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Measurement of Differential Branching Fractions of Inclusive ${B to X_u , ell^+, u_{ell}}$ Decays

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 Added by Lu Cao
 Publication date 2021
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and research's language is English




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The first measurements of differential branching fractions of inclusive semileptonic ${B to X_u , ell^+, u_{ell}}$ decays are performed using the full Belle data set of 711 fb$^{-1}$ of integrated luminosity at the $Upsilon(4S)$ resonance and for $ell = e, mu$. Differential branching fractions are reported as a function of the lepton momentum, the four-momentum-transfer squared, light-cone momenta, the hadronic mass, and the hadronic mass squared. They are obtained by subtracting the backgrounds from semileptonic ${B to X_c , ell^+, u_{ell}}$ decays and other processes, and corrected for resolution and acceptance effects. The measured distributions are compared to predictions from inclusive and hybrid ${B to X_u , ell^+, u_{ell}}$ calculations.



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We present measurements of partial branching fractions of inclusive semileptonic $B to X_u , ell^+, u_{ell}$ decays using the full Belle data set of 711 fb$^{-1}$ of integrated luminosity at the $Upsilon(4S)$ resonance and for $ell = e, mu$. Inclusive semileptonic $B to X_u , ell^+, u_{ell}$ decays are CKM suppressed and measurements are complicated by the large background from CKM-favored $B to X_c , ell^+, u_{ell}$ transitions, which have a similar signature. Using machine learning techniques, we reduce this and other backgrounds effectively, whilst retaining access to a large fraction of the $B to X_u , ell^+, u_{ell}$ phase space and high signal efficiency. We measure partial branching fractions in three phase-space regions covering about $31%$ to $86%$ of the accessible $B to X_u , ell^+, u_{ell}$ phase space. The most inclusive measurement corresponds to the phase space with lepton energies of $E_ell^B > 1 $ GeV, and we obtain $Delta mathcal{B}(B to X_u ell^+ , u_ell) = left( 1.59 pm 0.07 pm 0.16 right) times 10^{-3}$ from a two-dimensional fit of the hadronic mass spectrum and the four-momentum-transfer squared distribution, with the uncertainties denoting the statistical and systematic error. We find $left| V_{ub} right| = left( 4.10 pm 0.09 pm 0.22 pm 0.15 right) times 10^{-3}$ from an average of four calculations for the partial decay rate with the third uncertainty denoting the average theory error. This value is higher but compatible with the determination from exclusive semileptonic decays within 1.3 standard deviations. In addition, we report charmless inclusive partial branching fractions separately for $B^+$ and $B^0$ mesons as well as for electron and muon final states. No isospin breaking or lepton flavor universality violating effects are observed.
The branching fractions of the decays $B^{+} to eta ell^{+} u_{ell}$ and $B^{+} to eta^{prime} ell^{+} u_{ell}$ are measured, where $ell$ is either an electron or a muon, using a data sample of $711,{rm fb}^{-1}$ containing $772 times 10^6 Bbar{B}$ pairs collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. To reduce the dependence of the result on the form factor model, the measurement is performed over the entire $q^2$ range. The resulting branching fractions are ${cal B}(B^{+} rightarrow eta ell^{+} u_{ell}) = (2.83 pm 0.55_{rm (stat.)} pm 0.34_{rm (syst.)}) times 10^{-5}$ and ${cal B}(B^{+} rightarrow eta ell^{+} u_{ell}) = (2.79 pm 1.29_{rm (stat.)} pm 0.30_{rm (syst.)}) times 10^{-5}$.
We present the measurement of the first to fourth order moments of the four-momentum transfer squared, $q^2$, of inclusive $B rightarrow X_c ell^+ u_{ell}$ decays using the full Belle data set of 711 $mathrm{fb}^{-1}$ of integrated luminosity at the $Upsilon(4S)$ resonance where $ell = e, mu$. The determination of these moments and their systematic uncertainties open new pathways to determine the absolute value of the CKM matrix element $V_{cb}$ using a reduced set of matrix elements of the heavy quark expansion. In order to identify and reconstruct the $X_c$ system, we reconstruct one of the two $B$-mesons using machine learning techniques in fully hadronic decay modes. The moments are measured with progressively increasing threshold selections on $q^2$ starting with a lower value of 3.0 $mathrm{GeV}^2$ in steps of 0.5 $mathrm{GeV}^2$ up to a value of 10.0 $mathrm{GeV}^2$. The measured moments are further unfolded, correcting for reconstruction and selection effects as well as QED final state radiation. We report the moments separately for electron and muon final states and observe no lepton flavor universality violating effects.
We present a first measurement of the $bar{B^{0}} rightarrow D^{*+} ell^{-} u_{ell}$ branching fraction using fully reconstructed $B$ meson decays employing the Full Event Interpretation algorithm. Collision events corresponding to an integrated luminosity of lumi are analyzed, which were recorded by the Belle~II detector operated at the SuperKEKB accelerator complex. We measure$cal{B}(bar{B^{0}} rightarrow D^{*+} ell^{-} u_{ell}) =4.51 pm 0.41_{stat}pm0.27_{syst} pm0.45_{pi_s}$, with the first and second error denoting the statistical and systematic uncertainty, respectively, and the third dominant uncertainty is from the slow pion reconstruction efficiency.
We reassess the $Btopiell u_{ell}$ differential branching ratio distribution experimental data released by the BaBar and Belle Collaborations supplemented with all lattice calculations of the $Btopi$ form factor shape available up to date obtained by the HPQCD, FNAL/MILC and RBC/UKQCD Collaborations. Our study is based on the method of Pad{e} approximants, and includes a detailed scrutiny of each individual data set that allow us to obtain $|V_{ub}|=3.53(8)_{rm{stat}}(6)_{rm{syst}}times10^{-3}$. The semileptonic $B^{+}toeta^{(prime)}ell^{+} u_{ell}$ decays are also addressed and the $eta$-$eta^{prime}$ mixing discussed.
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