The role of theory input for exclusive Vcb determinations

Abstract

Available form factor parametrizations for $B\rightarrow D^*l\nu$ imply different theoretical assumptions and different treatments of theoretical uncertainties. They give results for $\vert V_{cb}\vert$ whose central values are apart by up to $8\%$. The way the Caprini Lellouch Neubert (CLN) parametrization has been used in experimental analyses sets theoretical uncertainties of the Heavy Quark Effective Theory~(HQET) results on slope and curvature of the form factor ratios $R_1$ and $R_2$ to zero. Furthermore, the relation of curvature and slope of the axial form factor $A_1$ is fixed to the HQET central value. In view of the current experimental precision these uncertainties cannot be neglected any more. Using the Boyd Grinstein Lebed~(BGL) parametrization and taking into account theoretical uncertainties in a conservative way, we extract $\vert V_{cb}\vert$ from recent preliminary Belle data and the world average of the total branching ratio. We include an $\mathcal{O}(10\%-20\%)$ theoretical uncertainty of HQET input due to unknown corrections beyond NLO which were neglected in all previous analyses. This is important for reliable extractions of $\vert V_{cb}\vert$ as well as precision tests of the Standard Model with robust predictions of the lepton flavor nonuniversality observable $R(D^*)$ and the $\tau$ polarization asymmetry $P_{\tau}$. Including input from Light Cone Sum Rules (LCSRs) we find $\vert V_{cb}\vert = 40.6\left(^{+1.2}_{-1.3}\right)\cdot 10^{-3}$, $R(D^*) = 0.260(8)$ and $P_{\tau}=-0.47(4)$. Without LCSRs we find $\vert V_{cb}\vert = 41.5(1.3)\cdot 10^{-3}$ and the same results for $R(D^*)$ and $P_{\tau}$. The $R(D^*)$ anomaly is persistent, but its statistical significance is slightly reduced to 2.6$\sigma$.