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Register a new userStudy of $Btopiell u_{ell}$ and $B^{+}toeta^{(prime)}ell^{+} u_{ell}$ decays and determination of $|V_{ub}|$
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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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This article analyses the available inputs in $btopilnu$ and $btorholnu$ decays which include the measured values of differential rate in different $q^2$-bins (lepton invariant mass spectrum), lattice, and the newly available inputs on the relevant form-factors from the light-cone sum rules (LCSR) approach. We define different fit scenarios, and in each of these scenarios, we predict a few observables in the standard model (SM). For example, $R(M) =frac{mathcal{B}(B to Mell_i u_{ell_i})}{mathcal{B}(Bto Mell_j u_{ell_j})} $, $R^{ell_i}_{ell_j}(M) =frac{mathcal{B}(Bto ell_i u_{ell_i})}{mathcal{B}(B to Mell_j u_{ell_j})}$ with M = $pi$ or $rho$ and $ell_{i,j} = e, mu$ or $tau$. We also discuss the new physics (NP) sensitivities of all these observables and obtain bounds on a few NP Wilson coefficients in $bto u tau u_{tau}$ decays using the available data. We have noted that the data at present allows sizeable NP contributions in this mode. Also, we have predicted a few angular observables relevant to these decay modes.
We discuss the general properties of the amplitude of the $Bto l^+l^-l u$ decays and calculate the related kinematical distributions $d^2Gamma/dq^2dq^2$, $q$ the momentum of the $l^+l^-$ pair emitted from the electromagnetic vertex and $q$ the momentum of the $l u$ pair emitted from the weak vertex. We emphasize that electromagnetic gauge invariance imposes essential constraints on the $Bto gamma^*l u$ amplitude at small $q^2$ which in the end yield the behaviour of the differential branching fraction as $dGamma(Bto l^+l^-l u)/dq^2propto 1/q^2$ and a mild logarithmic dependence of $Gamma(Bto l^{+}l^{-}l u)$ on the lepton mass $m_l$. Consequently, (i) the main contribution to the decay rate $Gamma(Bto mu^+mu^-e u_e )$ comes from the region of light vector resonances $rho^0$ and $omega$, $q^2simeq M_rho^2, M_omega^2$ and (ii) the decay rate $Gamma(Bto e^{+}e^{-}mu u_mu)$ receives comparable contributions from the region of small $q^2$ and from the resonance region. As the result, the decay rate $Gamma(Bto e^+e^-mu u_mu)$ is only a factor $sim 2$ larger than $Gamma(Bto mu^+mu^-e u_e)$. We perform a detailed analysis of the uncertainties in the theoretical predictions for the decays $Bto l^+l^-l u$ in the Standard Model. We found that the theoretical expectations for such decays in the Standard Model are only marginally compatible with the recent upper limits of the LHCb collaboration.
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 ${cal B}(B^{+} rightarrow eta ell^{+} u_{ell}) = (2.79 pm 1.29_{rm (stat.)} pm 0.30_{rm (syst.)}) times 10^{-5}$.
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.
We employ a mathematical framework based on rational approximants in order to calculate meson form factors. The method profits from unitary, is systematic and data based, and is able to ascribe a systematic uncertainty which provides for the desired model independence. Two examples are discussed: the transition form factor entering the pseudoscalar-pole piece of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, and the $B to pi$ form factor participating the $Btopiell u_{ell}$ differential branching ratios which allows to determine the $|V_{ub}|$ CKM parameter.
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