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Register a new userBayesian fit analysis to full distribution data of $bar B to D^{(*)} ellbar u$: $|V_{cb}|$ determination and New Physics constraints
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We investigate the semi-leptonic decays of $bar B to D^{(*)} ellbar u$ in terms of the Heavy-Quark-Effective-Theory (HQET) parameterization for the form factors, which is described with the heavy quark expansion up to $mathcal O(1/m_c^2)$ beyond the simple approximation considered in the original CLN parameterization. An analysis with this setup was first given in the literature, and then we extend it to the comprehensive analyses including (i) simultaneous fit of $|V_{cb}|$ and the HQET parameters to available experimental full distribution data and theory constraints, and (ii) New Physics (NP) contributions of the $V_2$ and $T$ types to the decay distributions and rates. For this purpose, we perform Bayesian fit analyses by using Stan program, a state-of-the-art public platform for statistical computation. Then, we show that our $|V_{cb}|$ fit results for the SM scenarios are close to the PDG combined average from the exclusive mode, and indicate significance of the angular distribution data. In turn, for the $text{SM} + text{NP}$ scenarios, our fit analyses find that non-zero NP contribution is favored at the best fit point for both $text{SM} + V_2$ and $text{SM} + T$ depending on the HQET parameterization model. A key feature is then realized in the $bar B to D^{(*)} taubar u$ observables. Our fit result of the HQET parameters in the $text{SM} (+T)$ produces a consistent value for $R_D$ while smaller for $R_{D^*}$, compared with the previous SM prediction in the HFLAV report. On the other hand, $text{SM}+V_2$ points to smaller and larger values for $R_D$ and $R_{D^*}$ than the SM predictions. In particular, the $R_{D^*}$ deviation from the experimental measurement becomes smaller, which could be interesting for future improvement on measurements at the Belle II experiment.
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We evaluate long-distance electromagnetic (QED) contributions to $bar{B}{}^0 to D^+ tau^{-} bar{ u}_{tau}$ and $B^- to D^0 tau^{-} bar{ u}_{tau}$ relative to $bar{B}{}^0 to D^+ mu^{-} bar{ u}_{mu}$ and $B^- to D^0 mu^{-} bar{ u}_{mu}$, respectively, in the standard model. We point out that the QED corrections to the ratios $R(D^{+})$ and $R(D^{0})$ are not negligible, contrary to the expectation that radiative corrections are almost canceled out in the ratio of the two branching fractions. The reason is that long-distance QED corrections depend on the masses and relative velocities of the daughter particles. We find that theoretical predictions for $R(D^{+})^{tau/mu}$ and $R(D^{0})^{tau/mu}$ can be amplified by $sim4%$ and $sim3%$, respectively, for the soft-photon energy cut in range $20$-$40$ MeV.
Besides being important to determine Standard Model parameters such as the CKM matrix elements $|V_{cb}|$ and $|V_{ub}|$, semileptonic $B$ decays seem also promising to reveal new physics (NP) phenomena, in particular in connection with the possibility of uncovering lepton flavour universality (LFU) violating effects. In this view, it could be natural to connect the tensions in the inclusive versus exclusive determinations of $|V_{cb}|$ to the anomalies in the ratios $R(D^{(*)})$ of decay rates into $tau$ vs $mu, e$. However, the question has been raised about the role of the parametrization of the hadronic $B to D^{(*)}$ form factors in exclusive $B$ decay modes. We focus on the fully differential angular distributions of $bar B to D^* ell^-{bar u}_ell$ with $D^* to D pi$ or $D^* to D gamma$, the latter mode being important in the case of $B_s to D_s^*$ decays. We show that the angular coefficients in the distributions can be used to scrutinize the role of the form factor parametrization and to pin down deviations from SM. As an example of a NP scenario, we include a tensor operator in the $b to c$ semileptonic effective Hamiltonian, and discuss how the angular coefficients allow to construct observables sensitive to this structure, also defining ratios useful to test LFU.
At present, the measurements of $R_{D^{(*)}}$ and $R_{J/psi}$ hint at new physics (NP) in $b to c tau^- {bar u}$ decays. The angular distribution of ${bar B} to D^* (to D pi) , tau^{-} {bar u}_tau$ would be useful for getting information about the NP, but it cannot be measured. The reason is that the three-momentum ${vec p}_tau$ cannot be determined precisely since the decay products of the $tau^-$ include an undetected $ u_tau$. In this paper, we construct a measurable angular distribution by considering the additional decay $tau^- to pi^- u_tau$. The full process is ${bar B} to D^* (to D pi) , tau^{-} (to pi^- u_tau) {bar u}_tau$, which includes three final-state particles whose three-momenta can be measured: $D$, $pi$, $pi^-$. The magnitudes and relative phases of all the NP parameters can be extracted from a fit to this angular distribution. One can measure CP-violating angular asymmmetries. If one integrates over some of the five kinematic parameters parametrizing the angular distribution, one obtains (i) familiar observables such as the $q^2$ distribution and the $D^*$ polarization, and (ii) new observables associated with the $pi^-$ emitted in the $tau$ decay: the forward-backward asymmetry of the $pi^-$ and the CP-violating triple-product asymmetry.
I discuss recent progress in lattice calculations of $B to D^{(*)} ell u$ form factors, important for the precision determination of $|V_{cb}|$ in the Standard Model (SM), and for testing SM expectations of lepton flavor universality in observables $R(D^{(*)})$. I also discuss progress in calculations of the related $b to c$ semileptonic decays $B_s to D_s^{(*)} ell u$ and $B_c to J/psi , ell u$ now experimentally accessible at the LHC.
We carry out an analysis of the full set of ten $bar{B}to D^{(*)}$ form factors within the framework of the Heavy-Quark Expansion (HQE) to order $mathcal{O}(alpha_s,,1/m_b,,1/m_c^2)$, both with and without the use of experimental data. This becomes possible due to a recent calculation of these form factors at and beyond the maximal physical recoil using QCD light-cone sum rules, in combination with constraints from lattice QCD, QCD three-point sum rules and unitarity. We find good agreement amongst the various theoretical results, as well as between the theoretical results and the kinematical distributions in $bar{B}to D^{(*)}lbrace e^-,mu^-rbracebar u$ measurements. The coefficients entering at the $1/m_c^2$ level are found to be of $mathcal{O}(1)$, indicating convergence of the HQE. The phenomenological implications of our study include an updated exclusive determination of $|V_{cb}|$ in the HQE, which is compatible with both the exclusive determination using the BGL parametrization and with the inclusive determination. We also revisit predictions for the lepton-flavour universality ratios $R_{D^{(*)}}$, the $tau$ polarization observables $P_tau^{D^{(*)}}$, and the longitudinal polarization fraction $F_L$. Posterior samples for the HQE parameters are provided as ancillary files, allowing for their use in subsequent studies.
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