Abstract
The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cb}|$ is extracted from exclusive semileptonic $B \to D^{(*)}$ decays adopting a novel unitarity-based approach which allows to determine in a full non-perturbative way the relevant hadronic form factors (FFs) in the whole kinematical range. By using existing lattice computations of the $B \to D^{(*)}$ FFs at small recoil from FNAL/MILC and JLQCD Collaborations, we show that it is possible to extrapolate their behavior also at large recoil without assuming any specific momentum dependence and without constraining their shape using experimental data. Thus, we address the extraction of $|V_{cb}|$ from the experimental data on the semileptonic $B \to D^{(*)} \ell \nu_\ell$ decays, obtaining $\vert V_{cb}\vert = (41.0 \pm 1.2 ) \cdot 10^{-3}$ from $B \to D$ using as input the final FNAL/MILC lattice data for the FFs and $|V_{cb}| = (40.4 \pm 1.8 ) \cdot 10^{-3}$ from $B \to D^*$ using the preliminary JLQCD lattice data. Our result from $B \to D$ is consistent within $\sim 1$ standard deviation with the most recent inclusive determination $|V_{cb}|_{incl} = (42.00 \pm 0.65) \cdot 10^{-3}$. The resulting uncertainty is comparable with those obtained in literature using experimental data to constrain the shape of the FFs. Our result from $B \to D^*$, though consistent with $|V_{cb}|_{incl} $, is still based on preliminary lattice data for the FFs and its uncertainty is greater than the ones obtained in literature using experimental data to constrain the shape of the FFs. We investigate also the issue of Lepton Flavor Universality thanks to new theoretical estimates of the ratios $R(D^{(*)})$, namely $R(D) = 0.296(8)$ using final FNAL/MILC lattice results, and $R(D^{*}) = 0.261(20)$ using preliminary JLQCD and FNAL/MILC lattice data. Our findings differ by $\sim 1.4\sigma$ from the latest experimental determinations.
Highlights
Exclusive semileptonic B → DðÃÞlν decays are among the most important and challenging processes in the phenomenology of flavor physics
The Cabibbo-Kobayashi-Maskawa matrix element jVcbj is extracted from exclusive semileptonic B → DðÃÞ decays adopting a novel unitarity-based approach which allows one to determine in a full nonperturbative way the relevant hadronic form factors (FFs) in the whole kinematical range
We address the extraction of jVcbj from the experimental data on the semileptonic B → DðÃÞlνl decays, obtaining jVcbj 1⁄4 ð41.0 Æ 1.2Þ × 10−3 from B → D using as input the final FNAL/MILC lattice data for the FFs and jVcbj 1⁄4 ð40.4 Æ 1.8Þ × 10−3 from B → Dà using the preliminary JLQCD lattice data
Summary
Exclusive semileptonic B → DðÃÞlν decays are among the most important and challenging processes in the phenomenology of flavor physics. From the theoretical point of view, the extraction of jVcbj from exclusive B → DðÃÞlν decays and the theoretical estimates of RðDðÃÞÞ depends on the value and the shape of the form factors (FFs) entering the matrix elements and amplitudes. These functions encode the nonperturbative strong interactions between the quarks and can be determined through lattice QCD (LQCD) computations. The fundamental question is whether we can describe the FFs in the full kinematical range To this aim, in the past some parametrization of the form factors has always
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