arXiv subjects

K. Belous

Publications and source records attributed to K. Belous.

At least 217 records · Page 12Linked to original sources

arXiv2023

Measurement of Angular Coefficients of $\bar{B} \to D^* \ell \barν_\ell$: Implications for $|V_{cb}|$ and Tests of Lepton Flavor Universality

We measure the complete set of angular coefficients $J_i$ for exclusive $\bar{B} \to D^* \ell \barν_\ell$ decays ($\ell = e, μ$). Our analysis uses the full $711\,\mathrm{fb}^{-1}$ Belle data set with hadronic tag-side reconstruction. The results allow us to extract the form factors describing the $B \to D^*$ transition and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{\rm cb}|$. Using recent lattice QCD calculations for the hadronic form factors, we find $|V_{\rm cb}| = (41.0 \pm 0.7) \times 10^3 $ using the BGL parameterization, compatible with determinations from inclusive semileptonic decays. We search for lepton flavor universality violation as a function of the hadronic recoil parameter $w$, and investigate the differences of the electron and muon angular distributions. We find no deviation from Standard Model expectations.

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arXiv2023

Precision measurement of $\it{CP} $ violation in the penguin-mediated decay $B_s^{0}\rightarrowϕϕ$

A flavor-tagged time-dependent angular analysis of the decay $B_s^{0}\rightarrowϕϕ$ is performed using $pp$ collision data collected by the LHCb experiment at $\sqrt{s}=13$ TeV, the center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6 fb^{-1}. The $\it{CP}$-violating phase and direct $\it{CP}$-violation parameter are measured to be $ϕ_{s\bar{s}s} = -0.042 \pm 0.075 \pm 0.009 $ rad and $|λ|=1.004\pm 0.030 \pm 0.009 $, respectively, assuming the same values for all polarization states of the $ϕϕ$ system. In these results, the first uncertainties are statistical and the second systematic. These parameters are also determined separately for each polarization state, showing no evidence for polarization dependence. The results are combined with previous LHCb measurements using $pp$ collisions at center-of-mass energies of 7 and 8 TeV, yielding $ϕ_{s\bar{s}s} = -0.074 \pm 0.069 $ rad and $|λ|=1.009 \pm 0.030$. This is the most precise study of time-dependent $\it{CP} $ violation in a penguin-dominated $B$ meson decay. The results are consistent with $\it{CP} $ symmetry and with the Standard Model predictions.

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arXiv2023

Observation of the decays $B_{(s)}^{0}\to D_{s1}(2536)^{\mp}K^{\pm}$

This paper reports the observation of the decays $B_{(s)}^{0}\to D_{s1}(2536)^{\mp}K^{\pm}$ using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9\,\mathrm{fb}^{-1}$. The branching fractions of these decays are measured relative to the normalisation channel $B^{0}\to \overline{D}^{0}K^{+}K^{-}$. The $D_{s1}(2536)^{-}$ meson is reconstructed in the $\overline{D}^{*}(2007)^{0}K^{-}$ decay channel and the products of branching fractions are measured to be $$\mathcal{B}(B_{s}^{0}\to D_{s1}(2536)^{\mp}K^{\pm})\times\mathcal{B}(D_{s1}(2536)^{-}\to\overline{D}^{*}(2007)^{0}K^{-})=(2.49\pm0.11\pm0.12\pm0.25\pm0.06)\times 10^{-5}, $$ $$\mathcal{B}(B^{0}\to D_{s1}(2536)^{\mp}K^{\pm})\times\mathcal{B}(D_{s1}(2536)^{-}\to\overline{D}^{*}(2007)^{0}K^{-}) = (0.510\pm0.021\pm0.036\pm0.050)\times 10^{-5}.$$ The first uncertainty is statistical, the second systematic, and the third arises from the uncertainty of the branching fraction of the $B^{0}\to \overline{D}^{0}K^{+}K^{-}$ normalisation channel. The last uncertainty in the $B_{s}^{0}$ result is due to the limited knowledge of the fragmentation fraction ratio, $f_{s}/f_{d}$. The significance for the $B_{s}^{0}$ and $B^{0}$ signals is larger than $10\,σ$. The ratio of the helicity amplitudes which governs the angular distribution of the $D_{s1}(2536)^{-}\to\overline{D}^{*}(2007)^{0}K^{-}$ decay is determined from the data. The ratio of the $S$- and $D$-wave amplitudes is found to be $1.11\pm0.15\pm 0.06$ and its phase $0.70\pm0.09\pm 0.04$ rad, where the first uncertainty is statistical and the second systematic.

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arXiv2023

Measurement of the $Λ_{b}^{0}\to Λ(1520) μ^{+}μ^{-}$ differential branching fraction

The branching fraction of the rare decay $Λ_{b}^{0}\to Λ(1520) μ^{+}μ^{-}$ is measured for the first time, in the squared dimuon mass intervals, $q^2$, excluding the $J/ψ$ and $ψ(2S)$ regions. The data sample analyzed was collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of $9\ \mathrm{fb}^{-1}$. The result in the highest $q^{2}$ interval, $q^{2} >15.0\ \mathrm{GeV}^2/c^4$, where theoretical predictions have the smallest model dependence, agrees with the predictions.

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arXiv2023

Observation of $Ξ_b^0 \rightarrow Ξ_c^+ D_s^-$ and $Ξ_b^- \rightarrow Ξ_c^0 D_s^-$ decays

The $Ξ_b^0 \rightarrow Ξ_c^+ D_s^-$ and $Ξ_b^- \rightarrow Ξ_c^0 D_s^-$ decays are observed for the first time using proton-proton collision data collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=13\mathrm{TeV}$, corresponding to an integrated luminosity of $5.1\mathrm{fb}^{-1}$. The relative branching fractions times the beauty-baryon production cross-sections are measured to be \begin{align*} \mathcal{R}\left(\frac{Ξ_b^0}{Λ_b^0}\right) \equiv \frac{σ\left(Ξ_b^0\right)}{σ\left(Λ_b^0\right)} \times \frac{\mathcal{B}\left(Ξ_b^0 \rightarrow Ξ_c^+ D_s^-\right)}{\mathcal{B}\left(Λ_b^0 \rightarrow Λ_c^0 D_s^-\right)} =(15.8\pm1.1\pm0.6\pm7.7)\%, \mathcal{R}\left(\frac{Ξ_b^-}{Λ_b^0}\right) \equiv \frac{σ\left(Ξ_b^-\right)}{σ\left(Λ_b^0\right)} \times \frac{\mathcal{B}\left(Ξ_b^- \rightarrow Ξ_c^0 D_s^-\right)}{\mathcal{B}\left(Λ_b^0 \rightarrow Λ_c^0 D_s^-\right)} =(16.9\pm1.3\pm0.9\pm4.3)\%, \end{align*} where the first uncertainties are statistical, the second systematic, and the third due to the uncertainties on the branching fractions of relevant charm-baryon decays. The masses of $Ξ_b^0$ and $Ξ_b^-$ baryons are measured to be $m_{Ξ_b^0}=5791.12\pm0.60\pm0.45\pm0.24\mathrm{MeV}/c^2$ and $m_{Ξ_b^-}=5797.02\pm0.63\pm0.49\pm0.29\mathrm{MeV}/c^2$, where the uncertainties are statistical, systematic, and those due to charm-hadron masses, respectively.

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arXiv2023

Evidence for modification of $b$ quark hadronization in high-multiplicity $pp$ collisions at $\sqrt{s} = 13$ TeV

The production rate of $B^{0}_{s}$ mesons relative to $B^{0}$ mesons is measured by the LHCb experiment in $pp$ collisions at a center-of-mass energy $\sqrt{s} = 13$ TeV over the forward rapidity interval $2<y<4.5$ as a function of the charged particle multiplicity measured in the event. Evidence at the 3.4$σ$ level is found for an increase of the ratio of $B^{0}_{s}$ to $B^{0}$ cross-sections with multiplicity at transverse momenta below 6 GeV/$c$, with no significant multiplicity dependence at higher transverse momentum. Comparison with data from $e^{+}e^{-}$ collisions implies that the density of the hadronic medium may affect the production rates of $B$ mesons. This is qualitatively consistent with the emergence of quark coalescence as an additional hadronization mechanism in high-multiplicity collisions.

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arXiv2023

Observation and branching fraction measurement of the decay $Ξ_b^-\toΛ_b^0π^-$

The decay $Ξ_b^-\toΛ_b^0π^-$ is observed using a proton-proton collision data sample collected at center-of-mass energy $\sqrt{s}=13$ TeV with the LHCb detector, corresponding to an integrated luminosity of 5.5 fb$^{-1}$. This process is mediated by the $s\to u\bar{u}d$ quark-level transition, where the $b$ quark in the $Ξ_b^-$ baryon is a spectator in the decay. Averaging the results obtained using the two $Λ_b^0$ decay modes, $Λ_b^0\toΛ_c^+π^-$ and $Λ_b^0\toΛ_c^+π^-π^+π^-$, the relative production ratio is measured to be $(f_{Ξ_b^-}/f_{Λ_b^0}){\cal{B}}(Ξ_b^-\toΛ_b^0π^-)=(7.3\pm0.8\pm0.6)\times10^{-4}$. Here the uncertainties are statistical and systematic, respectively, and $f_{Ξ_b^-}(f_{Λ_b^0})$ is the fragmentation fraction for a $b$ quark into a $Ξ_b^-$ ($Λ_b^0$) baryon. Using an independent measurement of $f_{Ξ_b^-}/f_{Λ_b^0}$, the branching fraction ${\cal{B}}(Ξ_b^-\toΛ_b^0π^-)=(0.89\pm0.10\pm0.07\pm0.29)\%$ is obtained, where the last uncertainty is due to the assumed SU(3) flavor symmetry in the determination of $f_{Ξ_b^-}/f_{Λ_b^0}$.

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arXiv2023

Study of the Bose-Einstein correlations of same-sign pions in proton-lead collisions

Correlations of same-sign charged particles are analysed using proton-lead collision data collected by the LHCb experiment at a nucleon-nucleon centre-of-mass energy of 5.02 TeV, corresponding to an integrated luminosity of 1.06 nb-1. Bose-Einstein correlations are observed in the form of an enhancement of pair production for same-sign charged pions with a small four-momentum difference squared. The dependence of the correlation radius and the intercept parameter on the reconstructed charged-particle multiplicity is investigated. The measured correlation radii scale linearly with the cube root of the reconstructed charged-particle multiplicity, being compatible with predictions of hydrodynamic models on the collision system evolution.

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arXiv2023

Measurements of $CP$ asymmetries and branching fraction ratios of $B^-$ decays to two charm mesons

The $CP$ asymmetries of seven $B^-$ decays to two charm mesons are measured using data corresponding to an integrated luminosity of $9\text{ fb}^{-1}$ of proton-proton collisions collected by the LHCb experiment. Decays involving a $D^{*0}$ or $D^{*-}_s$ meson are analysed by reconstructing only the $D^0$ or $D^-_s$ decay products. This paper presents the first measurement of $\mathcal{A}^{CP}(B^- \rightarrow D^{*-}_s D^0)$ and $\mathcal{A}^{CP}(B^- \rightarrow D^{-}_s D^{*0})$, and the most precise measurement of the other five $CP$ asymmetries. There is no evidence of $CP$ violation in any of the analysed decays. Additionally, two ratios between branching fractions of selected decays are measured.

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arXiv2023

Search for $B{}^0_s \rightarrow \ell^{\mp} τ^{\pm}$ with the Semi-leptonic Tagging Method at Belle

We present a search for the lepton-flavor-violating decays $B{}^0_s \rightarrow \ell^{\mp}τ^{\pm}$, where $\ell = e, μ$, using the full data sample of $121~\mathrm{fb}^{-1}$ collected at the $Υ(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. We use $B{}^0_s \overline{B}{}^0_s$ events in which one $B{}^0_s$ meson is reconstructed in a semileptonic decay mode and the other in the signal mode. We find no evidence for $B{}^0_s \rightarrow \ell^{\mp}τ^{\pm}$ decays and set upper limits on their branching fractions at $90\%$ confidence level as $\mathcal{B}(B{}^0_s \rightarrow e^{\mp}τ^{\pm}) < 14 \times 10^{-4}$ and $\mathcal{B}(B{}^0_s \rightarrow μ^{\mp}τ^{\pm}) < 7.3 \times 10^{-4}$. Our result represents the first upper limit on the $B{}^0_s \rightarrow e^{\mp}τ^{\pm}$ decay rate.

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arXiv2023

Associated production of prompt $J/ψ$ and $\mathitΥ$ mesons in $pp$ collisions at $\sqrt{s}=13\,\mathrm{TeV}$

The associated production of prompt $J/ψ$ and $\mathit{\mathitΥ}$ mesons in $pp$ collisions at a centre-of-mass energy of $\sqrt{s}=13\,\mathrm{TeV}$ is studied using LHCb data, corresponding to an integrated luminosity of $4\,\mathrm{fb}^{-1}$. The measurement is performed for $J/ψ$ ($\mathitΥ$) mesons with a transverse momentum $p_{\mathrm{T}}<10\,(30)\,\mathrm{GeV}/c$ in the rapidity range $2.0<y<4.5$. In this kinematic range, the cross-section of the associated production of prompt $J/ψ$ and $\mathitΥ(1S)$ mesons is measured to be $133 \pm 22 \pm 7 \pm 3 \, \mathrm{pb}$, with a significance of $7.9\,σ$, and that of prompt $J/ψ$ and $\mathitΥ(2S)$ mesons to be $76\pm 21 \pm 4 \pm 7 \, \mathrm{pb}$, with a significance of $4.9\,σ$. The first uncertainty is statistical, the second systematic, and the third due to uncertainties on the used branching fractions. This is the first observation of the associated production of $J/ψ$ and $\mathitΥ(1S)$ in proton-proton collisions. Differential cross-sections are measured as functions of variables that are sensitive to kinematic correlations between the $J/ψ$ and $\mathitΥ(1S)$ mesons. The effective cross-sections of the associated production of prompt $J/ψ$ and $\mathitΥ$ mesons are obtained and found to be compatible with measurements using other particle productions.

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arXiv2023

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

We observe the process $Υ(2S)\to D_s^{(*)+} D_{sJ}^{-}$ 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 ${\cal B}(Υ(2S) \to D_{s}^{(*)+} D_{sJ}^-) {\cal B}(D_{sJ}^-\to \bar{K} \bar{D}^{(*)})$ and the Born cross sections $σ^{\rm Born}(e^+e^- \to D_{s}^{(*)+} D_{sJ}^-) {\cal B}(D_{sJ}^-\to \bar{K} \bar{D}^{(*)})$, and then compare the ratios $R_1 \equiv {\cal B}(Υ(2S)\to D_{s}^{(*)+} D_{sJ}^-)/{\cal B}(Υ(2S)\toμ^{+}μ^-)$ for $Υ(2S)$ decays and $R_2 \equiv σ^{\rm Born}(e^+e^-\to D_{s}^{(*)+}D_{sJ}^-)/σ^{\rm Born}(e^+e^-\to μ^{+}μ^-)$ 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 $Υ(2S)\to D_{s}^{(*)+}D_{sJ}^-$ 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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arXiv2023

Measurement of the $e^+e^- \to B_s^0 \bar{B}_s^0 X$ cross section in the energy range from $10.63$ to $11.02$ GeV using inclusive $D_s^{\pm}$ and $D^0$ production

We report the first measurement of the inclusive $e^+e^- \to b\bar{b} \to D_s^{\pm}X$ and $e^+e^- \to b\bar{b} \to D^0/\bar{D}^0X$ cross sections in the energy range from $10.63$ to $11.02$. Based on these results, we determine $σ(e^+ e^- \to B_s^0 \bar{B}_s^0 X)$ and $σ(e^+ e^- \to B\bar{B}X)$ in the same energy range. We measure the fraction of $B_s^0$ events at $Υ(10860)$ to be $f_{\rm s}=(22.0^{+2.0}_{-2.1})\%$. We determine also the ratio of the $B_s^0$ inclusive branching fractions $\mathcal{B}(B_s^0 \to D^0/\bar{D}^0X)/\mathcal{B}(B_s^0 \to D_s^{\pm} X)=0.416 \pm 0.018 \pm 0.092$. The results are obtained using the data collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.

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arXiv2023

Evidence for $B^0 \to p\barΣ^0π^-$ at Belle

We search for the $B^0\to p\barΣ^0π^-$ decay with $\barΣ^0 \to \barΛγ$, where the $γ$ is not measured, using a data sample corresponding to an integrated luminosity of 711 $\rm{fb^{-1}}$ which contains 772 $\times$ $10^{6}$ $B\bar{B}$ pairs, collected around the $Υ$(4S) resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. We measure for the first time the $B^0\to p\barΣ^0π^-$ branching fraction to be $\mathcal{B}(B^0 \to p \barΣ^0 π^-) = (1.17^{+0.43}_{-0.40}(\text{stat})\pm 0.07(\text{syst})) \times 10^{-6}$ with a significance of $3.0σ$. We simultaneously measure the branching fraction for the related channel $B^{0}\to p\barΛπ^{-}$ with much improved precision.

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arXiv2023

Study of charmonium decays to $K^0_S K π$ in the $B \to (K^0_S K π) K$ channels

A study of the $B^+\to K^0_SK^+K^-π^+$ and $B^+\to K^0_SK^+K^+π^-$ decays is performed using proton-proton collisions at center-of-mass energies of 7, 8 and 13 TeV at the LHCb experiment. The $K^0_SK π$ invariant mass spectra from both decay modes reveal a rich content of charmonium resonances. New precise measurements of the $η_c$ and $η_c(2S)$ resonance parameters are performed and branching fraction measurements are obtained for $B^+$ decays to $η_c$, $J/ψ$, $η_c(2S)$ and $χ_{c1}$ resonances. In particular, the first observation and branching fraction measurement of $B^+ \to χ_{c0} K^0 π^+$ is reported as well as first measurements of the $B^+\to K^0K^+K^-π^+$ and $B^+\to K^0K^+K^+π^-$ branching fractions. Dalitz plot analyses of $η_c \to K^0_SKπ$ and $η_c(2S) \to K^0_SKπ$ decays are performed. A new measurement of the amplitude and phase of the $K π$ $S$-wave as functions of the $K π$ mass is performed, together with measurements of the $K^*_0(1430)$, $K^*_0(1950)$ and $a_0(1700)$ parameters. Finally, the branching fractions of $χ_{c1}$ decays to $K^*$ resonances are also measured.

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arXiv2023

Observation of a resonant structure near the $D_s^+ D_s^-$ threshold in the $B^+\to D_s^+ D_s^- K^+$ decay

An amplitude analysis of the $B^+\to D_s^+ D_s^- K^+$ decay is carried out to study for the first time its intermediate resonant contributions, using proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV. A near-threshold peaking structure, referred to as $X(3960)$, is observed in the $D_s^+ D_s^-$ invariant-mass spectrum with significance greater than 12 standard deviations. The mass, width and the quantum numbers of the structure are measured to be $3956\pm5\pm10$ MeV, $43\pm13\pm8$ MeV and $J^{PC}=0^{++}$, respectively, where the first uncertainties are statistical and the second systematic. The properties of the new structure are consistent with recent theoretical predictions for a state composed of $c\bar{c}s\bar{s}$ quarks. Evidence for an additional structure is found around 4140 MeV in the $D_s^+ D_s^-$ invariant mass, which might be caused either by a new resonance with the $0^{++}$ assignment or by a $J/ψϕ\leftrightarrow D_s^+ D_s^-$ coupled-channel effect.

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arXiv2023

Observation of the mass difference between neutral charm-meson eigenstates

A measurement of mixing and $C\!P$ violation in neutral charm mesons is performed using data reconstructed in proton-proton collisions collected by the LHCb experiment from 2016 to 2018, corresponding to an integrated luminosity of 5.4$\textrm{fb}^{-1}$. A total of $30.6$ million $D^{0}\rightarrow K^{0}_{\mathrm{S}}π^{+}π^{-}$ decays are analyzed using a method optimized for the measurement of the mass difference between neutral charm-meson eigenstates. Allowing for $C\!P$ violation in mixing and in the interference between mixing and decay, the mass and decay-width differences are measured to be $x_{C\!P} = \left[3.97\pm0.46\textrm{(stat)}\pm 0.29\textrm{(syst)}\right]\times10^{-3}$ and $y_{C\!P} = \left[4.59\pm1.20\textrm{(stat)}\pm0.85\textrm{(syst)}\right]\times10^{-3}$, respectively. The $C\!P$-violating parameters are measured as $Δx = \left[-0.27\pm0.18\textrm{(stat)}\pm0.01\textrm{(syst)}\right]\times10^{-3}$ and $Δy = \left[0.20\pm0.36\textrm{(stat)}\pm0.13\textrm{(syst)}\right]\times10^{-3}$. This is the first observation of a nonzero mass difference in the $D^0$ meson system, with a significance exceeding seven standard deviations. The data are consistent with $C\!P$ symmetry, and improve existing constraints on the associated parameters.

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arXiv2023

First Simultaneous Determination of Inclusive and Exclusive $\left|V_{ub}\right|$

The first simultaneous determination of the absolute value of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$ using inclusive and exclusive decays is performed with the full Belle data set at the $Υ(4S)$ resonance, corresponding to an integrated luminosity of 711 fb${}^{-1}$. We analyze collision events in which one $B$ meson is fully reconstructed in hadronic modes. This allows for the reconstruction of the hadronic $X_u$ system of the semileptonic $b \to u \ell \bar ν_\ell$ decay. We separate exclusive $B \to π\, \ell\, \bar ν_{\ell}$ decays from other inclusive $B \to X_u \, \ell\, \bar ν_{\ell}$ and backgrounds with a two-dimensional fit, that utilizes the number of charged pions in the $X_u$ system and the four-momentum transfer $q^2$ between the $B$ and $X_u$ system. Combining our measurement with information from lattice QCD and QCD calculations of the inclusive partial rate as well as external experimental information on the shape of the $B \to π\, \ell\, \bar ν_{\ell}$ form factor, we determine $\left|V_{ub}^{\mathrm{excl.}} \right| = (3.78 \pm 0.23 \pm 0.16 \pm 0.14)\times 10^{-3}$ and $\left|V_{ub}^{\mathrm{incl.}} \right| = (3.88 \pm 0.20 \pm 0.31 \pm 0.09)\times 10^{-3}$, respectively, with the uncertainties being the statistical error, systematic errors, and theory errors. The ratio of $\left|V_{ub}^{\mathrm{excl.}} \right| / \left|V_{ub}^{\mathrm{incl.}} \right| = 0.97 \pm 0.12$ is compatible with unity.

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