > m(χ_{1})$, is induced by a dark Higgs field and a corresponding dark Higgs boson $h^{\prime}$. We present a search for dark matter in events with two vertices, at least one of which must be displaced from the interaction region, and missing energy. Using a $365\,\mbox{fb}^{-1}$ data sample collected at Belle II, which operates at the SuperKEKB $e^+e^-$ collider, we observe no evidence for a signal. We set upper limits on the product of the production cross section $σ\left(e^+e^- \to h^\prime χ_1 χ_2\right)$, and the product of branching fractions $\mathcal{B}\left(χ_2\toχ_1 e^+ e^-\right)\times\mathcal{B}\left(h^\prime\to x^+x^-\right)$, where $x^+x^-$ indicates $μ^+μ^-, π^+π^-$, or $K^+K^-$, as functions of $h^{\prime}$ mass and lifetime at the level of $10^{-1}\,\mbox{fb}$. We set model-dependent upper limits on the dark Higgs mixing angle at the level of $10^{-5}$ and on the dark photon kinetic mixing parameter at the level of $10^{-3}$. This is the first search for dark Higgs bosons in association with inelastic dark matter.

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arXiv2025

Determination of $|V_{cb}|$ using $B\to D\ellν_\ell$ Decays at Belle II

We present a determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ from the decay $B\to D\ellν_\ell$ using a $365~\mathrm{fb}^{-1}$ $e^+e^-\toΥ(4S)\to B\bar B$ data sample recorded by the Belle II experiment at the SuperKEKB collider. The semileptonic decay of one $B$ meson is reconstructed in the modes $B^0\to D^-(\to K^+π^-π^-)\ell^+ν_\ell$ and $B^+\to \bar D^0(\to K^+π^-)\ell^+ν_\ell$, where $\ell$ denotes either an electron or a muon. Charge conjugation is implied. The second $B$ meson in the $Υ(4S)$ event is not reconstructed explicitly. Using an inclusive reconstruction of the unobserved neutrino momentum, we determine the recoil variable $w=v_B\cdot v_D$, where $v_B$ and $v_D$ are the 4-velocities of the $B$ and $D$ mesons. We measure the total decay branching fractions to be $\mathcal{B}(B^0\to D^-\ell^+ν_\ell)=(2.06 \pm 0.05\,(\mathrm{stat.}) \pm 0.10\,(\mathrm{sys.}))\%$ and $\mathcal{B}(B^+\to\bar D^0\ell^+ν_\ell)=(2.31 \pm 0.04\,(\mathrm{stat.}) \pm 0.09\,(\mathrm{sys.}))\%$. We probe lepton flavor universality by measuring $\mathcal{B}(B\to Deν_e)/\mathcal{B}(B\to Dμν_μ)=1.020 \pm 0.020\,(\mathrm{stat.})\pm 0.022\,(\mathrm{sys.})$. Fitting the partial decay branching fraction as a function of $w$ and using the average of lattice QCD calculations of the $B\to D$ form factor, we obtain $ |V_{cb}|=(39.2\pm 0.4\,(\mathrm{stat.}) \pm 0.6\,(\mathrm{sys.}) \pm 0.5\,(\mathrm{th.})) \times 10^{-3}$.

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